[Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources: realized volatilities, S& P500 returns, and an extensive panel of option data. The three sources of data all point to the same conclusion: the best volatility specification is one with linear rather than square root diffusion for variance. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared error in and out of sample.]

[We provide results for the valuation of European-style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state space setup using the no-arbitrage principle and an equivalent martingale measure (EMM). Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional nonnormal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of EMMs for which the resulting risk-neutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a time-varying price of risk and nonnormal innovations. We provide extensions of these results to more general EMMs and to discrete-time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous-time models.]

Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources: realized volatilities, S&P500 returns, and an extensive panel of option data. The three sources of data all point to the same conclusion: the best volatility specification is one with linear rather than square root diffusion for variance. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, andit has the lowest option implied volatility mean squared error in and out of sample.

Nous prsentons les rsultats d'une tude portant sur l'valuation de crances ventuelles de style europen pour une grande varit de caractristiques lies au rendement des actifs sousjacents. Les rsultats de notre valuation proposent en temps discret une formule tat-espace infinie, partir du principe de non-arbitrage et d'une mesure de martingale quivalente. Notre approche permet de tenir compte de formes gnrales d'htroscdasticit dans les rendements et d'obtenir, dans des cas spciaux, des rsultats d'valuation lis aux processus homoscdastiques. Elle permet aussi de considrer les innovations conditionnellement non normales en matire de rendement, ce qui reprsente un facteur critique, compte tenu du fait que l'htroscdasticit ne permet pas, elle seule, de saisir pleinement le caractre ironique de l'option. Nous analysons une catgorie de mesures de martingale quivalentes dont la dynamique du rendement risque-neutre obtenu est de la mme famille de distribution que la dynamique du rendement physique. Dans ce cas, notre cadre d'tude soutient les rsultats d'valuation obtenus par Nous tendons ces rsultats aux mesures de martingale quivalentes plus gnrales et aux modles de volatilit stochastique en temps discret et analysons aussi la relation entre nos rsultats et ceux obtenus dans le cas des modles en temps continu.