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The Econometrics of Option Pricing

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  • René Garcia
  • Eric Ghysels

    ()

  • Éric Renault

    ()

Abstract

In this survey, we review econometric models for conducting statistical inference on option price data. We limit our review to European options on a stock index as well as to statistical methods which have been specifically developped for options. Emphasis is put on the synthesis of the various models used in the literature. We start with discrete-time models based on the unifying principle of stochastic discount factor. We cover multinomial trees as well as risk neutral valuation in a conditionally log-normal setting. Extensions to mixtures of log-normals lead to stochastic volatility models, including models with leverage effect. We characterize implications of such models for volatility smiles and show that they are fully similar to the ones derived from continuous-time stochastic volatility models. We then review usual continuous-time models, in particular affine jump-diffusion models or models with several nonlinear factors, as well as extensions with Levy processes or long memory in volatility. We analyze in this context implicit state methods, both parametric (maximum likelihood) and semiparametric (method of moments). We conclude with a review of nonparametric methods which are used to extract pricing probability measures: canonical, implied binomial trees, and seminonparametric approaches (kernels, neural networks and splines). Extraction of preferences based on these measures are also discussed. Dans ce survol, nous passons en revue les modèles économétriques adaptés à l'inférence statistique sur données de prix d'options. Nous nous limitons aux options de type européen sur un indice de marché d'actions. Seules sont explicitées les techniques d'inférence statistique qui ont connu des développements spécifiques pour les données de prix d'options. L'accent est mis sur la modélisation. On commence par une synthèse des modèles en temps discret à partir du principe unificateur de facteur d'actualisation stochastique. Ceci nous permet de couvrir tant les modèles d'arbres multinomiaux que la valorisation risque neutre dans un contexte de log-normalité conditionnelle. L'extension aux mélanges de lois log-normales conduit aux modèles de volatilité stochastique, y compris les modèles avec effet de levier. Nos caractérisons les implications en termes de sourire de volatilité et montrons qu'elles sont pleinement similaires à celles d'un modèle de volatilité stochastique en temps continu. Nous passons ensuite aux modèles usuels en temps continu, notamment les modèles de diffusion avec sauts ou avec plusieurs facteurs non-linéaires, ainsi que les extensions avec processus de Lévy ou mémoire longue dans la volatilité. Nous abordons dans ce contexte les méthodes avec états implicites, à la fois paramétriques (maximum de vraisemblance) ou semiparamétriques (méthode des moments). Enfin, nous passons en revue les méthodes nonparamétriques qui permettent d'extraire directement les mesures de probabilité d'évaluation : canoniques, arbres binomiaux impliqués et approches semi-nonparamétriques (noyaux, réseaux de neurones et splines). Les implications en termes d'extraction des préférences sont aussi discutées.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-04.

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Date of creation: 01 Jan 2004
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Handle: RePEc:cir:cirwor:2004s-04

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Keywords: Stock PriceDynamics; Multivariate Jump-DiffusionModels; Latent variables; Stochastic Volatility; Objective and Risk Neutral Distributions; Nonparametric Option Pricing; Discretetime Option Pricing Models; Risk Neutral Valuation; Preference-free Option Pricing; Dynamique des prix d'actions; modèles de diffusion-sauts à plusieurs variables; variables latentes; volatilité stochastique; distributions objective et risque neutre; modèles nonparamétriques d'évaluation des options; modèles d'évaluation des options en temps discret; évaluation risque neutre; évaluation des options sans paramètres de préférence;

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