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159
The CrossSection of Volatility and Expected Returns
 Journal of Finance
, 2006
"... We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF. ..."
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Cited by 267 (9 self)
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We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF.
The Impact of Jumps in Volatility and Returns
 Journal of Finance
, 2002
"... This paper examines a class of continuoustime models with stochastic volatility that incorporate jumps in returns and volatility. We develop a likelihoodbased es timation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using S&P 500 and Nasdaq ..."
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Cited by 245 (12 self)
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This paper examines a class of continuoustime models with stochastic volatility that incorporate jumps in returns and volatility. We develop a likelihoodbased es timation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998.
An empirical investigation of continuoustime equity return models
 Journal of Finance
, 2002
"... This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of timevarying intensity. We find that any reasonably descriptive continuoustime model for equityindex returns must allow for discrete jumps as well as stochastic volatility with a pronou ..."
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Cited by 240 (12 self)
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This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of timevarying intensity. We find that any reasonably descriptive continuoustime model for equityindex returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equityindex returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuoustime representations for asset returns
Separating microstructure noise from volatility
, 2006
"... There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moment ..."
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Cited by 130 (9 self)
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There are two variance components embedded in the returns constructed using high frequency asset prices: the timevarying variance of the unobservable efficient returns that would prevail in a frictionless economy and the variance of the equally unobservable microstructure noise. Using sample moments of high frequency return data recorded at different frequencies, we provide a simple and robust technique to identify both variance components. In the context of a volatilitytiming trading strategy, we show that careful (optimal) separation of the two volatility components of the observed stock returns yields substantial utility gains.
Maximum likelihood estimation for stochastic volatility models
 JOURNAL OF FINANCIAL ECONOMICS
, 2007
"... We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure ..."
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Cited by 113 (3 self)
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We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated atthemoney option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
Model specification and risk premia: Evidence from futures options
 Journal of Finance
, 2007
"... This paper examines specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a test to detect the presence of jumps in volatility, and find strong evidence supporting their presence. Based on the crosssectional fit of ..."
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Cited by 94 (7 self)
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This paper examines specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a test to detect the presence of jumps in volatility, and find strong evidence supporting their presence. Based on the crosssectional fit of option prices, we find strong evidence for jumps in prices and modest evidence for jumps in volatility. We are not able to identify a statistically significant diffusive volatility risk premium. We do find modest but statistically and economically significant jump risk premia.
Variance risk premiums
 Review of Financial Studies 000
, 2008
"... We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the riskneutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the di ..."
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Cited by 91 (7 self)
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We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the riskneutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13) It has been well documented that return variance is stochastic. When investing in a security, an investor faces at least two sources of uncertainty, namely the uncertainty about the return as captured by the return variance, and the uncertainty about the return variance itself. It is important to know how investors deal with the uncertainty in return variance to effectively manage risk and allocate assets, to accurately price and hedge derivative securities, and to understand the behavior of financial asset prices in general. We develop a direct and robust method for quantifying the return variance
CAPM Over the LongRun: 19262001
, 2003
"... The CAPM can account for the spread in the average returns of portfolios sorted by booktomarket ratios over the longrun from 19262001. In contrast, other studies document strong evidence of a booktomarket effect using post1963 data, but they do so by relying on asymptotic standard errors. We ..."
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Cited by 66 (6 self)
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The CAPM can account for the spread in the average returns of portfolios sorted by booktomarket ratios over the longrun from 19262001. In contrast, other studies document strong evidence of a booktomarket effect using post1963 data, but they do so by relying on asymptotic standard errors. We show that making inferences that rely on asymptotic distributions is misleading. Using robust small sample inference, we fail to find a statistically significant booktomarket effect. The differences between the small sample and the asymptotic distributions can be attributed mostly to persistent timevarying betas. Rather than incorporating additional risk factors to explain these portfolio returns, our results suggest using a conditional CAPM with
Option Valuation with LongRun and ShortRun Volatility
 Components.” Journal of Financial Economics,
, 2008
"... Abstract This paper presents a new model for the valuation of European options. In our model, the volatility of returns consists of two components. One of these components is a longrun component, and it can be modeled as fully persistent. The other component is shortrun and has a zero mean. Our m ..."
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Cited by 53 (4 self)
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Abstract This paper presents a new model for the valuation of European options. In our model, the volatility of returns consists of two components. One of these components is a longrun component, and it can be modeled as fully persistent. The other component is shortrun and has a zero mean. Our model can be viewed as an affine version of that in Engle and Lee (1999) allowing for easy valuation of European options. We investigate the model empirically integrating returns and options data. The performance of the model is spectacular when compared to a benchmark singlecomponent volatility model that is wellestablished in the literature. The improvement in the model's performance is due to its richer dynamics which enable it to jointly model longmaturity and shortmaturity options. JEL Classification: G12
MCMC methods for continuoustime financial econometrics

, 2003
"... This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for explor ..."
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Cited by 41 (1 self)
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This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuoustime asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these highdimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the CliffordHammersley theorem, the Gibbs sampler, the MetropolisHastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuoustime asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regimeswitching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.