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The Econometrics of Option Pricing

Author

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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.

Suggested Citation

  • René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
  • Handle: RePEc:cir:cirwor:2004s-04
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    Cited by:

    1. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 407-458, Fall.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    3. Rubio Irigoyen, Gonzalo & Ferreira García, María Eva & Gago, Mónica & León, Angel, 2002. "An empirical comparison of the performance of alternative option pricing models," DFAEII Working Papers 2002-04, University of the Basque Country - Department of Foundations of Economic Analysis II.
    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Papers 2005-W16, Economics Group, Nuffield College, University of Oxford.
    5. Ming Yuan, 2009. "State price density estimation via nonparametric mixtures," Papers 0910.1430, arXiv.org.
    6. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    7. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    8. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, EconWPA.
    9. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    10. Sílvia Gonçalves & Massimo Guidolin, 2006. "Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1591-1636, May.
    11. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
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    13. Vázquez, Miguel & Sánchez-Úbeda, Eugenio F. & Berzosa, Ana & Barquín, Julián, 2008. "Short-term evolution of forward curves and volatility in illiquid power market," MPRA Paper 8932, University Library of Munich, Germany, revised May 2008.
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    15. Cyrus Ramezani & Yong Zeng, 2007. "Maximum likelihood estimation of the double exponential jump-diffusion process," Annals of Finance, Springer, vol. 3(4), pages 487-507, October.
    16. repec:ebl:ecbull:v:30:y:2010:i:1:p:182-191 is not listed on IDEAS
    17. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2005. "State Dependence in Fundamentals and Preferences Explains Risk-Aversion Puzzle," Staff Working Papers 05-9, Bank of Canada.
    18. Thomas Busch, 2008. "Testing the martingale restriction for option implied densities," Review of Derivatives Research, Springer, vol. 11(1), pages 61-81, March.

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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;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

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