Nous examinons un ensemble de diffusions avec volatilité stochastique et de sauts afin de modéliser la distribution des rendements d'actifs boursiers. Puisque certains modèles sont nonemboîtés, nous utilisons la méthode EMM afin d'étudier et de comparer le comportement des différents modèles. This paper evaluates the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions. We use estimation technology that facilitates non-nested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns. We consider two broad families of models: (1) the multifactor loglinear family, and (2) the affine-jump family. Both classes of models have attracted much attention in the derivatives and econometrics literatures. There are various trade-offs in considering such diverse specifications. If pure diffusion SV models are chosen over jump diffusions, it has important implications for hedging strategies. If logaritmic models are chosen over affine ones, it may seriously complicate option pricing. Comparing many different specifications of pure diffusion multi-factor models and jump diffusion models, we find that (1) log linear models have to be extented to 2 factors with feedback in the mean reverting factor, (2) affine models have to have a jumps in r eturns, stochastic volatility and probably both. Models (1) and (2) are observationally equivalent on the data set in hand. In either (1) or (2) the key is that the volatility can move violently. As we obtain models with comparable empirical fit, one must make a choice based on arguments other than statistical goodness of fit criteria. The considerations include facility to price options, to hedge and parsimony. The affine specification with jumps in volatility might therefore be preferred because of the closed-form derivatives prices. * We would like to thank Torben Andersen, the Editor, two anonymous referees and Nour Medahi, the third referee, for comments that substantially improved the paper. We are also grateful to Luca Benzoni, Paul Glasserman, Micheal Johannes, David Robinson, the conference and seminar participants at the CAP Mathematical Finance Workshop, Columbia University, the Conference on Risk Neutral and Objective Probability Distributions, Fuqua School of Business, Duke University, CIRANO and Vanderbilt University for their comments. All remaining errors are our own. This paper subsumes part of the material presented in the working paper titled. "A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation."

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This paper examines model specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a time series test to detect the presence of jumps in volatility, and find strong evidence in support of their presence. Next, using the cross section of option prices, we find strong evidence for jumps in prices and modest evidence for jumps in volatility based on model fit. The evidence points toward economically and statistically significant jump risk premia, which are important for understanding option returns.THERE ARE TWO CENTRAL, RELATED, issues in empirical option pricing. The first issue is model specification, which comprises identifying and modeling the factors that jointly determine returns and option prices. Recent empirical work on index options identifies factors such as stochastic volatility, jumps in prices, and jumps in volatility. The second issue is quantifying the risk premia associated with the jump and diffusive factors using a model that passes reasonable specification hurdles.The results in the literature regarding these issues are mixed. For example, tests using option data disagree over the importance of jumps in prices:

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 cross-sectional 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.

We use equity index options to quantify the probability and magnitude of disasters: extreme negative realizations of consumption growth and stock returns. We show that option prices imply smaller probabilities of these extreme outcomes than have been estimated from international macroeconomic data. A useful byproduct is a novel characterization of departures from lognormality in asset pricing models based on high-order cumulants: skewness, excess kurtosis, and so on. JEL Classification Codes: E44, G12.