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113
Closedform likelihood expansions for multivariate diffusions
, 2008
"... This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial ..."
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Cited by 109 (3 self)
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This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.
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
Convergence of numerical methods for stochastic differential equations in mathematical finance
, 1204
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Optimal filtering of jump diffusions: extracting latent states from asset prices
, 2007
"... This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing mo ..."
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Cited by 44 (8 self)
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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines timediscretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jumpdiffusion models with nonlinear characteristics and even nonanalytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns.
The price of correlation risk: Evidence from equity options
 Journal of Finance, 64(3):1377
"... We study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exp ..."
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Cited by 38 (5 self)
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We study whether exposure to marketwide correlation shocks affects expected option returns, using data on S&P100 index options, options on all components, and stock returns. We find evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the crosssection of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limitstoarbitrage interpretation of our finding of a high price of correlation risk. CORRELATIONS PLAY A CENTRAL ROLE in financial markets. There is considerable evidence that correlations between asset returns change over time1 and that stock return correlations increase when returns are low.2 A marketwide increase in correlations negatively affects investor welfare by lowering diversification benefits and by increasing market volatility, so that states of nature with unusually high correlations may be expensive. It is therefore natural to ask whether marketwide correlation risk is priced in the sense that assets that pay off well when marketwide correlations are higher than expected (thereby providing a ∗Driessen is at the University of Amsterdam. Maenhout and Vilkov are at INSEAD. We would
Estimation of objective and riskneutral distributions based on moments of integrated volatility
 Journal of Econometrics
, 2011
"... Abstract In this paper, we present an estimation procedure which uses both option prices and highfrequency spot price feeds to estimate jointly the objective and riskneutral parameters of stochastic volatility models. This procedure is based on series expansions of option prices and implied volat ..."
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Cited by 19 (2 self)
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Abstract In this paper, we present an estimation procedure which uses both option prices and highfrequency spot price feeds to estimate jointly the objective and riskneutral parameters of stochastic volatility models. This procedure is based on series expansions of option prices and implied volatilities and on a methodofmoment estimation that uses analytical expressions for the moments of the integrated volatility. This results in an easily implementable and rapid estimation technique.
OptionImplied Correlations and the Price of Correlation Risk, Working paper
, 2012
"... Motivated by extensive evidence that stockreturn correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing optionimplied correlations between stock returns (obtained by com ..."
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Cited by 18 (0 self)
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Motivated by extensive evidence that stockreturn correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. We propose a direct and intuitive test by comparing optionimplied correlations between stock returns (obtained by combining index option prices with prices of options on all index components) with realized correlations. Our parsimonious model shows that the substantial gap between average implied (38% for S&P500 and 44% for DJ30) and realized correlations (31% and 34%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that optionimplied correlations have remarkable predictive power for future stock market returns.
Jump and Volatility Risk Premiums Implied by VIX
"... An estimation method is developed for extracting the latent stochastic volatility from VIX, a volatility index for the S&P 500 index return produced by the Chicago Board Options Exchange (CBOE) using the socalled modelfree volatility construction. Our model specification encompasses all meanr ..."
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Cited by 16 (0 self)
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An estimation method is developed for extracting the latent stochastic volatility from VIX, a volatility index for the S&P 500 index return produced by the Chicago Board Options Exchange (CBOE) using the socalled modelfree volatility construction. Our model specification encompasses all meanreverting stochastic volatility option pricing models with a constantelasticity of variance and those allowing for price jumps under stochastic volatility. Our approach is made possible by linking the latent volatility to the VIX index via a new theoretical relationship under the riskneutral measure. Because option prices are not directly used in estimation, we can avoid the computational burden associated with option valuation for stochastic volatility/jump option pricing models. Our empirical findings are: (1) incorporating a jump risk factor is critically important; (2) the jump and volatility risks are priced; and (3) the popular squareroot stochastic volatility process is a poor model specification irrespective of allowing for price jumps or not.
Supplement to “High frequency market microstructure noise estimates and liquidity measures.” DOI: 10.1214/08AOAS200SUPP
, 2009
"... Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise ..."
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Cited by 15 (0 self)
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Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liquidity. We find that more liquid stocks based on financial characteristics have lower noise and noisetosignal ratio measured from their high frequency returns. We then examine whether there exists a common, marketwide, factor in high frequency stocklevel measurements of noise, and whether that factor is priced in asset returns. 1. Introduction. Understanding
Estimation of dynamic models with nonparametric simulated maximum likelihood
, 2007
"... We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observa ..."
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Cited by 15 (7 self)
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We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observations, we estimate the unknown density of the model nonparametrically by kernel methods, and then obtain the SMLEs of the model parameters. Our method avoids the issue of nonidentification arising from poor choice of auxiliary models in simulated methods of moments (SMM) or indirect inference. More importantly, our SMLEs achieve higher efficiency under weak regularity conditions. Finally, our method allows for potentially nonstationary processes, including timeinhomogeneous dynamics.