We formally incorporate parameter uncertainty and model error in the estimation of contingent claim models and the formulation of forecasts. This allows an inference on any function of interest (option values, bias functions, hedge ratios) consistent with the uncertainty in both parameters and models. We show how to recover the exact posterior distributions of the parameters or any function of interest. It is crucial to obtain exact posterior or predictive densities because the most likely implementation, a frequent updating setup, results in small samples and requires the incorporation of specific prior information. We develop Markov Chain Monte Carlo estimators to solve the estimation problem posed. We provide both within sample and predictive model specification tests which can be used in dynamic testing or trading systems, making use of both the cross-sectional and time series information in the options data. Finally, we generalize the error distribution by allowing for the (small) probability that an observation has a larger error. For each observation, this produces the probability of its being an outlier, and may help distinguish market from model error. We apply these new techniques to equity options. When model error is taken into account, the black-Scholes appears very robust, in contrast with previous studies which at best only incorporated parameter uncertainty. We then extend the base model, e.g., Black-Scholes, by polynomial functions of parameters. This allows for intuitive specification tests. The Black-Scholes in-sample error properties can be improved by the use of these simple extended models but this does not result in major improvements in out of sample predictions. The differences between these models may be important however because, as we document it, they produce different functions of economic interest such as hedge ratios, probability of mispricing. Nous incorporons formellement l'incertitude des parametres et l'erreur de modele dans l'estimation des modeles d'option et la formulation de previsions. Ceci permet l'inference de fonctions d'interet (prix de l'option, biais, ratios) coherentes avec l'incertitude des parametres et du modele. Nous montrons comment extraire la distribution posterieure exacte (de fonctions) des parametres. Ceci est crucial parce que l'utilisation la plus probable, reestimation periodique des parametres, est analogues a des echantillons de petite taille et demande l'incorporation d'informations a priori specifiques. Nous developpons des modeles Monte Carlo de chaines markoviennes afin de resoudre les problemes d'estimation poses. Nous fournissons des tests de specification, a la fois pour l'echantillon et le modele predictif, qui peuvent etre utilises pour les tests dynamiques et les systemes de trading en utilisant l'information en coupe transversale et temporelle des donnees d'option. Finalement, nous generalisons la distribution d'erreurs en tenant compte de la (faible) probabilite qu'une observation ait une plus grande probabilite d'erreur. Cela fournit pour chaque observation la probabilite d'une donnee aberrante et peut aider a differencier erreur de modele et erreur de marche. Nous appliquons ces nouvelles techniques aux options d'equite. Quand l'erreur de modele est prise en consideration, le Black-Scholes apparait tres robuste, en contraste avec les etudes precedentes qui, au mieux, incluait l'erreur de parametre. Apres, nous etendons le modele de base, i.e. Black-Schles, par des fonctions polynomiales des parametres. Cela permet des tests intuitifs de specification. Les erreurs en echantillon du B-S sont ameliorees par l'utilisation de ces simples modeles etendus,0501s cela n'apporte pas d'amelioration majeure dans les predictions hors-echantillon. Quoi qu'il en soit, les differences entre ces modeles peuvent etre importantes parcequ'elles produisent differentes fonctions d'interet telles que les ratios et la probabilite d'erreur d'evaluation.
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