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Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : New version February 2002) / Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : Nouvelle version Février 2002)

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  • René Garcia
  • Richard Luger
  • Éric Renault

    ()

Abstract

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility alone as in the Hull-White case. When we specialize this model to an equilibrium recursive utility model, we show through simulations that option prices are more informative than stock prices about the structural parameters of the model. We also show that a simple method of moments with a panel of option prices provides good estimates of the parameters of the model. This lays the ground for an empirical assessment of this equilibrium model with S&P 500 option prices in terms of pricing errors. On évalue dans cet article la performance empirique d'un modèle dynamique d'évaluation d'options qui fournit une formule de prix fondée sur des processus latents de variables d'état. Cette formule est une généralisation de la formule dite de Hull et White (1987) qui évalue une option européenne écrite sur un actif à volatilité stochastique. On propose dans un premier temps de fonder sur cette formule une procédure empirique ad hoc permettant l'évaluation d'une option à partir du calcul de deux paramètres implicites extraits sur les prix d'options observés la veille. Appliquée à la prévision des prix d'options sur l'indice S&P 500, cette procédure offre un gain de précision significatif par rapport à la pratique usuelle de prévision des prix à travers une volatilité implicite conformément à ce que suggère la formule de Hull et White. Dans un second temps, on propose de particulariser le modèle dans un contexte d'équilibre intertemporel avec utilité récursive. On fournit alors des résultats d'expériences de Monte Carlo montrant que les statistiques de prix d'options produisent des estimateurs des paramètres structurels de l'équilibre beaucoup plus précis que les données de prix de l'actif sous-jacent. Ceci suggère en retour que les paramètres structurels devraient jouer un rôle important dans l'évaluation d'options. Cette affirmation est validée empiriquement sur les données d'options sur l'indice S&P 500 en montrant que la formule de Hull et White est dominée, en termes de prévision des prix d'options hors-échantillon par une formule dépendant explicitement de paramètres de préférence, a fortiori si ceux-ci prennent en compte de façon non contrainte à la fois l'aversion pour le risque et l'élasticité de substitution intertemporelle.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-02.

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Date of creation: 01 Jan 2001
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Handle: RePEc:cir:cirwor:2001s-02

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Keywords: Option pricing; stochastic discount factor; stochastic volatility; Black-Scholes implied volatility; smile effect; equilibrium option pricing; Évaluation d'options; facteur d'actualisation stochastique; volatilité stochastique; volatilité implicite de Black-Scholes; effet de sourire; modèle d'équilibre d'évaluation d'options;

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References

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