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Abstract:
The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the S&P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.

Abstract:
In one of the early attempts to model stochastic volatility, Clark [1973] conjectured that the size of asset price movements is tied to the rate at which transactions occur. To formally analyze the econometric implications, he distinguished between transaction time and calendar time. The present paper exploits Clark's strategy for a different purpose, namely, asset pricing. It studies arbitrage-based pricing in economies where: (i)trade takes place in transaction time, (ii) there is a single state variable whose transaction-time price path is binomial, (iii) there are riskfree bonds with calendar-time maturities, and (iv) the relation between transaction time and calendar time is stochastic. The state variable could be interpreted in various ways. E.g., it could be the price of a share of stock, as in Black and Scholes [1973], or a factor that summarizes changes in the investment opportunity set, as in Cox, Ingersoll and Ross [1985] or one that drives changes in the term structure of interest rates (Ho and Lee [1986], Heath, Jarrow and Morton [1992]). Property (iv) generally introduces stochastic volatility in the process of the state variable when recorded in calendar time.

The paper investigates the pricing of derivative securities with calendar-time maturities. The restrictions obtained in Merton [1973] using simple buy-and-hold arbitrage portfolio arguments do not necessarily obtain. Conditions are derived for all derivatives to be priced by dynamic arbitrage, i.e., for market completeness in the sense of Harrison and Pliska [1981]. A particular class of stationary economies where markets are indeed complete is characterized.

Abstract:
In this paper we propose a generic procedure for estimating and pricing options in the context of stochastic volatility models using simultaneously the fundamental price and a set of option contracts. We appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. A by-product of this finding is that we uncover a remarkably simple volatility extraction filter based on a polynomial lag structure of implied volatilities. The bivariate approach involving both the fundamental and an option appears useful when the information from the cash market provides support via the conditional kurtosis to price options. This is the case for some long term options. Moreover, having estimated separately the risk-neutral and objective measures allows us to appraise the typical risk-neutral representations used in the literature. Using Heston's (1993) model as example we show that the usual transformation from objective to risk neutral density is not supported by the data.

Abstract:
We consider a log-linearized version of a discounted rents model to price commercial real estate as an alternative to traditional hedonic models. First, we verify a key implication of the model, namely, that cap rates forecast commercial real estate returns. We do this using two different methodologies: time series regressions of 21 US metropolitan areas and mixed data sampling (MIDAS) regressions with aggregate REITs returns. Both approaches confirm that the cap rate is related to fluctuations in future returns. We also investigate the provenance of the predictability. Based on the model, we decompose fluctuations in the cap rate into three parts: (i) local state variables (demographic and local economic variables); (ii) growth in rents; and (iii) an orthogonal part. About 30% of the fluctuation in the cap rate is explained by the local state variables and the growth in rents. We use the cap rate decomposition into our predictive regression and find a positive relation between fluctuations in economic conditions and future returns. However, a larger and significant part of the cap rate predictability is due the orthogonal part, which is unrelated to fundamentals. This implies that economic conditions, which are also used in hedonic pricing of real estate, cannot fully account for future movements in returns. We conclude that commercial real estate prices, at least at an aggregate level, are better modeled as financial assets and that the discounted rent model might be more suitable than traditional hedonic models, at least at an aggregate level.

Real Estate, MIDAS, Cap rate, Predictive regression

Abstract:
The paper surveys the recent literature on the econometric analysis of option pricing models.

Stock Price Dynamics, Multivariate Jump-Diffusion Models, Latent variables, Stochastic Volatility, Objective and Risk Neutral Distributions, Nonparametric Option Pricing, Discrete time Option Pricing Models, Risk Neutral Valuation, Preference-free Option Pricing

Abstract:
The purpose of this paper is to shed further light on the tensions that exist between the empirical fit of stochastic volatility (SV) models and their linkage to option pricing. A number of recent papers have investigated several specifications of one-factor SV diffusion models associated with option pricing models. The empirical failure of one-factor affine, Constant Elasticity of Variance (CEV), and one-factor log-linear SV models leaves us with two strategies to explore: (1) add a jump component to better fit the tail behavior or (2) add an additional (continuous path) factor where one factor controls the persistence in volatility and the second determines the tail behavior. Both have been partially pursued and our paper embarks on a more comprehensive examination which yields some rather surprising results. Adding a jump component to the basic Heston affine model is known to be a successful strategy as demonstrated by Andersen et al. (1999), Eraker et al. (1999), Chernov et al. (1999), and Pan (1999). Unfortunately, the presence of a jump component introduces quite a few unpleasant econometric issues. In addition, several financial issues, like hedging and risk factors become more complex. In this paper we show that a two-factor log-linear SV diffusion model (without jumps) appears to yield a remarkably good empirical fit. We estimate the model via the EMM procedure of Gallant and Tauchen (1996) which allows us to compare the non-nested log-linear SV diffusion with the affine jump specification. Obviously, there is one drawback to the log-linear SV models when it comes to pricing derivatives since no closed-form solutions are available. Against this cost weights the advantage of avoiding all the complexities involved with jump processes.

Abstract:
This paper is part of a larger research program pertaining to the role of derivatives during financial crisis and also part of the research pertaining to the causes of the Asian financial crisis. The Korean market is studied because of two reasons: (1) it is a representative example of the Asian financial meltdown and (2) there is a detailed data set available of all transactions by different types of protagonists, including foreign investors. Several authors including Kim and Wei (1999), Park and Song (1999) and Radelet and Sachs (1998) put the blame for the Asian crisis on foreign investors. Choe, Kho and Stulz (1999), who focused exclusively on equity trading in the Korean stock market, found no evidence supporting market de-stabilization by foreign investors during the crisis. They did not find any evidence showing that the foreign investors' herding is more important and they engaged in positive feedback trading during the crisis. They also found no evidence that foreign investors de-stabilized the stock market in event studies that examined the abnormal returns centered around large trades by foreign market participants. The paper begins with establishing first the role of derivative securities during the crisis. None of the studies so far have examined futures trading. Our paper focuses on this largely overlooked and important feature of the crisis. Once the role of futures contracts is understood, the paper complements Choe et al.'s analysis by examining whether derivatives trading by either domestic or non-resident investors, or both together, exerted a de-stabilizing influence during the crash. The results in this paper indicate that futures market played a key role during the Korean stock market turbulence in 1997. We find that the fraction of index futures volume started to rise dramatically in July 1997, three months ahead of the crash, and died out after the crash. Furthermore, we also report that selling pressures in the futures market during the crisis were transmitted to the cash market causing a decline in cash prices, a pattern which was not observed prior to the crisis. Given the significance of futures trading, we examine whether futures trading by either domestic or foreign investors, or both together, exerted a de-stabilizing influence during the crisis. We find that foreign investors increased their presence in the futures market and dramatically increase their herding of futures trading. Foreign traders also become negative feedback traders of futures and the permanent impact of their futures contracts sales increases substantially during the crisis.

Abstract:
We rely on recently developed general equilibrium asset pricing models, from which we derive some predictions about how heterogeneity of beliefs affects return and volatility dynamics. The first contribution of our paper is the derivation of a simple decomposition of the conditional stock returns and volatility into two components, one component determined by traditional fundamental factors, the other component dependent on the heterogeneity of beliefs. The second contribution of our paper is that we suggest a new empirical measure of heterogeneity of beliefs of agents. We address the practical question of whether we can observe good proxies that capture informational heterogeneity and obey the predictions of theoretical models. It is argued factors that capture the dispersion of analysts' earnings forecasts are such proxies. We use factor asset pricing models to construct conventional predictions of returns and volatility. First, we determine dispersion is a priced risk factor in traditional asset pricing models. Second, we show dispersion is significantly and positively related to both out-of-sample returns and volatility, which is coherent with the theoretical decomposition.

Abstract:
This paper introduces a new estimation for the dynamics of betas. It combines two previously separate approaches in the literature, data-driven filters and parametric methods. Namely, we show how to estimate the parametric beta dynamics by instrumental variables combined with block-sampling - but not overlapping window filters - of data-driven betas. Instrumental variables are needed because of the measurement errorsin empirical betas. We find that, while betas are very strongly autocorrelated, neither aggregate nor firm-specific variables explain much of their quarterly variation. We then compare block-samplers and overlapping window filters using a criterion of economic significance. Namely, we track the out-of-sample performance of portfolios optimized subject to target beta constraints. For target betas of zero, the case of many hedge funds, we show that estimation error results in systematic overshooting of the target beta. These portfolios benefit from the use of medium to long term estimation windows of daily returns.

beta, systematic risk, portfolio efficiency, errors in the variables

Abstract:
This paper studies the ICAPM intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns -- the Mixed Data Sampling (or MIDAS) approach. Using MIDAS, we find that there is a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process, and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the ICAPM based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.

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:
This paper studies the ICAPM intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns - the Mixed Data Sampling (or MIDAS) approach. Using MIDAS, we find that there is a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process, and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the ICAPM based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.

ICAPM, risk-return tradeoff, conditional variance, forecasting returns

Abstract:
This paper reviews the literature on structural breaks in financial time series. First we discuss the implications of structural breaks in financial time series for statistical inference purposes. In the second section we discuss the relevant asymptotic results and issues involved in general classifications of change-point tests in financial time series such historical versus sequential tests, parametric versus nonparametric tests and single versus multiple break tests. The third section reviews a number of structural change tests by focusing on certain characteristics or moments of financial time series such as structural break tests in the financial asset returns and volatility, long memory, tails and distribution. In addition, we review changepoint tests for the co-dependence between financial asset returns processes in the context of multivariate volatility models, copulae and last but not least asset pricing. In concluding we provide some areas of future research in the subject.

Structural change, historical tests, sequential tests

Abstract:
We provide theoretical explanations for (1) the empirical stylized fact recognized at least since Taylor (1986) and Ding, Granger, and Engle (1993) that absolute returns show more persistence than squared returns and (2) the empirical funding reported in recent work by Ghysels, Santa-Clara, and Valkanov (2006) showing that realized absolute values outperform square return-based volatility measures in predicting future increments in quadratic variation. We start from a continuous time stochastic volatility model for asset returns suggested by Barndorff-Nielsen and Shephard (2001) and study the persistence and linear regression properties of various volatility-related processes either observed directly or with sampling error. We also allow for jumps in the asset return processes and investigate their impact on persistence and linear regression. Extensive empirical results complement the theoretical analysis.

MIDAS regressions, Realized variance

Abstract:
A general estimation approach combining the attractive features of method of moments with the efficiency of ML is proposed. The moment conditions are computed via the characteristic function. The two major difficulties with the implementation is that one needs to use an infinite set of moment conditions leading to the singularity of the covariance matrix in the GMM context, and the optimal instrument yielding the ML efficiency was previously shown to depend on the unknown probability density function. We resolve the two problems simultaneously in the framework of C-GMM (GMM with a continuum of moment conditions) of Carrasco and Florens (2000a). First, we extend their results to dependent data and provide a reformulation of their estimator that enhances its computational ease. Second, we propose to span the unknown optimal instrument by an infinite basis consisting of simple exponential functions. Since the estimation framework already relies on a continuum of moment conditions, adding a continuum of spanning functions does not pose any problems. As a result, we achieve ML efficiency when we use the values of conditional CF indexed by its argument as moment functions. We also introduce HAC-type estimators so that the estimation methods are not restricted to settings involving martingale difference sequences. Hence, our methods apply to Markovian and non-Markovian dynamic models. Finally, a simulated method of moments type estimator is proposed to deal with the cases where the characteristic function does not have a closed-form expression. Extensive Monte-Carlo study based on the models typically used in term-structure literature favorbaly documents the performance of our methodology.

maximum likelihood estimation, jump diffusion processes, generalized method of moments, continuum of moment conditions, characteristic function, term structure models

Abstract:
We consider various MIDAS (Mixed Data Sampling) regression models to predict volatility. The models differ in the specification of regressors (squared returns, absolute returns, realized volatility, realized power, and return ranges), in the use of daily or intra-daily (5-minute) data, and in the length of the past history included in the forecasts. The MIDAS framework allows us to compare models across all these dimensions in a very tightly parameterized fashion. Using equity return data, we find that daily realized power (involving 5-minute absolute returns) is the best predictor of future volatility (measured by increments in quadratic variation) and outperforms model based on realized volatility (i.e. past increments in quadratic variation). Surprisingly, the direct use of high-frequency (5-minute) data does not improve volatility predictions. Finally, daily lags of one to two months are sufficient to capture the persistence in volatility. These findings hold both in- and out-of-sample.

Abstract:
We use the MIDAS (Mixed Data Sampling) approach to study regressions of future realized volatility at low-frequency horizons (one to four weeks) on lagged daily and intra-daily (1) squared returns, (2) absolute returns, (3) realized volatility, (4) realized power and (5) return ranges. We document first of all that daily realized power and daily range are surprisingly good predictors of future realized volatility and outperform models based on realized volatility. Moreover, MIDAS models with daily data - range, realized power, realized volatility - require a polynomial with at least 30 days. We document that high-frequency absolute returns are also better at forecasting future low frequency realized volatility than high-frequency squared returns. We also discuss many issues that are encountered in practice, such as long memory and seasonality.
All the results are based on a commonly used FX data set.

variance estimation, volatility, asset pricing, MIDAS

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:
It is common practice to use the sum of frequently sampled squared returns to estimate volatility, yielding so called realized volatility. Unfortunately, returns are contaminated by market microstructure noise. Several noise-corrected realized volatility measures have been proposed. We assess to what extend correction for microstructure noise improves forecasting future volatility using the MIxed DAta Sampling (MIDAS) framework. We start by studying the population properties of predictions using various realized volatility measures. We do this in a general regression setting and with both i.i.d. as well as depend microstructure noise. Next we study optimal sampling issues theoretically, when the objective is forecasting and microstructure noise contaminates realized volatility. For the volatility measures constructed using five-minute returns, microstructure corrections tend to reduce predictability. The subsampling and averaging class of estimators (Zhang, Mykland, and Aıt-Sahalia 2005) predicts volatility the best at this frequency. In particular, a new power variation estimator constructed by averaging over subsamples has the best performance. This result reinforces earlier findings of (Ghysels, Santa-Clara, and Valkanov 2006) and Forsberg and Ghysels (2004). Finally, the volatility dynamics are more complicated for one-minute returns and the results are not that clear-cut. Moreover, when we study optimal sampling empirically, we find its implementation hampered by the requirement to estimate fourth order moments.

Realized volatility, MIDAS regressions

Abstract:
We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996) for estimating the quadratic variation of asset returns, which is also referred to as integrated or realized volatility. The new approach treats integrated volatility as a continuous time stochastic process sampled at high frequencies and suggests rolling sample estimators which share many features with spot volatility estimators. We also discuss asymptotically efficient window lengths and optimal weighting schemes for estimators of the quadratic variation and establish the links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

Rolling sample estimators, quadratic variation, volatility, efficient filtering, continuous record asymptotics, high-frequency data

Abstract:
We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996) for estimating the quadratic variation of asset returns, which is also referred to as integrated or realized volatility. The new approach treats integrated volatility as a continuous time stochastic process sampled at high frequencies and suggests rolling sample estimators which share many features with spot volatility estimators. We also discuss asymptotically efficient window lengths and optimal weighting schemes for estimators of the quadratic variation and establish the links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

Rolling sample estimators, quadratic variation, volatility, efficient filtering, continuous record asymptotics, high-frequency data

Abstract:
We show that using data which are properly available in real time when assessing the sensitivity of asset prices to economic news leads to different empirical findings than when data availability and timing issues are ignored. We do this by focusing on a particular example, namely Chen, Roll and Ross (1986), and examine whether innovations to economic variables can be viewed as risks that are rewarded in asset markets. Our findings support the view that data uncertainty is sufficiently prevalent to warrant careful use of real-time data when forming real-time news measures, and in general when undertaking empirical financial investigations involving macroeconomic data.

Market efficiency, expectations, news, data revision process

Abstract:
This paper studies the relation between liquidity and optimal portfolio allocations. Given that the portfolio problem of a constant relative risk aversion investor does not have a closed-form solution, we use a nonparametric approach to estimate the optimal allocations. Using a sample of NYSE stocks from 1963-2000, we find that the optimal portfolio weight in small stocks is strongly increasing in liquidity at short daily and weekly horizons. This result is consistent for three different measures of liquidity: price impact, dollar volume, and turnover. However, liquidity does not influence the optimal portfolio choice for large stocks, nor for longer monthly investment horizons.

Conditional Portfolio Choice, Liquidity, Nonparametric

Abstract:
The paper evaluates the performance of several recently proposed tests for structural breaks in conditional variance dynamics of asset returns. The tests apply to the class of ARCH and SV type processes as well as data-driven volatility estimators using high-frequency data. In addition to testing for the presence of breaks, the statistics identify the number and location of multiple breaks. We study the size and power of the new tests for detecting breaks in the conditional variance under various realistic univariate heteroskedastic models, change-point hypotheses and sampling schemes. The paper concludes with an empirical analysis using data from the stock and FX markets for which we find multiple breaks associated with the Asian and Russian financial crises. These events resulted in changes in the dynamics of volatility of asset returns in the samples prior and post the breaks.

change-point, break dates, ARCH, high-frequency data

Abstract:
Over the last four decades, a large number of structural models have been developed to estimate and price credit risk. The focus of the paper is on a much neglected issue pertaining to fundamental shifts in the structural parameters governing default. We propose formal quality control procedures that allow risk managers to monitor fundamental shifts in the structural parameters of credit risk models. The procedures are sequential - hence apply in real time. The basic ingredients are the key processes used in credit risk analysis, such as most prominently the Merton distance to default process as well as financial returns. Moreover, while we propose different monitoring processes, we also show that one particular process is optimal in terms of minimal detection time of a break in the drift process and relates to the Radon-Nikodym derivative for a change of measure.

Structural Change, Sequential Tests Merton Model

Abstract:
It is difficult to define news, and many definitions are model-based since part of what is announced is anticipated. Therefore, news is typically defined as a residual within the context of some type of prediction model, and the prediction model locks in the sampling frequency that is the reference time scale for analyzing propagation mechanisms. We try to accomplish two goals: (1) characterize news as much as possible as a model-free observation, and (2) measure the impact of news over any arbitrary horizon of interest. We revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. Instead of taking a single horizon fixed parametric specification, we recast many of the original ideas in a very flexible multi-horizon semi-parametric setting. Technically speaking we introduce semi-parametric MIDAS regressions and study their asymptotic properties. The analysis relates to and extends recent work by Linton and Mammen (2005). In addition we also introduce various new parametric models. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years. In this context we discuss the link between diffusions and news impact curves.

MIDAS regressions, high frequency financial data

Abstract:
We explore Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not so recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk-return tradeoff. We also report empirical evidence on microstructure noise and volatility forecasting.

Volatility, Risk, tick-by-tick applications, nonlinear MIDAS, microstructure noise

Abstract:
Survey of forecasters, containing respondents' predictions of future values of growth, inflation and other key macroeconomic variables, receive a lot of attention in the financial press, from investors, and from policy makers. They are apparently widely perceived to provide useful information about agents' expectations. Nonetheless, these survey forecasts suffer from the crucial disadvantage that they are often quite stale, as they are released only infrequently, such as on a quarterly basis. In this paper, we propose methods for using asset price data to construct daily forecasts of upcoming survey releases, which we can then evaluate. Our methods allow us to estimate what professional forecasters would predict if they were asked to make a forecast each day, making it possible to measure the effects of events and news announcements on expectations. We apply these methods to forecasts for several macroeconomic variables from both the Survey of Professional Forecasters and Consensus Forecasts.

Survey forecasts, mixed frequency data sampling, forecast evaluation, rational expectations, Kalman filter, Kalman smoother, news announcement

Abstract:
We examine whether the sign and magnitude of discretely sampled high frequency returns have impact on future volatility predictions. We first let the 'data speak', namely with minimal interference we capture the mapping between returns over short horizons and future volatility over longer horizons. Technically speaking, we introduce semi-parametric MIDAS regressions. Compared to the semi-parametric infinite ARCH estimation in Linton and Mammen (2005) we show that the asymptotic distribution of semi-parametric MIDAS regressions depends on the mixed data sampling scheme. Also novel is the parametric specification we consider to deal with for intra-daily/daily lags. In the empirical work we revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years.

MIDAS regressions, high frequency financial data

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:
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:
We study historical and sequential CUSUM change-point tests for strongly dependent nonlinear processes. These tests are used to monitor the conditional variance of asset returns and to provide real-time information regarding instabilities or disruptions in financial risk. We discuss in detail the theoretical underpinnings of applying historical and sequential CUSUM change-point tests to monitor the stability of dynamic variance processes. Data-driven volatility monitoring schemes are investigated that satisfy the FCLT and provide various advantages for sequential analysis. We examine various issues that emerge when using such processes. One such issue is the sampling frequency since the processes can be sampled at alternative frequencies. We study the power of detection as sampling frequencies vary. Analytical relative local power results are obtained for the CUSUM test for monitoring volatility processes at low versus high sampling frequencies. The analytical results provide evidence of some nontrivial trade-offs between relative local power and the role of sampling frequency, persistence and tails of the volatility process. A comprehensive simulation analysis unfolds the finite sample properties of the CUSUM volatility change-point test and provides additional support to the analytical asymptotic results on relative local power.

Structural change, CUSUM, GARCH, quadratic variation, power variation, high frequency data, Brownian bridge, boundary crossing, sequential tests, local power

Abstract:
The volatility component models have received much attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or non-stationarities in asset price volatility. The paper studies the distributional properties of various volatility component models. Sufficient conditions for the existence or/and uniqueness of (strictly) stationary (ergodic) solutions with mixing property to the volatility component models are derived. Hence, the paper revisits the component models from a statistical perspective and attempts to explore the stationarity and mixing properties of the underlying processes. There is a clear need for such an analysis, since any discussion about non-stationarity presumes we know when component models are stationary. As it turns out, this is not the case and the purpose of the paper is to rectify this. We also look into the sampling behavior of the maximum likelihood estimates of recently proposed volatility component models and establish their local consistency and asymptotic normality are established as well.

Abstract:
Multi-period forecasts of stock market return volatilities are often used in many applied areas of finance where long horizon measures of risk are necessary. Yet, very little is known about how to forecast variances several periods ahead, as most of the focus has been placed on one-period ahead forecasts. In this paper, we compare several approaches of producing multi-period ahead forecasts -iterated, direct, and mixed data sampling (MIDAS)- as alternatives to the often-used "scaling-up" method. The comparison is conducted (pseudo) out-of-sample using returns data of the US stock market portfolio and a cross section of size and book-to-market portfolios. The comparison results are surprisingly sharp. For the market, size, and book-to-market portfolios, we obtain the same precision ordering of the forecasting methods. The direct approach provides the worse (in MSFE sense) forecasts; it is dominated even by the naive "scaling-up" method. Iterated forecasts are suitable for shorter horizons (5 to 10 periods ahead), but their MSFEs deteriorate as the horizon increases. The MIDAS forecasts perform well at long horizons: they dominate all other approaches at horizons of 10-periods ahead and higher. The MIDAS forecasting advantage becomes most apparent at horizons of 30-periods ahead and longer. In sum, this study dispels the notion that volatility is not forecastable at long horizons and offers an approach that delivers accurate pseudo out-of-sample predictions.

Volatility forecasting, multi-period forecasts, mixed-data sampling

Abstract:
We find that price momentum in stocks was a pervasive phenomenon during the Victorian age (1866-1907) as well. Momentum strategy profits have little systematic risk even at business cycle frequencies; disappear periodically only to reappear later; exhibit long run reversal; and are higher following up markets, suggesting limited availability of arbitrage capital relative to opportunities during those times. Since there were no capital gains taxes during the Victorian age, the long run reversal of momentum profits must have a fundamental component, that is unrelated to tax based trading, identified by Grinblatt and Moskowitz (2004) using CRSP era data.

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Abstract:
Time series are demeaned when sample autocorrelation functions are computed. By the same logic it would seem appealing to remove seasonal means from seasonal time series before computing sample autocorrelation functions. Yet, standard practice is only to remove the overall mean and ignore the possibility of seasonal mean shifts in the data. Whether or not time series are seasonally demeaned has very important consequences on the asymptotic behavior of autocorrelation functions. The effect on the asymptotic distribution of seasonal mean shifts and their removal is investigated and the practical consequences of these theoretical developments are discussed. We also examine the small sample behavior of autocorrelation function estimates through Monte Carlo simulations.

Abstract:
The article evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for ²-mixing processes and EDF-based tests for the residuals of such nonlinear dependent processes. Hence the tests apply to the class of ARCH- and SV-type processes as well as data-driven volatility estimators using high-frequency data. It is shown that some of the high-frequency volatility estimators substantially improve the power of the structural break tests, especially for detecting changes in the tail of the conditional distribution. Similarly certain types of filtering and transformation of the returns process can improve the power of CUSUM statistics. We also explore the impact of sampling frequency on each of the test statistics.

change-point tests, CUSUM, GARCH, high-frequency data, Kolmogorov-Smirnov, location-scale distribution family, power variation, quadratic variation

Abstract:
We study how heterogeneous beliefs affect returns and examine whether they are a priced factor in traditional asset pricing models. To accomplish this task, we suggest new empirical measures based on the disagreement among analysts about expected earnings (short-term and long-term) and show they are good proxies. We first establish that the heterogeneity of beliefs matters for asset pricing and then turn our attention to estimating a structural model in which we use the forecasts of financial analysts to proxy for agents` beliefs. Finally, we investigate whether the amount of heterogeneity in analysts` forecasts can help explain asset pricing puzzles.

time optimal control problems, Neumann parabolic equations with an infinite number of variables, Dubovitskii-Milyutin theorem, conical approximations, optimality conditions, Weierstrass theorem

Abstract:
We consider a log-linearized version of a discounted rents model to price commercial real estate as an alternative to traditional hedonic models. First, we verify a key implication of the model, namely, that cap rates forecast commercial real estate returns. We do this using two different methodologies: time series regressions of 21 US metropolitan areas and mixed data sampling (MIDAS) regressions with aggregate REIT returns. Both approaches confirm that the cap rate is related to fluctuations in future returns. We also investigate the provenance of the predictability. Based on the model, we decompose fluctuations in the cap rate into three parts: (i) local state variables (demographic and local economic variables); (ii) growth in rents; and (iii) an orthogonal part. About 30% of the fluctuation in the cap rate is explained by the local state variables and the growth in rents. We use the cap rate decomposition into our predictive regression and find a positive relation between fluctuations in economic conditions and future returns. However, a larger and significant part of the cap rate predictability is due to the orthogonal part, which is unrelated to fundamentals. This implies that economic conditions, which are also used in hedonic pricing of real estate, cannot fully account for future movements in returns. We conclude that commercial real estate prices are better modelled as financial assets and that the discounted rent model might be more suitable than traditional hedonic models, at least at an aggregate level.

Abstract:
Our objective is volatility forecasting, which is core to many risk management problems. We provide theoretical explanations for (i) the empirical stylized fact recognized at least since Taylor () and Ding, Granger, and Engle () that absolute returns show more persistence than squared returns and (ii) the empirical finding reported in recent work by Ghysels, Santa-Clara, and Valkanov () showing that realized absolute values outperform square return-based volatility measures in predicting future increments in quadratic variation. We start from a continuous time stochastic volatility model for asset returns suggested by Barndorff-Nielsen and Shephard () and study the persistence and linear regression properties of various volatility-related processes either observed directly or with sampling error. We also allow for jumps in the asset return processes and investigate their impact on persistence and linear regression. Extensive empirical results complement the theoretical analysis.

MIDAS regressions, realized variance

Abstract:
We study regression models that involve data sampled at different frequencies. We derive the asymptotic properties of the NLS estimators of such regression models and compare them with the LS estimators of a traditional model that involves aggregating or equally weighting data to estimate a model at the same sampling frequency. In addition we provide a new aggregation bias test. We explore the above theoretical aspects and verify them via an extensive Monte Carlo simulation study and an empirical application.

MIDAS regressions

Abstract:
We study asset pricing in economies featuring both risk and uncertainty. In our empirical analysis, we measure risk via return volatility and uncertainty via the degree of disagreement of professional forecasters, attributing different weights to each forecaster. We empirically model the typical risk-return trade-off and augment these models with our measure of uncertainty. We find stronger empirical evidence for an uncertainty-return trade-off than for the traditional risk-return trade-off. Finally, we investigate the performance of a two-factor model with risk and uncertainty in the cross section.

Conditional volatility, model uncertainty, disagreement, factor models

Abstract:
The purpose of this paper is to bridge two strands of the literature, one pertaining to the objective or physical measure used to model an underlying asset and the other pertaining to the risk-neutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental
price and a set of option contracts. We use Heston's (1993, Review of Financial Studies 6, 327--343) model as an example, and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract show dominance of univariate approach, which relies solely on options data. A by-product of this finding is that we uncover a remarkably simple volatility extraction filter based on a polynomial lag structure of implied volatilities. The bivariate approach, involving both the fundamental security and an option contract, appears useful when the information from the cash market reflected in the conditional kurtosis provides support to price long term.

Keyword(s): Derivative securities; Efficient method of moments; State price densities; Stochastic volatility models; Filtering

Abstract:
This paper studies Nasdaq market makers' activities during the one-and-half hour pre-opening period. Price discovery during the pre-opening is conducted via price signaling as opposed to the auction used to open the NYSE or the continuous market used during trading. In the absence of trades, Nasdaq dealers use crossed and locked inside quotes to signal to other market makers which direction the price should move. Furthermore, we find evidence of price leadership among market makers that bears little resemblance to their IPO/SEO lead underwriter participation.

Abstract:
This paper studies Nasdaq market makers' activities during the one-and-half hour pre-opening period. Price discovery during the pre-opening is conducted via price signaling as opposed to the auction used to open the NYSE or the continuous market used during trading. In the absence of trades, Nasdaq dealers use crossed and locked inside quotes to signal to other market makers which direction the price should move. Furthermore, we find evidence of price leadership among market makers that bears little resemblance to their IPO/SEO lead underwriter participation.

Abstract:
High frequency asset returns generally exhibit time dependent and seasonal clustering of volatility. This paper proposes a new class of models featuring periodicity in conditional heteroskedasticity explicitly designed to capture the repetitive seasonal time variation in the second order moments. The structures of this new class of Periodic ARCH, or P-ARCH, models share many properties with the periodic ARMA processes for the mean. The implicit relation between P-GARCH structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroskedastic periodicity may give rise to a loss in efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. An empirical example for the daily bilateral Deutschemark - British Pound spot exchange rate highlights the practical relevance of the new P-GARCH class of models. Extensions to other periodic ARCH structures, including P-IGARCH and P- EGARCH processes along with possible discrete time periodic representations of stochastic volatility models subject to time deformation, are also discussed, along with issues related to multivariate representations and the possibility of common persistence in the seasonal volatility across multiple time series.

Abstract:
The paper complements the reviews on the stochastic volatility models and option pricing. We discuss recent advances in modeling and estimation techniques which allow to investigate models with latent factors and non-unique risk-neutral probability measures. The issues related to the optimal data utilization and volatility filtering are highlighted. We also discuss some of the future research in this area.

Abstract:
Much of the research describing the cross-sectional and time series behavior of asset returns can be characterized as a search for the relevant state variables and also a search for the relevant model specification. Ultimately the scope of such efforts is to find a satisfactory and stable asset pricing structure. In this paper we discuss various methods to accomplish this and appraise the success of two recently proposed classes of asset pricing models in tracking predictable patterns in risk and return trade-offs. The two classes are the conditional CAPM and the nonlinear APT. The parameters of both models are estimated via a set of moment conditions using the GMM estimator and the model fit is judged on the basis of the overidentifying restrictions. The fundamental problem is that overidentifying restrictions tests are not designed to diagnose whether a model provides a stable relationship between the return series and the risk factors. We use a set of recently developed tests for structural stability of parameter estimates for the GMM estimator to diagnose which factor structures appear stable through time in the context of the two aforementioned classes of models. In the course of trying to sort out whether there is systematic mispricing we also try to determine what type of model looks most promising for further development. In that regard we find the nonlinear APT more satisfactory than the conditional CAPM and APT. The paper covers several empirical examples ranging from international asset pricing to the pricing of size-sorted and industry classified portfolios of stocks listed on the NYSE.

Abstract:
In this paper, we study stochastic volatility models with time deformation. Such processes relate to the early work by Mandelbrot and Taylor (1967), Clark (1973), Tauchen and Pitts (1983), among others. In our setup, the latent process of stochastic volatility evolves in an operational time which differs from calendar time. The time deformation can be determined by past volume of trade, past returns, possibly with an asymmetric leverage effect, and other variables setting the pace of information arrival. The econometric specification exploits the state-space approach for stochastic volatility models proposed by Harvey, Ruiz and Shephard (1994) as well as the matching moment estimation procedure using SNP densities of stock returns and trading volume estimated by Gallant, Rossi and Tauchen (1992). Daily data on returns and trading volume of the NYSE are used in the empirical application. Supporting evidence for a time deformation representation is found and its impact on the behavior of returns and volume is analyzed. We find that increases in volume accelerate operational time, resulting in volatility being less persistent and subject to shocks with a higher innovation variance. Downward price movements have similar effects while upward price movements increase the persistence in volatility and decrease the dispersion of shocks by slowing down market time. We present the basic model as well as several extensions; in particular, we formulate and estimate a bivariate return-volume stochastic volatility model with time deformation. The latter is examined through bivariate impulse response profiles following the example of Gallant, Rossi and Tauchen (1993).

Abstract:
Simulation-based estimation methods have become more widely used in recent years. We propose a set of tests for structural change in models estimates via Simulated Method of Moments (see Duffie and Singleton (1993)). These tests extend the recent work of Andrews (1993) and Sowell (1996a, b) which covered Generalized Method of Moments estimators not involving simulation. We derive the asymptotic distributions of various tests. We show that the number of simulations does not affect the asymptotic distribution nor the asymptotic local power of tests for structural change. A Monte Carlo investigation of the finite sample size and power reveals, however, that simulation uncertainty does affect the properties of tests. Nevertheless, even a relatively small number of simulations suffices to obtain tests with desirable small sample size and power properties.

Abstract:
There is now considerable evidence suggesting that estimated betas of unconditional CAPM models exhibit statistically significant time variation. Therefore, many have advocated the use of conditional CAPM models. If we succeed in capturing the dynamics of beta risk, we are sure to outperform constant beta models. However, if the beta risk is inherently misspecified there is a real possibility that we commit serious pricing errors, potentially larger than with a constant traditional beta model. In this paper we show that this is indeed the case, namely that pricing errors with constant traditional beta models are smaller than with conditional CAPM models.

Abstract:
Subordinated stochastic processes, also called time deformed stochastic processes, have been proposed in a variety of contexts to describe asset price behavior. They are used when the movement of prices is tied to the number of market transactions, trading volume or the more elusive concept of information arrival. The aim of the paper is to present a comprehensive treatment of the stochastic process theory as well as the statistical inference of subordinated processes. Numerous applications in finance are provided to illustrate the use of the processes to model market behavior and asset returns.

Abstract:
In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility.