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Abstract:
The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a regression technique.
The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models perform best with heavy-tailed DGP.

Value at Risk; CAViaR; Extreme Value Theory

Abstract:
We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

G13

Abstract:
We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

Option pricing, GARCH model, state price density, Monte Carlo simulation

Abstract:
Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations andprovide sensible empirical results.

Abstract:
Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of returns. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and give sensible empirical results.

ARCH, GARCH, Correlation, Time Series, Value at Risk

Abstract:
We propose a dynamic model of trade and estimate the model on 16 actively traded stocks on the New York Stock Exchange over 15 years of transaction data. We investigate (1) how the arrival rates of informed and uninformed trades vary over time, (2) how they interact with each other, and (3) what the implications are of the trade dynamics on the securities price processes such as market liquidity, depth, and volatility.

In particular, we extend the model of Easley and O'Hara (1992) to allow the arrival rates of informed and uninformed trades to be time-varying and forecastable. We specify a generalized autoregressive bivariate process for (1) the arrival rates of trades and (2) the logarithm of the arrival rates. Calibration results indicate that the two specifications exhibit similar performance. They both point to some common features of the trade dynamics. First, the arrival rates of both informed and uninformed trades are highly persistent. Heavy trading is more likely to be followed by heavy trading. Second, uninformed traders tend to follow their own type but to avoid the informed traders. Uninformed traders refrain from entering the market after a day with many informed traders. Informed traders, on the other hand, are not as responsive to the arrival of uninformed traders. Finally, while the arrival rates of both types of traders increase over time, it is mainly the increase in the arrival of uninformed traders that contributes to the surge in trading activities.

Given the forecasted arrival rates, we investigate the correlation between the arrival rates of trades and trade composition on market volatility and liquidity. First, we find that the forecasted arrival rates of both types of trades are positively correlated with intra-day volatility measures such as the absolute returns on daily open-close and high-low. Hence, potentially we could use the forecasted arrival rates to enhance the forecasting of daily volatilities. Second, under our model structure, the opening bid-ask spread, a measure of market liquidity, is proportional to the relative proportion of informed trades and the significance of the information event. We find that the proportion of informed trades is negatively correlated with the total number of trades. As the number of trades increases over time, the relative proportion of informed trades increases and hence, assuming relative time stability on the significance of information events, the opening bid-ask spread becomes narrower and the market becomes more liquid. Finally, we compute the price impact curve of consecutive buy orders and report the half life of the price impact as a measure of market depth. The difference in mean half life across stocks indicates their difference in market depth. The positive correlation between the half life and total trades indicates that the market is deeper in presence of more trades.

Abstract:
This paper proposes a new generalized autoregressive conditionally heteroskedastic (GARCH) process, the asymmetric generalized dynamic conditional correlation (AG-DCC) model. The AG-DCC process extends previous specifications along two dimensions: it allows for series-specific news impact and smoothing parameters and permits conditional asymmetries in correlation dynamics. The AG-DCC specification is well suited to examine correlation dynamics among different asset classes and investigate the presence of asymmetric responses in conditional variances and correlations to negative returns. We employ the AG-DCC model to analyze the behavior of international equities and government bonds. While equity returns show strong evidence of asymmetries in conditional volatility, little is found for bond returns. However, both equities and bonds exhibit asymmetries in conditional correlations, with equities responding stronger than bonds to joint bad news. The article also finds that, during periods of financial turmoil, equity market volatilities show important linkages, and conditional equity correlations among regional groups increase dramatically. Furthermore, in January 1999 with the introduction of the euro, we document significant evidence of a structural break in correlation although not in volatility. The introduction of a fixed exchange rate regime leads to near-perfect correlation among bond returns within the European Monetary Union (EMU) countries, which is not surprising when considering the harmonization in monetary policy. However, the increase in return correlation is not restricted to bond returns in EMU countries: equity return correlation both within and outside the EMU also increases.

dynamic conditional correlation' international stock and bond correlation' multivariate GARCH' variance targeting

Abstract:
This paper investigates the presence of asymmetric conditional second moments in international equity and bond returns. The analysis is carried out through an asymmetric version of the Dynamic Conditional Correlation model of Engle (2002). Widespread evidence is found that national equity index return series show strong asymmetries in conditional volatility, while little evidence is seen that bond index returns exhibit this behaviour. However, both bonds and equities exhibit asymmetry in conditional correlation. Worldwide linkages in the dynamics of volatility and correlation are examined. It is also found that beginning in January 1999, with the introduction of the Euro, there is significant evidence of a structural break in correlation, although not in volatility. The introduction of a fixed exchange rate regime leads to near perfect correlation among bond returns within EMU countries. However, equity return correlation both within and outside the EMU also increases after January 1999.

International Finance, Correlation, Variance Targeting, Multivariate GARCH, International Stock and Bond correlation

Abstract:
The paper proposes a new measure, VNET, of market liquidity which directly measures the depth of the market. The measure is constructed from the excess volume of buys or sells during a market event defined by a price movement. As this measure varies over time, it can be forecast and explained. Using TORQ data, it is found that market depth varies positively but less than proportionally with past volume and negatively with the number of transactions. Both findings suggest that over time high volumes are associated with an influx of informed traders and reduce market liquidity. High expected volatility as measured by the ACD model of Engle and Russell (1995) and wide spreads both reduce expected depth. If the asymmetric trades are transacted in shorter than expected times, the costs will be greater giving an estimate of the value of patience.

Abstract:
The paper proposes a new measure of market liquidity, VNET, which directly measures the depth of the market. VNET is constructed from the excess volume of buys or sells during a market event defined by a price movement. As this measure varies over time, it can be forecast and explained. Using NYSE TORQ data, it is found that market depth varies positively but less than proportionally with past volume and negatively with the number of transactions. Both findings suggest that over the day high volumes are associated with an influx of informed traders and reduce market liquidity. The timing of events plays an intimate role in the analysis. High expected volatility as measured by the ACD model of Engle and Russell (1997) reduces expected liquidity. Finally, market depth is smaller when the one-sided trading volume is transacted in a shorter than expected time, providing an estimate of the value of patience.

Abstract:
This paper examines the intertemporal relation between expected return and risk for 30 stocks in the Dow Jones Industrial Average. The mean-reverting dynamic conditional correlation model of Engle (2002) is used to estimate a stock s conditional covariance with the market and test whetherthe conditional covariance predicts time-variation in the stock s expected return. The risk-aversion coefficient, restricted to be the same across stocks in panel regression, is estimated to be betweentwo and four and highly significant. This result is robust across different market portfolios, different sample periods, alternative specifications of the conditional mean and covariance processes, and including a wide variety of state variables that proxy for the intertemporal hedging demand component of the ICAPM. Risk premium induced by the conditional covariation of individual stocks with the market portfolio remains economically and statistically significant after controlling for risk premiums induced by conditional covariation with macroeconomic variables (federal funds rate, default spread, and term spread), financial factors (size, book-to-market, and momentum), and volatility measures (implied, GARCH, and range volatility).

ICAPM, Dynamic conditional correlation, ARCH, Risk aversion, Dow Jones

Abstract:
This paper examines the intertemporal relation between expected return and risk for 30 stocks in the Dow Jones Industrial Average. The mean-reverting dynamic conditional correlation model of Engle (2002) is used to estimate a stock's conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock's expected return. The risk-aversion coefficient, restricted to be the same across stocks in panel regression, is estimated to be between two and four and highly significant. This result is robust across different market portfolios, different sample periods, alternative specifications of the conditional mean and covariance processes, different data sets including book-to-market portfolios and stocks in the S&P 100 index, and including a wide variety of state variables that proxy for the intertemporal hedging demand component of the ICAPM. The risk premium induced by the conditional covariation of individual stocks with the market portfolio remains economically and statistically significant after controlling for risk premia induced by conditional covariation with macroeconomic variables (federal funds rate, default spread, and term spread), financial factors (size, book-to-market, and momentum), and volatility measures (implied, GARCH, and range volatility).

ICAPM, Dynamic conditional correlation, ARCH, Risk aversion, Dow Jones

Abstract:
Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations andprovide sensible empirical results.

Abstract:
This paper develops a method for option hedging which is consistent with time-varying preferences and probabilities. The preferences are expressed in the form of an empirical pricing kernel (EPK), which measures the state price per unit probability, while probabilities are derived from an estimated stochastic volatility model of the form GARCH components with leverage. State prices are estimated using the flexible risk-neutral density method of Rosenberg (1995) and a daily cross-section of option premia. Time-varying preferences over states are linked to a dynamic model of the underlying price to obtain a one-day ahead forecast of derivative price distributions and minimum variance hedge ratios. Empirical results suggest that risk aversion over S&P500 return states is substantially higher than risk aversion implied by Black-Scholes state prices and probabilities using long run estimates of S&P500 return moments. It is also found that the daily level of risk aversion is strongly positively autocorrelated, negatively correlated with S&P500 price changes,and positively correlated with the spread between implied and objective volatilities. Hedging results reveal that typical hedging techniques for out-of-the-money S&P500 index options, such as Black-Scholes or historical minimum variance hedging, are inferior to the EPK hedging method. Thus, time-varying preferences and probabilities appear to be an important factor in the day-to-day pricing of S&P500 options.

Abstract:
This paper develops a method for option hedging which is consistent with time-varying preferences and probabilities. The preferences are expressed in the form of an empirical pricing kernel (EPK), which measures the state price per unit probability, while probabilities are derived from an estimated stochastic volatility model of the form GARCH components with leverage. State prices are estimated using the flexible risk-neutral density method of Rosenberg (1995) and a daily cross-section of option premia. Time-varying preferences over states are linked to a dynamic model of the underlying price to obtain a one-day ahead forecast of derivative price distributions and minimum variance hedge ratios. Empirical results suggest that risk aversion over S&P500 return states is substantially higher than risk aversion implied by Black-Scholes state prices and probabilities using long run estimates of S&P500 return moments. It is also found that the daily level of risk aversion is strongly positively autocorrelated, negatively correlated with S&P500 price changes, and positively correlated with the spread between implied and objective volatilities. Hedging results reveal that typical hedging techniques for out-of-the-money S&P500 index options, such Black-Scholes or historical minimum variance hedging, are inferior to the EPK hedging method. Thus, time-varying preferences and probabilities appear to be an important factor in the day-to-day pricing of S&P500 options.

Abstract:
We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short run from secular movements. We combine insights from Engle and Rangel (2007) and the recent work on mixed data sampling (MIDAS), as in e.g. Ghysels, Santa-Clara, and Valkanov (2005). The new class of models is called GARCH-MIDAS, since it uses a mean reverting unit daily GARCH process, similar to Engle and Rangel (2007), and a MIDAS polynomial which applies to monthly, quarterly, or bi-annual macroeconomic or financial variables. We study long historical data series of aggregate stock market volatility, starting in the 19th century, as in Schwert (1989). We formulate models with the long term component driven by inflation and industrial production growth that are at par in terms of out-of-sample prediction for horizons of one quarter and out-perform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long horizon forecasting. We also find that at a daily level, inflation and industrial production growth, account for between 10 % and 35 % of one-day ahead volatility prediction. Hence, macroeconomic fundamentals play a significant role even at short horizons. Unfortunately, all the models - purely time series ones as well as those driven by economic variables - feature structural breaks over the entire sample spanning roughly a century and a half of daily data. Consequently, our analysis also focuses on subsamples - pre-WWI, the Great Depression era, and post-WWII (also split to examine the so called Great Moderation). Our main findings remain valid across subsamples.

stock market volatility, macroeconomic variables, volatility decomposition, cross-section of returns

Abstract:
This paper proposes a new approach to modeling financial transactions data. A model for discrete valued time series is introduced in the context of generalized linear models. Since the model specifies probabilities of return outcomes conditional on both the previous state and the historic distribution, we call the it the Autoregressive Conditional Multinomial (ACM) model. Recognizing that prices are observed only at transactions, the process is interpreted as a marked point process. The ACD model proposed in Engle and Russell (1998) allows for joint modeling of the price transition probabilities and the arrival times of the transactions. The transition probabilities are formulated to allow general types of duration dependence. Estimation and testing are based on Maximum Likelihood methods. The data are IBM transactions from the TORQ dataset. Variations of the model allow for volume and spreads to impact the conditional distribution of price changes. Impulse response studies show the long run price impact of a transaction can be very sensitive to volume but is less sensitive to the spread and transaction rate.

Abstract:
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation spectrum as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews.

Abstract:
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation spectrum as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews.

Abstract:
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation spectrum as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews.

Abstract:
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches.

credit risk, credit derivatives, credit correlation, downside risk, tail risk, time series, GARCH

Abstract:
In this paper we analyze and interpret the quote price dynamics of 100 NYSE stocks stratified by trade frequency. We specify an error-correction model for the log difference of the bid and the ask price with the spread acting as the error-correction term, and include as regressors the characteristics of the trades occurring between quote observations, if any. From this model we are also able to extract the implied model for the spread and the mid-quote. We find that short duration and medium volume trades have the largest impacts on quote prices for all one hundred stocks. Further, we find that buys have a greater impact on the ask price than on the bid price, while sells have a greater impact on the bid price than on the ask price. Both buys and sells increase spreads in the short run, but in the absence of further trades, the spreads mean revert. Trades have a greater impact on quotes for the infrequently traded stocks than for the more actively traded stocks.

market microstructure, error-correction, vector autoregression, price dynamics

Abstract:
The paper builds an econometric model for estimating the volatility of unobserved efficient price change using tick by tick data. We model the joint density of the marked point process of duration and tick by tick returns within an ACD-GARCH framework. We first model the duration variable as an ACD process that could potentially depend on past returns. We then model the return variable conditioning on its current duration as well as past information. The observed return process admits a state space model, where the unobserved efficient price innovation and microstructure noises serve as state variables. After adjusting for bid-ask spread and a non-linear function of durations, tick by tick returns are distributed independently of durations, with volatility that admits a GARCH process. We apply the above model to frequently traded NYSE stock transactions data. It appears that contemporaneous duration has little affect on the conditional volatility per trade, which means per second volatility is inversely related to the duration between trades. This is consistent with the result of Engle (2000) and Easley and O'Hara (1987). The model is used to obtain a new, model-based estimate of daily, realized volatility as well as the volatility of efficient price changes.Volatility is forecasted over calendar time intervals by simulation. The distribution of the number of trades is central in forming these forecasts.

volatility, tick by tick data, duration, microstructure noise, ACD, Kalman Filter

Abstract:
To study the impact of institutional features of target zones on the conditional volatility of exchange rates, this paper proposes a simple and intuitive model to incorporate the announced information in the bands. Observing the statistical characteristics of the EMS cross rate returns- mean reversion and heteroskedasticity, we t a GARCH(1,1)- MA(1) speci cation incorporating the deviation of exchange rates from the central parity. This model allows us to easily examine the relationship between the conditional volatility and the position of spot rates. We nd in particular, that for the Irish punt and Italian lira DM rates, the conditional volatility increases as the exchange rate approaches the edges of the band. We extend the above univariate model to a multivariate setting to take account of the cross country interactions in the EMS, by including a vector consisting of all EMS currencies' positions in the GARCH equation. The estimation results show that other currencies' positions do a ect the conditional volatility of a speci c EMS currency. Understanding the importance of intra-ERM coherence and the multilateral commitment on the central parity, we follow Pill(1994) to derive an \e ective band" model to examine how the multilateral grid affects the conditional volatility. However, the estimation results suggest that the full set of all deviations from ocial central parity of each member country explains the volatility better than does simply the deviation from the effective band.

Abstract:
Financial markets are considered to be liquid if a large quantity can be traded quickly and with minimal price impact. Although the idea of a liquid market involves both a cost as well as a time component, most measures of execution costs tend to focus on only a single number reflecting average costs and do not explicitly account for the temporal dimension of liquidity. In reality, trading takes time since larger orders are often broken up into smaller transactions or when limit orders are used. Recent work shows that the time taken to transact introduces a risk component in execution costs. In this setting, the decision can be viewed as a risk/reward tradeoff faced by the investor who can solve for a mean variance utility maximizing trading strategy. We introduce an econometric method to jointly model the expected cost and the risk of the trade thereby characterizing the mean variance tradeoffs associated of different trading approaches given market and order characteristics. We apply our methodology to a novel data set and show that the risk component is a non-trivial part of the transaction decision. The conditional distribution of transaction costs is also used to construct a new measure of liquidation risk that we refer to as liquidation value at risk (LVaR).

Abstract:
ARCH and GARCH models have become important tools in the analysis of time series data, particularly in financial applications. These models are especially useful when the goal of the study is to analyze and forecastvolatility. This paper gives the motivation behind the simplest GARCH model and illustrates its usefulness in examining portfolio risk. Extensions are briefly discussed.

Abstract:
In this paper, we develop the theoretical and empirical properties of a new class of multivariate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need to be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indices and Dow Jones Industrial Average stocks, and conduct specification tests of the estimator using an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

Dynamic Correlation, Multivariate GARCH, Volatility

Abstract:
In this paper, we develop the theoretical and empirical properties of a new class of multivariate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indicesand Dow Jones Industrial Average stocks, and conduct specification tests of the estimatorusing an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

Abstract:
In this paper, we develop the theoretical and empirical properties of a new class of multivariate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indicesand Dow Jones Industrial Average stocks, and conduct specification tests of the estimatorusing an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

Abstract:
In this paper, we develop the theoretical and empirical properties of a new class of multi-variate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indices and Dow Jones Industrial Average stocks, and conduct specification tests of the estimator using an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

Abstract:
Exchange Traded Funds are equity issues of companies whose assets consist entirely of cash and shares of stock approximating particular indexes. These companies resemble closed end funds except for the unique feature that additional shares can be created or redeemed by a number of registered entities. This paper investigates the extent and properties of the resulting premiums and discounts of ETFs from their fair market value.Measured premiums and discounts can be misleading because the net asset value of the portfolio is not accurately represented or because the price of the fund is not accurately recorded. These features are incorporated into a model with errors-in-variables that accounts for these effects and measures the standard deviation of the remaining pricing errors. Time variation in this standard deviation is investigated. Both domestic and international ETFs are examined, each from an end-of-day perspective and from a minute-by-minute intra-daily framework. The overall finding is that the premiums/discounts for the domestic ETFs are generally small and highly transient, once mismatches in timing are accounted for. Large premiums typically last only several minutes. The standard deviation of the premiums/discount is 15 basis points on average across all ETFs, which is substantially smaller than the bid-ask spread. For international ETFs, the findings are not so dramatic. Premiums and discounts are much larger and more persistent, frequently lasting several days. The spreads are also much wider and are comparable to the standard deviation of the premiums. This finding is insensitive to the timing of overlap with the foreign market, the use of futures data, or different levels of time scale. In fact there are only a small number of trades and quote changes in a typical day for most of these funds. An explanation for this difference may rest with the higher cost of creation and redemption for the international products. Nevertheless, when compared with closed end funds where there are no opportunities for creation or redemption, the ETFs have smaller and less persistent premiums and discounts.The implication is that the pricing of ETFs is highly efficient for the domestic products and somewhat less precise for the international funds since they face more complex financial transactions and risks.

Abstract:
25 years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macroeconomic effects and time series dynamics. High frequency return volatility is specified to be the product of a slow moving component, represented by an exponential spline, and a unit GARCH. This slow moving component is the low frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data.

Low frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low frequency component of volatility is greater when the macroeconomic factors GDP, inflation and short term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher for emerging markets and for markets with small numbers of listed companies and market capitalization, but also for large economies.

Spline-GARCH, Global Equity Volatility, Low-frequency Volatility, Semi-Parametric Models, Macroeconomic Determinants

Abstract:
A new covariance matrix estimator is proposed under the assumption that at every time period all pairwise correlations are equal. This assumption, which is pragmatically applied in various areas of finance, makes it possible to estimate arbitrarily large covariance matrices with ease. The model, called DECO, is a special case of the CCC and DCC models which involve first adjusting for individual volatilities and then estimating the correlations. A QMLE result shows that DECO can continue to give consistent parameter estimates when the equicorrelation assumption is violated. Generalizations to block equicorrelation structures, models with exogenous variables, and alternative specifications are explored and diagnostic tests are proposed. Estimation is evaluated by Monte Carlo and using US stock return data.

Dynamic Correlation, Multivariate GARCH, Conditional Correlation

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework iscrucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate theequality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework is crucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk-aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate the equality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

G12; G13; C51

Abstract:
Seasonal patterns in economic time series are generally examined from a univariate point of view. Using extensions of the unit root literature, important classes of seasonal processes are deterministic, stationary stochastic or mean reverting, and unit root stochastic. Time series tests have been developed for each of these. This paper examines seasonality in a multivariate context. Systems of economic variables can have trends, cycles and unit roots as well as the various types of seasonality. Restrictions such as cointegration and common cycles are here applied also to examine multivariate seasonal behavior of economic variables. If each of a collection of series has a certain type of seasonality but a linear combination of these series can be found without seasonality, then the seasonal is said to be ?common?. New tests are developed to determine if seasonal characteristics are common to a set of time series. These tests can be employed in the presence of various other time series structures. The analysis is applied to OECD data on unemployment for the period 1975.1 to 1993.4, and it is found that four diverse countries (Australia, Canada, Japan and USA) not only have common trends in their unemployment, but also have common deterministic seasonal features and a common cycle/stochastic seasonal feature. Such a collection of characteristics were not found in other groups of OECD countries.

Abstract:
This paper introduces the News Impact Curve to measure how new information is incorporated into volatility estimates. A variety of new and existing ARCH models are compared and estimated with daily Japanese stock return data to determine the shape of the News Impact Curve. New diagnostic tests are presented which emphasize the asymmetry of the volatility response to news. A partially non-parametric ARCH model is introduced to allow the data to estimate this shape. A comparison of this model with the existing models suggests that the best models are one by Glosten Jaganathan and Runkle (GJR) and Nelson's EGARCH. Similar results hold on a pre--crash sample period but are less strong.

Abstract:
A new covariance matrix estimator is proposed under the assumption that at every time period all pairwise correlations are equal. This assumption, which is pragmatically applied in various areas of finance, makes it possible to estimate arbitrarily large covariance matrices with ease. The model, called DECO, involves first adjusting for individual volatilities and then estimating correlations. A quasi-maximum likelihood result shows that DECO provides consistent parameter estimates even when the equicorrelation assumption is violated. We demonstrate how to generalize DECO to block equicorrelation structures. DECO estimates for US stock return data show that (block) equicorrelated models can provide a better fit of the data than DCC. Using out-of-sample forecasts, DECO and Block DECO are shown to improve portfolio selection compared to an unrestricted dynamic correlation structure.

Abstract:
We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short run from secular movements. We combine insights from Engle and Rangel (2007) and the recent work on mixed data sampling (MIDAS), as in e.g. Ghysels, Santa-Clara, and Valkanov (2005). The new class of models is called GARCH-MIDAS, since it uses a mean reverting unit daily GARCH process, similar to Engle and Rangel (2007), and a MIDAS polynomial which applies to monthly, quarterly, or bi-annual macroeconomic or financial variables. We study long historical data series of aggregate stock market volatility, starting in the 19th century, as in Schwert (1989). We formulate models with the long term component driven by inflation and industrial production growth that are at par in terms of out-of-sample prediction for horizons of one quarter and out-perform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long horizon forecasting. We also find that at a daily level, inflation and industrial production growth, account for between 10% and 35% of one-day ahead volatility prediction. Hence, macroeconomic fundamentals play a significant role even at short horizons. Unfortunately, all the models - purely time series ones as well as those driven by economic variables - feature structural breaks over the entire sample spanning roughly a century and a half of daily data. Consequently, our analysis also focuses on subsamples - pre-WWI, the Great Depression era, and post-WWII (also split to examine the so called Great Moderation). Our main findings remain valid across subsamples.

Abstract:
We introduce a new analysis of transaction costs that explicitly recognizes the importance of the timing of execution in assessing transaction costs. Time induces a risk/cost tradeoff. The price of immediacy results in higher costs for quickly executed orders while more gradual trading results in higher risk since the value of the asset can vary more over longer periods of time. We use a novel data set that allows a sequence of transactions to be associated with individual orders and measure and model the expected cost and risk associated with different order execution approaches. The model yields a risk/cost tradeoff that depends upon the state of the market and characteristics of the order. We show how to assess liquidation risk using the notion of liquidation value at risk (LVAR).

Abstract:
We introduce a new analysis of transaction costs that explicitly recognizes the importance of the timing of execution in assessing transaction costs. Time induces a risk/cost tradeoff. The price of immediacy results in higher costs for quickly executed orders while more gradual trading results in higher risk since the value of the asset can vary more over longer periods of time. We use a novel data set that allows a sequence of transactions to be associated with individual orders and measure and model the expected cost and risk associated with different order execution approaches. The model yields a risk/cost tradeoff that depends upon the state of the market and characteristics of the order. We show how to assess liquidation risk using the notion of liquidation value at risk (LVAR).

Abstract:
We evaluate alternative models of variances and correlations with an economic loss function. We construct portfolios to minimize predicted variance subject to a required return. It is shown that the realized volatility is smallest for the correctly specified covariance matrix for any vector of expected returns. A test of relative performance of two covariance matrices is based on Diebold and Mariano (1995). The method is applied to stocks and bonds and then to highly correlated assets. On average dynamically correct correlations are worth around 60 basis points in annualized terms but on some days they may be worth hundreds.

GARCH, DCC, Forecast Evaluation

Abstract:
Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter problem which has troubled existing methods when applied to hundreds or even thousands of assets. Indeed we can handle the case where the cross-sectional dimension is larger than the time series one. The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method. The out of sample hedging performance of various models estimated using this method are compared.

Abstract:
The idea of component models for volatility is extended to dynamic correlations. We propose a model of dynamic correlations with a short- and long-run component specification. We call this class of models DCC-MIDAS as the key ingredients are a combination of the Engle (2002) DCC model, the Engle and Lee (1999) component GARCH model to replace the original DCC dynamics with a component specification and the Engle, Ghysels, and Sohn (2006) GARCH-MIDAS component specification that allows us to extract a long-run correlation component via mixed data sampling. We provide a comprehensive econometric analysis of the new class of models, including conditions for positive semi-definiteness, and provide extensive empirical evidence that supports the model specification.

Abstract:
A new representation of the diagonal Vech model is given using the Hadamard product. Sufficient conditions on parameter matrices are provided to ensure the positive definiteness of covariance matrices from the new representation. Based on this, some new and simple models are discussed. A set of diagnostic tests for multivariate ARCH models is proposed. The tests are able to detect various model misspecifications by examing the orthogonality of the squared normalized residuals. A small Monte-Carlo study is carried out to check the small sample performance of the test. An empirical example is also given as guidance for model estimation and selection in the multivariate framework. For the specific data set considered, it is found that the simple one and two parameter models and the constant conditional correlation model perform fairly well.

conditional covariance, Multivariate ARCH, Hadamard product, M-test

Abstract:
A new representation of the diagonal Vech model is given using the Hadamard product.Sufficient conditions on parameter matrices are provided to ensure the positive definiteness of covariance matrices from the new representation. Based on this, some new and simple models are discussed. A set of diagnostic tests for multivariate ARCH models is proposed. The tests are able to detect various model misspecifications by examing the orthogonality of the squared normalized residuals. A small Monte-Carlo study is carried out to check the small sampleperformance of the test. An empirical example is also given as guidance for model estimation and selection in the multivariate framework. For the specific data set considered, it is found that the simple one and two parameter models and the constant conditional correlation model performfairly well.

conditional covariance, Multivariate ARCH, Hadamard product, M-test

Abstract:
We investigate the sources of skewness in aggregate risk-factors and the cross-section of stock returns. In an ICAPM setting with conditional volatility, we find theoretical time series predictions on the relationships among volatility, returns, and skewness for priced risk factors. Market returns resemble these predictions; however, size, book-to-market, and momentum factor returns show alternative behavior, leading us to conclude these factors are not priced risks. We link aggregate risk and skewness to individual stocks and find empirically that the risk aversion effect manifests in individual stock skewness. Additionally, we find several firm characteristics that explain stock skewness. Smaller firms, value firms, highly levered firms, and firms with poor credit ratings have more positive skewness.

Abstract:
Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We postulate a variety of dynamic processes for updating the quantile and use regression quantile estimation to determine the parameters of the updating process. Tests of model adequacy utilize the criterion that each period the probability of exceeding the VaR must be independent of all the past information. We use a differential evolutionary genetic algorithm to optimize an objective function which is non-differentiable and hence cannot be optimized using traditional algorithms. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

Abstract:
This paper studies the joint distribution of tick by tick returns and durations between trades. Returns are decomposed into changes in full information prices and microstructure noise, but the noise is modeled in accordance with various models of market microstructure allowing rich correlation structures both with the efficient price and over time. The full information price has time varying volatility which depends upon the arrival time of trades. The paper aims at three contributions: First, the noise is modeled to allow asymmetric information, inventory and order processing costs, and delayed quote setting. Second, the response to the trade arrival times allows trade durations to be informative on future volatility. Third, the estimated state space models can act as a laboratory to examine various non-parametric approaches to realized volatility estimation. Both simulated and actual data can be compared across methods and the accuracy and efficiency assessed as long as the parameteric model is viewed as a sufficiently accurate representation. We apply the above model to 10 NYSE stock transactions data series with varying transaction rates. It appears that contemporaneous duration has little effect on the volatility per trade after conditioning on the past, which means average per second volatility is inversely related to the duration between trades. Microstructure noise is found to be informative about the unobserved efficient price, and the informational component explains 45% of the total variation of the microstructure noise.

Abstract:
This paper develops time series methods for forecasting correlations in high dimensional problems. The Dynamic Conditional Correlation model is given a new convenient estimation approach called the MacGyver method. It is compared with the FACTOR ARCH model and a new model called the FACTOR DOUBLE ARCH model. Finally the latter model is blended with the DCC to give a FACTOR DCC model. This family of models is estimated with daily returns from 18 US large cap stocks. Economic loss functions designed to form optimal portfolios and optimal hedges are used to compare the performance of the methods. The best approach invariably is the FACTOR DCC and the next best is the FACTOR DOUBLE ARCH.

Abstract:
The volatility term structure (VTS) reflects market expectations of average asset volatility over different time horizons. Various stochastic volatility models provide forecasts of the VTS and how it shifts in response to changes in market conditions. This paper develops a methodology for testing VTS forecasts using option hedging performance. An innovative feature of the hedging approach is its increased sensitivity to several important forms of model misspecification relative to previous testing methods. Hedging tests using S&P 500 index options indicate that the GARCH components with leverage VTS estimate is most accurate. The poorer hedging performance of the alternative models suggests that volatility term structure shifts are related to the magnitude and level of recent returns. Strong evidence is obtained for mean-reversion in volatility.

Abstract:
The volatility term structure (VTS) reflects market expectations of asset volatility over different horizons. These expectations change over time, giving dynamic structure to the VTS. This paper evaluates volatilitymodels on the basis of their performance in hedging option price changes due to shifts in the VTS. An innovative feature of the hedging approach is its increased sensitivity to several important forms of model misspecification relative to previous testing methods. Volatility hedge parameters are derived for several volatility models incorporating different predicted VTS dynamics and information variables. Hedging tests using S&P500 index options indicate that the GARCH components with leverage VTS estimate is most accurate. Evidence is obtained for meanreversion in volatility and correlation between VTS shifts and S&P500 returns. While a convexity hedge dominates the volatility hedges for the observed sample, this result appears to be due to sample selection bias.

Abstract:
A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylised facts aboutvolatility that should be incorporated in a model; pronounced persistence and meanreversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial index to illustrate these stylised facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area.

volatility modelling, ARCH, GARCH, volatility forecasting

Abstract:
volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylised facts aboutvolatility that should be incorporated in a model; pronounced persistence and meanreversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial index to illustrate these stylised facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area.

volatility modelling, ARCH, GARCH, volatility forecasting

Abstract:
In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models.Wide-ranging applications to financial data have discovered important stylized facts and illustrated both the strengths and weaknesses of the models. There are now many surveys of this literature.This paper looks forward to identify promising areas of new research. The paper lists five new frontiers. It briefly discusses three high frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models. Two further frontiers are examined in more detail application of ARCH models to the broadclass of non-negative processes, and use of Least Squares Monte Carlo to examine non-linear properties of any model that can be simulated. Using this methodology, the paper analyzes more general types of ARCH models, stochastic volatility models, long memory models and breaking volatility models. The volatility of volatility is defined,estimated and compared with option implied volatilities.

ARCH, GARCH, volatility, non-linear process, non-negative process, option pricing, stochastic volatility, long memory, Least Squares Monte Carlo, ACD, Multiplicative Error Model, MEM

Abstract:
Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a â¬Strueâ¬? or "best" measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high-low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by an average of implied volatilities of index options as measured by VIX.

volatility modeling, volatility forecasting, GARCH, VIX, high-low range, realized volatility

Abstract:
Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a 'true' or 'best' measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high-low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by an average of implied volatilities of index options as measured by VIX.

Abstract:
We investigate whether or not a beta increases with bad news and decreases with good news, just as does volatility. Using daily returns for nine stocks in a double beta model with EGARCH specifications, we show that news asymmetrically affects the betas of individual stocks. We find that betas depend on two source of news: market shocks and idiosyncratic shocks. Some stock betas depend on both while others depend on one. We categorize each stock return as belonging to one of three beta process models, a joint, an idiosyncratic, and a market model based on the role of market shocks and idiosyncratic shocks. Our conclusions differ from those of Brown, Nelson, and Sunnier (1995) who worked with monthly aggregated data in a bivariate EGARCH model. We believe that stock price aggregation in this previous research resulted in a loss of cross sectional variation and consequently lead to weak results. If the asymmetric effect is more readily apparent in daily data, then this may again explain previous researchers' inability to detect asymmetric effects. Our findings shed light on the controversy as to whether abnormalities in stock returns result from overreaction to information or from changes in expected returns in an efficient market. Finding an asymmetric effect in betas leads us to conclude that abnormalities can, at least partially, be explained by changes in expected returns through a change in beta.

Abstract:
We introduce a new model to measure unconditional volatility, the Spline-GARCH. The model is applied to equity markets for 50 countries for up to 50 years of daily data. Macroeconomic determinants of unconditional volatility are investigated. It is found that volatility in macroeconomic factors such as gdp growth, inflation and short term interest rates are important explanatory variables that increase volatility. There is evidence that high inflation and low growth of output are positive determinants. Volatility is higher for emerging markets and for markets with small numbers of listings but also for large economies.

Abstract:
Transaction costs in trading involve both risk and return. The return is associated with the cost of immediate execution and the risk is a result of price movements during a more gradual trading. The paper shows that the trade-off between risk and return in optimal execution should reflect the same risk preferences as in ordinary investment. The paper develops models of the joint optimization of positions and trades, and shows conditions under which optimal execution does not depend upon the other holdings in the portfolio. Optimal execution however may involve trades in assets other than those listed in the order; these can hedge the trading risks. The implications of the model for trading with reversals and continuations are developed. The model implies a natural measure of liquidity risk

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
In this paper, we examine the impact of market activity on the percentage bid-ask spreads of S&P 100 index options using transactions data. We propose a new market microstructure theory which we call derivative hedge theory, in which option market percentage spreads will be inversely related to the option market maker's ability to hedge his positions in the underlying market, as measured by the liquidity of the latter market. In a perfect hedge world, spreads arise from the illiquidity of the underlying market, rather than from inventory risk or informed trading in the option market itself. We find option market volume is not a significant determinant of option market spreads. This finding leads us to question the use of volume as a measure of liquidity and supports the derivative hedge theory. Option market spreads are positively related to spreads in the underlying market, again supporting our theory. However, option market duration does affect option market spreads, with very slow and very fast option markets both leading to bigger spreads. The fast market result would be predicted by the asymmetric information theory. Inventory model predicts big spreads in slow markets. Neither result would be observed if the underlying securities market provided a perfect hedge. We interpret these mixed results as meaning that the option market maker is able to only imperfectly hedge his positions in the underlying securities market. Our result of insignificant options volume casts doubt on the price discovery argument between stock and option market (Easley, O'Hara, and Srinivas (1998)). Asymmetric information costs in either market are naturally passed to the other market maker's hedgeing and therefore it is unimportant where the informed traders trade.

Abstract:
To forecast future option prices, autoregressive models of implied volatility derived from observed option prices are commonly employed [see Day and Lewis (1990), and Harvey and Whaley (1992)]. In contrast, the ARCH model proposed by Engle (1982) models the dynamic behavior in volatility, forecasting future volatility using only the return series of an asset. We assess the performance of these two volatility prediction models from S&P 500 index options market data over the period from September 1986 to December 1991 by employing two agents who trade straddles, each using one of the two different methods of forecast. Straddle trading is employed since a straddle does not need to be hedged. Each agent prices options according to her chosen method of forecast, buying (selling) straddles when her forecast price for tomorrow is higher (lower) than today's market closing price, and at the end of each day the rates of return are computed. We find that the agent using the GARCH forecast method earns greater profit than the agent who uses the implied volatility regression (IVR) forecast model. In particular, the agent using the GARCH forecast method earns a profit in excess of a cost of $0.25 per straddle with the near-the-money straddle trading.

Abstract:
Ultra-high frequency data are complete transactions data which inherently arrive at random times. Marked point processes provide a theoretical framework for analysis of such data sets. The ACD model developed by Engle and Russell (1995) is then applied to IBM transactions data to develop semi-parametric hazard estimates and measures of instantaneous conditional variances. The variances are negatively influenced by surprisingly long durations as suggested by some of the market micro-structure literature

Abstract:
Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel way of estimating models of time-varying covariances that overcome some of the computational problems which have troubled existing methods when applied to 1,000s of assets. The theory of this new strategy is developed in some detail, allowingformal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method.

Abstract:
This paper proposes a new way of modeling and forecasting intraday returns. We decompose the volatility of high frequency asset returns into components that may be easily interpreted and estimated. The conditional variance is expressed as a product of daily, diurnal and sto-chastic intraday volatility components. This model is applied to a comprehensive sample consisting of 10-minute returns on more than 2500 US equities. We apply a number of dif-ferent specifications. Apart from building a new model, we obtain several interesting fore-casting results. In particular, it turns out that forecasts obtained from the pooled cross section of companies seem to outperform the corresponding forecasts from company-by-company estimation.

Abstract:
This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework is crucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The risk-aversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate the equality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework.

ICAPM, Risk-return tradeoff, Risk aversion, Multivariate GARCH-in-mean

Abstract:
Transmission mechanisms in financial markets reflect the degree of integration of capital markets and of real economies. As a matter of fact, volatility has components which may behave differently across quiet and turbulent periods, but appear to behave in similar ways from market to market. In this paper we suggest a Multiplicative Error Model (MEM) approach which is suitable for modeling directly the conditional expectation of the market daily range which is a good proxy for volatility. In the present context, the dynamics of the expected volatility of one market is extended to include interactions with the past daily ranges of other markets, thus building a potentially fully interdependent model. We analyze eight East Asian markets in the period 1995-2006, devoting particular attention to the treatment of the 1997-1998 turbulence period. We show that for some of the markets there is no evidence of changes in the dynamic impacts within the crisis and without and for other markets such a change is limited to a level shift: this suggests that the links may have been stable across sub-periods.

Volatility, Multiplicative Error Models, Asian Crisis, Market integration

Abstract:
This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which is referred to as the empirical pricing kernel (EPK). The empirical pricing kernel is the preference function that rationalizes a contemporaneous cross-section of assetprices, given a forecast payoff probability density. We estimate the EPK on a monthly basis from 1991 to 1995 using S&P500 index option data and a stochastic volatility model for the S&P500 return process. We find substantial evidence of time-varying riskaversion over S&P500 return states. In addition, we find that empirical risk aversion over S&P500 return states is linked to business conditions; the level of risk aversion is positively correlated with indicators of recession and negatively correlated with indicators of expansion.An option hedging methodology is developed to test the predictive information in the empirical pricing kernel and its associated state probability model. Hedging performance is significantly improved using hedgeratios based on a time-varying pricing kernel rather than a time-invariant pricing kernel.

Abstract:
This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a daily semi-parametric pricing kernel. The two key features of this estimator are: (1) the functional form of the pricing kernel is estimated semi-parametrically, instead of being prespecified and (2) the pricing kernel is re-estimated on a daily basis, allowing measurement of time-variation in riskaversion over equity return states.Important empirical findings of the paper are as follows. Constant relative risk aversion over S&P500 return states is rejected in favor of a model in which relative risk aversion is stochastic. Empirical relative risk aversion over equity return states is found to be positively autocorrelated and positively correlated with the spread between implied and objective volatilities. In addition, the constant relative risk aversion (power utility) pricing kernel is found to underestimate the value of payoffs in large negative return states.An option hedging methodology is developed as a test of the predictive information in the empirical pricing kernel and its associated state probability model. The results of hedging performance tests for out-of-the-money S&P500 index put options indicate that time-varying risk aversion over equity return states is an important factor affecting option prices.

Abstract:
This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a daily semi-parametric pricing kernel. The two key features of this estimator are: (1) the functional form of the pricing kernel is estimated semi-parametrically, instead of being prespecified and (2) the pricing kernel is re-estimated on a daily basis, allowing measurement of time-variation in risk-aversion over equity return states.Important empirical findings of the paper are as follows. Constant relative risk aversion over S&P500 return states is rejected in favor of a model in which relative risk aversion is stochastic. Empirical relative risk aversion over equity return states is found to be positively autocorrelated and positively correlated with the spread between implied and objective volatilities. In addition, the constant relative risk aversion (power utility) pricing kernel is found to underestimate the value of payoffs in large negative return states.An option hedging methodology is developed as a test of the predictive information in the empirical pricing kernel and its associated state probability model. The results of hedging performance tests for out-of-the-money S&P500 index put options indicate that time-varying risk aversion over equity return states is an important factor affecting option prices.

Abstract:
This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits counter cyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.

Pricing kernels, Risk aversion, Derivatives, Hedging

Abstract:
This paper will propose a new statistical model for the analysis of data that does not arrive in equal time intervals such as financial transactions data, telephone calls, or sales data on commodities that are tracked electronically. In contrast to fixed interval analysis, the model treats the time between observation arrivals as a stochastic time varying process and therefore is in the spirit of the models of time deformation initially proposed by Tauchen and Pitts (1983), Clark (1973) and more recently discussed by Stock (1988), Lamoureux and Lastrapes (1992), Muller et al. (1990) and Ghysels and Jasiak (1994) but does not require auxiliary data or assumptions on the causes of time flow. Strong evidence is provided for duration clustering beyond a deterministic component for the financial transactions data analyzed. We will show that a very simple version of the model can successfully account for the significant autocorrelations in the observed durations between trades of IBM stock on the consolidated market. A simple transformation of the duration data allows us to include volume in the model.

Abstract:
In this paper we document the presence of a term structure of risk and we propose how to measure it using alternative models to forecast volatility and the Value at Risk at different horizons. We then quantify the benefits of an investor that is aware of the existence of a term structure of risk in the context of an asset allocation exercise.

Abstract:
In this paper we document the presence of a term structure of risk and we propose how to measure it using alternative models to forecast volatility and the Value at Risk at different horizons. We then quantify the benefits of an investor that is aware of the existence of a term structure of risk in the context of an asset allocation exercise.

Abstract:
In financial time series analysis we encounter several instances of non-negative valued processes (volumes, trades, durations, realized volatility, daily range, and so on) which exhibit clustering and can be modeled as the product of a vector of conditionally autoregressive scale factors and a multivariate iid innovation process (vector Multiplicative Error Model). Two novel points are introduced in this paper relative to previous suggestions: a more general specification which sets this vector MEM apart from an equation by equation specification; and the adoption of a GMM-based approach which bypasses the complicated issue of specifying a general multivariate non-negative valued innovation process. A vMEM for volumes, number of trades and realized volatility reveals empirical support for a dynamically interdependent pattern of relationships among the variables on a number of NYSE stocks.

GARCH, GMM, MEM, NYSE, number of trades, realized volatility, volumes

Abstract:
No abstract is available for this paper.

Abstract:
This paper addresses the issue of hedging option positions when the underlying asset exhibits stochastic volatility. By parameterizing the volatility process as GARCH, and utilizing risk- neutral valuation, we estimate hedging parameters (delta and gamma) using Monte-Carlo simulation. We estimate hedging parameters for options on the Standard and Poor's 500 index, a bond futures index, a weighted foreign exchange rate index, and an oil futures index. We find that Black-Scholes and GARCH deltas are similar for all the options considered, while GARCH gammas are significantly higher than BS gammas for all options. For near the money options, GARCH gamma hedge ratios are higher than BS hedge ratios when hedging a long term option with a short term option. Away from the money, GARCH gamma hedge ratios are lower than BS.

Abstract:
This article addresses the issue of hedging options positions when the underlying asset exhibits stochastic volatility. By parameterizing the volatility process as GARCH, and utilizing risk-neutral valuation, we approximate hedging parameters (delta and gamma) using Monte Carlo simulation. We estimate hedging parameters for options on the Standard & Poor's 500 index, a bond futures index, a weighted foreign exchange rate index, and an oil futures index.We find that Black-Scholes and GARCH deltas are similar for all the options considered, while GARCH gammas are significantly higher than BS gammas for all options. For near-the-money options, GARCH gamma hedge ratios are higher than BS hedge ratios when hedging a long-term option with a short-term option. Away from the money, GARCH gamma hedge ratios are lower than BS.

Abstract:
This article formulates a bivariate point process to jointly analyze trade and quote arrivals. In microstructure models, trades may reveal private information that is then incorporated into new price quotes. This article examines the speed of this information flow and the circumstances that govern it. A joint likelihood function for trade and quote arrivals is specified in a way that recognizes that an intervening trade sometimes censors the time between a trade and the subsequent quote. Models of trades and quotes are estimated for eight stocks using Trade and Quote database (TAQ) data. The essential finding for the arrival of price quotes is that information flow variables, such as high trade arrival rates, large volume per trade, and wide bid-ask spreads, all predict more rapid price revisions. This means prices respond more quickly to trades when information is flowing so that the price impacts of trades and ultimately the volatility of prices are high in such circumstances.

duration analysis, market microstructure, transaction data

Abstract:
Recent empirical work has studied point processes of transactions in financial markets and observed clear time dependent patterns in these arrival times. However these studies do not examine the timing of quoted price changes. This paper formulates a bivariate point process to jointly analyze transaction and quote arrivals. In microstructure models, transactions may reveal private information which is then incorporated into new prices. This paper examines the speed of this information flow and the circumstances which govern it. One of the main conclusions are that conditional on past quote times, the impact of trade information is to make quote durations longer when there is more information flow rather than less. This is interpreted as evidence that limit order suppliers become more cautious in the presence of apparent informational trading.

Abstract:
The Multiplicative Error Model for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows the innovations to be contemporaneously correlated. The estimation procedure is hindered by the lack of sufficiently flexible probability density functions for such processes. We adopt copula functions to be able to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate the feasibility of the procedure and the gains over the equation by equation approach using a model with different volatility measures.

GARCH, MEM, Volatility, Copula, financial time series

Abstract:
Transmission mechanisms in financial markets reflect the degree of integrationof capital markets, as well as the relative importance of real economies. Market volatility has components which may behave differently across quiet and turbulent periods, but appear to behave in similar ways from market to market. In this paper we suggest a Multiplicative Error Model (MEM) approach to study volatility spillovers among a set of markets, using as a proxy, the market daily range. We model the dynamics of the expected volatility of one market including interactions with the past daily ranges of other markets, building a fully interdependent model. We analyze eight East Asian markets in the period 1995-2006, devoting particular attention to the treatment of the 1997-1998 turbulent period. We find no evidence of independent markets while several interdependence relationships can be stressed. Hong Kong turns out to be the most important market while Taiwan seems to have suffered quite limited effects from the crisis. Impulse response functions and multiperiod forecast profiles are developed and suggest a build-up in the spillover effects.

Abstract:
In this paper, we consider a framework with which the cross sectional and time series behavior of the yield curve can be studied simultaneously. We examine the relationship between the yield curve and the time-varying conditional volatility of the Treasury bill market. We demonstrate that differently shaped yield curves can result given different combinations of volatility and expectations about future spot rates. Moreover, adjusting the forward rate for the volatility related liquidity premium can improve its performance as a predictor of future spot rates at least for the period from August 1964 to August 1979.

Abstract:
This paper defines and tests a form of market efficiency called market dexterity which requires that asset prices adjust instantaneously and completely in response to new information. Examining the behavior of the yen/dollar exchange rate while each of the major markets are open it is possible to test for informational effects from one market to the next. Assuming that news has only country specific autocorrelation such as a heat wave. any intra-daily volatility spillovers (meteor showers) become evidence against market dexterity. ARCII models are employed to model heteroskedasticity across intra-daily market segments. Statistical tests lead to the rejection of the heat wave and therefore the market dexterity hypothesis. Using a volatility type of vector autoregression we examine the impact of news in one market on the time path of volatility in other markets.

Abstract:
In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, the gain from improved pricing of options would be a measure of the value of a forecast of underlying asset returns. NYSE index returns over the period of 1968-1991 are used to suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White`s (1987) adjustment for stochastic variance in Black and Scholes`s (1973) formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed.

Abstract:
This paper introduces a class of statistical tests for the hypothesis that some feature of a data set is common to several variables. A feature is detected in a single series by a hypothesis test where the null is that it is absent, and the alternative is that it is present. Examples are serial correlation, trends, seasonality, heteroskedasticity, ARCH, excess kurtosis and many others. A feature is common to a multivariate data set if a linear combination of the series no longer has the feature. A test for common features can be based on the minimized value of the feature test over all linear combinations of the data. A bound on the distribution for such a test is developed in the paper. For many important cases, an exact asymptotic critical value can be obtained which is simply a test of overidentifying restrictions in an instrumental variable regression.

Abstract:
This paper proposes a new way of modeling and forecasting intraday returns. We decompose the volatility of high frequency asset returns into components that may be easily interpreted and estimated. The conditional variance is expressed as a product of daily, diurnal and stochastic intraday volatility components. This model is applied to a comprehensive sample consisting of 10-minute returns on more than 2500 US equities. We apply a number of different specifications. Apart from building a new model, we obtain several interesting forecasting results. In particular, it turns out that forecasts obtained from the pooled cross section of companies seem to outperform the corresponding forecasts from company-by-company estimation.

Volatility, ARCH, Intra-day Returns

Abstract:
Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of returns. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled1 with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on thelikelihood function. It is shown that they perform well in a variety of situationsand give sensible empirical results.

Abstract:
This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S&P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

Abstract:
This paper derives relationships between frequency-domain and standard time-domain distributed-lag and autoregessive moving-average models. These relations are well known in the literature but are presented here in a pedogogic form in order to facilitate interpretation of spectral and cross-spectral analyses. In addition, the paper employs the conventions and discusses the estimation procedures used in TROLL. Some aspects of these estimation procedures are new and have not been discussed in the literature.

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Abstract:
No abstract is available for this paper.

Abstract:
Twenty-five years of volatility research has left the macroeconomic environment playing a minor role. This paper proposes modeling equity volatilities as a combination of macroeconomic effects and time series dynamics. High frequency return volatility is specified to be the product of a slow-moving component, represented by an exponential spline, and a unit GARCH. This slow-moving component is the low frequency volatility, which in this model coincides with the unconditional volatility. This component is estimated for nearly 50 countries over various sample periods of daily data.Low frequency volatility is then modeled as a function of macroeconomic and financial variables in an unbalanced panel with a variety of dependence structures. It is found to vary over time and across countries. The low frequency component of volatility is greater when the macroeconomic factors GDP, inflation, and short-term interest rates are more volatile or when inflation is high and output growth is low. Volatility is higher for emerging markets and for markets with small numbers of listed companies and market capitalization relative to GDP, but also for large economies.The model allows long horizon forecasts of volatility to depend on macroeconomic developments, and delivers estimates of the volatility to be anticipated in a newly opened market.

Abstract:
In financial time series analysis we encounter several instances of non negative valued processes (volumes, trades, durations, realized volatility, daily range, and so on) which exhibit clustering and can be modeled as the product of a vector of conditionally autoregressive scale factors and a multivariate iid innovation process (vector Multiplicative Error Model). Two novel points are introduced in this paper relative to previous suggestions: amore general specification which sets this vector MEM apart from an equation by equation specification; and the adoption of a GMM-based approach which bypasses the complicated issue of specifying a general multivariate non negative valued innovation process. A vMEM for volumes, number of trades and realized volatility reveals empirical support for a dynamically interdependent pattern of relationships among the variables on a number of NYSE stocks.

Abstract:
The Multiplicative Error Model introduced by Engle (2002) for positive valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support. In this paper we propose a multi-variate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated. The estimation procedure is hindered by the lack of probability density functions for multivariate positive valued random variables. We suggest the use of copulafunctions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure.

Abstract:
This paper tests for cointegration between regional output of an industry and national output of the same industry. An equilibrium economic theory is presented to argue for the plausibility of cointegration, however, regional economic forecasting using the shift and share framework often acts as if cointegration does not exist. Data analysis on broad industrial sectors for 20 states finds very little evidence for cointegration. Forecasting models with and without imposing cointegration are then constructed and used to forecast out of sample. The simplest, non-cointegrating models are the best.