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Abstract:
This paper undertakes a simulation study to investigate (a) the performance of alternative hedging strategies against various derivatives risks and (b) the impact of model misspecification on hedging performance. The hedging strategies considered in this paper include the single-instrument hedge, the delta-neutral hedge, and the ad hoc Black-Scholes delta-vega-(rho)-neutral hedge, while the risk factors of the derivatives include the underlying asset return risk, stochastic volatility risk, stochastic interest rate risk, and random jump or market crash risk. In addition, we investigate the performance of the delta-neutral hedge with the use of potentially traded volatility derivatives. Our simulation results provide guidance for how a risk factor can be hedged based on certain hedging strategies and evidence of how severe model risk can be when hedging strategies are based on misspecified models.

Derivatives Risks, Model Risk, Hedging Strategies, Hedging Performance, Simulation Study

Abstract:
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic
volatility can reduce the pricing errors and allowing for asymmetric volatility or "leverage effect" does help to explain the skewness of the volatility "smile", allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, an SV model with fatter-tailed noise or jump component may have better explanatory power.

Swaps, default risk

Abstract:
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model?s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or "leverage effect" does help to explain the skewness of the volatility "smile", allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, an SV model with fatter-tailed noise or jump component may have better explanatory power.

Swaps, default risk

Abstract:
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model?s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or "leverage effect" does help to explain the skewness of the volatility "smile", allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino & Turnbull (1990), our empirical findings strongly suggest the existence of a non zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficient in modeling short-term kurtosis of asset returns, an SV model with fatter-tailed noise or jump component may have better explanatory power.

Stochastic Volatility, Efficient Method of Moments (EMM), Reprojection, Option Pricing.

Abstract:
The Chicago Board Options Exchange (CBOE) recently redesigned its widely followed VIX volatility index. While the new VIX is conceptually more appealing than its predecessor, the CBOE's implementation of the index is flawed. Using option prices simulated under typical market conditions, we show that the CBOE procedure may underestimate the true volatility by as much as 198 index basis points or overestimate it by as much as 79 index basis points. As each index basis point is worth $10 per VIX futures contract, these errors are economically significant. More importantly, these errors exhibit predictable patterns in relations to volatility levels. We propose a simple solution to fix the problems, based on a smooth interpolation-extrapolation of the implied volatility function. This alternative method is accurate and robust across a wide range of model specifications and market conditions.

volatility index, VIX, investor fear gauge, volatility smile, fair value of future variance, model-free implied volatility

Abstract:
Previous research find insignificant or even negative market timing ability for mutual funds using tests based on realized fund returns. The return-based tests, however, are subject to "articial timing" bias due to the dynamic trading effect and option-like features of stock returns. In this paper, we propose new measures of market timing based on mutual fund holdings. Our holdings-based measures do not suffer from the artificial timing bias and are statistically more powerful. Applying the holdings-based tests, we find that, on average, actively managed US domestic equity funds have positive timing ability. Market timing funds tend to have high industry concentration, large fund size, and a tilt toward small-cap stocks. We also provide evidence that mutual funds use more than public information to predict market returns and industry rotation is key to mutual fund market timing strategy.

market timing, mutual fund

Abstract:
This paper uses adverse selection in corporate information disclosure to explain a recently documented asset pricing anomaly. Ang, Hodrick, Xing, and Zhang (2006a) show that stocks with high idiosyncratic return volatilities tend to have low future returns. In this paper, we find that idiosyncratic volatility is also inversely related to future earning shocks. More importantly, we show that the return predictive power of idiosyncratic volatility is induced by its information content on future earnings. We provide empirical results to support our explanation that firms with poor prospect of future earnings tend to disclose less information, resulting in a higher degree of heterogeneity in investors beliefs, which in turn leads to higher stock return volatility and trading volume. Further analysis suggests that investors tend to underreact to earnings information in idiosyncratic volatility, and the mispricing of idiosyncratic volatility is inversely related to both investor sophistication and stock liquidity.

Idiosyncratic Volatility, Corporate Disclosure

Abstract:
This paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps. Formally, the test follows by a direct application of Ito's lemma to the semi-Martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments. Intuitively, the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps. Simulations show that the jump test has nice properties and is generally more powerful than the widely used bi-power variation test. An important feature of our test is that it can be applied - in analytically modified form - to noisy high frequency data and still retains power. As a by-product of our analysis, we obtain novel analytical results regarding the impact of noise on bi-power variation. An empirical illustration using IBM trade data is also included.

swap variance, jumps, bi-power variation, market microstructure noise

Abstract:
In rational asset pricing models, predictable returns associated with firm characteristics are driven by risk premium; on the other hand, the surprise component of returns should be uncorrelated with em ex ante firm characteristics. We quantify large information shocks using stock price jumps and then resort to the distinction between jumps and risk premium to evaluate risk-based explanations of stock return predictability. Based on the CRSP data from 1927 to 2005, we find that several well-known patterns of return predictability, including the size effect, the liquidity premium, and to a certain extent the value premium, are driven by cross-sectional differences in stock price jumps. The evidence presents a challenge to theories attributing such predictability to a simple risk premium effect. We further explore several alternative rational hypotheses based on jump risk premium, discontinuity in expected returns, and the martingale restriction on jumps. However, none of them provides satisfactory reconciliation with the data.

Jumps, Stock Return Predictability, Risk Premium

Abstract:
This paper proposes a new approach to exploit the information in high frequency data for the statistical inference of continuous-time affine jump diffusion (AJD) models with latent variables. For this purpose, we construct unbiased estimators of the latent variables and their power functions based on the observed state variables over extended horizons. With the estimates of the latent variables, we propose a GMM procedure for the estimation of AJD models with the distinguishing feature that moments of both observed and latent state variables can be used without resorting to path simulation or discretization of the continuous-time process. Using high frequency return observations of the S&P 500 index, we implement our estimation approach to various continuous-time asset return models with stochastic volatility and random jumps.

affine jump diffusion, latent state variables, unbiased minimum-variance estimator, generalized method of moments, high frequency data

Abstract:
To comply with the new Financial Accounting Standards Board's requirement for expensing stock options, U.S. firms must calculate the fair value of stock options granted to its employees and deduct it from its reported earnings. Opponents to the FASB requirement argue that the fair value of stock options is difficult to estimate and, in particular, stock return volatility cannot be reliably estimated. In this paper, we investigate the effectiveness of various volatility estimation methods in forecasting stock return volatility for the purpose of expensing stock options. In particular, we propose a new volatility forecasting method that is based on the long-memory (LM) properties of stock returns and the comovement of stock returns with the market portfolio and other common factors (VAR). The LM-VAR forecasting method provides a unified framework for incorporating volatility persistence and comovement as well as a more effective implementation of the shrinkage forecast. Using a large sample of large-, medium- and small-size U.S. firms, we show that our LM-VAR approach is more accurate than existing forecasting methods and is a reliable method for forecasting long-term stock return volatility. Relative to the benchmark forecasting method used in prior research, our approach consistently improves the forecasting accuracy under all scenarios tested and generally reduce the errors in calculated option values by half. Our results provide empirical support for the feasibility of accounting for and expensing stock options.

volatility forecasting, option expensing, option valuation, long memory, vector autoregression, shrinkage forecast

Abstract:
In this paper, we propose a unifying class of affine-quadratic term structure models (AQTSMs) in the general jump-diffusion framework. Extending existing term structure models, the AQTSMs incorporate random jumps of stochastic intensity in the short rate process. Using information from the Treasury futures market, we propose a GMM approach for the estimation of the risk-neutral process. A distinguishing feature of the approach is that the time series estimates of stochastic volatility and jump intensity are obtained, together with model parameter estimates. Our empirical results suggest that stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a stochastic jump intensity process that is negatively correlated with interest rate changes. Overall, negative jumps tend to have a larger size than positive ones. Our empirical results also suggest that, at monthly frequency, while stochastic volatility has certain predictive power of inflation, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with informational shocks in the financial market.

Term Structure, Affine, Quadratic, Jumps, GMM

Abstract:
Chapman and Pearson (2000) document that the nonparametric drift function estimator proposed by Stanton (1997) for the short rate diffusion can produce spurious nonlinearities due to the persistent dependence of interest rate data and limited sampling period. In this paper, we propose a nonparametric estimator of the short rate diffusion that can greatly reduce the bias of the Stanton estimator. The proposed estimator uses a panel of yields with different maturities instead of a single time series of short rate observations. It is implemented in two steps. In the first step, we pool all the yields together and obtain a nonparametric "pooled" estimator of the drift function. Ideally, if the drift functions of interest rates with different maturities were identical, then the optimal estimator of the short rate drift function would simply pool the data of all the yields. In practice, while the drift functions of interest rates with different maturities may be similar in functional shape, they are unlikely to be identical. Therefore in the second step, we correct the bias of the pooled estimator using a nonparametric correction factor. The advantage of the two-step procedure is that when the pooled estimator of the drift function is similar to the drift function of the short rate in functional shape, the correction factor is a smooth function and much easier to estimate nonparametrically. Our simulations confirm that the proposed method significantly attenuates the spurious nonlinearities of the Stanton drift function estimator. We estimate the US short rate diffusion process using a panel of six Treasury yields with maturities ranging from 3 months to 10 years, and show that the proposed method has both significant economic implications and substantial efficiency gain. With observations of the panel of yields over the past 50 years, the new drift function estimator has the same efficiency as the Stanton estimator implemented with 145 years of daily short rate observations.

drift function, nonparametric estimation, panel of yields

Abstract:
The paper analyzes the real options under jump diffusion processes with diversifiable jump and non-diversifiable jump in either positive or negative direction. We find that the total variance of asset return on the investment decision is not monotone when there is jump, not like that without jump. In addition, the diversifiable jump tends to increase the threshold value, while, the non-diversifiable, negative jump may decrease the threshold value. Therefore, the traditional views that jump decrease the threshold value under the framework of real options (McDonald and Siegel, 1986; Dixit and Pindyck, 1994; Boyarchenko, 2004) can not be extended to the general situations. We give the conditions whether the compound Poisson jump alters the threshold value relative to that in the continuous cases. Finally, we test the existence of jump, direction and diversifiability of jump for two financial-type assets and two non-financial-type assets. The null hypothesis of diversifiable jump can not be rejected in most cases.

Real Options, Jump Diffusion Processes

Abstract:
Recent literature documents that analyst recommendations tend to coincide with important corporate events, but offers mixed evidence on whether such recommendations have added value. In this paper, we use jump in stock price as a proxy for generic corporate “information event” and examine market reactions to recommendation revisions made around such events. Consistent with the literature, we find that analysts revise their recommendations more frequently on days with jumps in stock prices. Although such contemporaneous revisions account for only 10% of the sample, they explain up to a half (a third) of the initial market reactions for downgrades (upgrades). Nevertheless, when focusing on revisions made after stock price jumps - which are less likely influenced by confounding corporate events - we still find that these revisions contain significant price information. The added value is most pronounced for upgrades following positive jumps, with an extra 4.5% average return above those not following jumps over a 6-month horizon.

Analyst Recommendations, Information Processing Ability, Stock Price Jumps, Corporate Event, Market Reactions

Abstract:
This article proposes stochastic conditional duration (SCD) models with "leverage effect" for financial transaction data, which extends both the autoregressive conditional duration (ACD) model (Engle and Russell, 1998, Econometrica, 66, 1127-1162) and the existing SCD model (Bauwens and Veredas, 2004, Journal of Econometrics, 119, 381-412). The proposed models belong to a class of linear nongaussian state-space models, where the observation equation for the duration process takes an additive form of a latent process and a noise term. The latent process is driven by an autoregressive component to characterize the transition property and a term associated with the observed duration. The inclusion of such a term allows the model to capture the asymmetric behavior or "leverage effect" of the expected duration. The Monte Carlo maximum-likelihood (MCML) method is employed for consistent and efficient parameter estimation with applications to the transaction data of IBM and other stocks. Our analysis suggests that trade intensity is correlated with stock return volatility and modeling the duration process with "leverage effect" can enhance the forecasting performance of intraday volatility.

autoregressive conditional duration (ACD) model, ergodicity, financial transaction data, leverage effect, Monte Carlo maximum-likelihood (MCML) estimation, stationarity, stochastic conditional duration (SCD) model

Abstract:
In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous-time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk-neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk-neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk-neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long-term options, random jump tends to price the short-term options better, and option pricing based on multiple risk-neutral distributions significantly outperforms that based on a single risk-neutral distribution.

Abstract:
Illiquid common stock is worth less than stock that can be readily sold because the investor incurs an opportunity cost by being locked into the investment. Quantifying the amount of this illiquidity discount is an important issue in valuing certain common stock, especially for estate valuations. We examine whether a previously developed analytical model for valuing the lost "option to sell" when a stock is illiquid is a useful, practical tool for valuing illiquid common stock.

Equity Investments, Fundamental Analysis and Valuation Models, Alternative Investments, Other

Abstract:
This article proposes a new approach to exploit the information in high-frequency data for the statistical inference of continuous-time affine jump diffusion (AJD) models with latent variables. For this purpose, we construct unbiased estimators of the latent variables and their power functions on the basis of the observed state variables over extended horizons. With the estimates of the latent variables, we propose a generalized method of moments (GMM) procedure for the estimation of AJD models with the distinguishing feature that moments of both observed and latent state variables can be used without resorting to path simulation or discretization of the continuous-time process. Using high frequency return observations of the S&P 500 index, we implement our estimation approach to various continuous-time asset return models with stochastic volatility and random jumps.

affine jump diffusion, generalized method of moments, high-frequency data, latent state variables, unbiased minimum-variance estimator