A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models

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A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models

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René Garcia
Éric Renault ()

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René Garcia

Abstract

Recently, Duan (1995) proposed a GARCH option pricing formula and a corresponding hedging formula. In a similar ARCH-type model for the underlying asset, Kallsen and Taqqu (1994) arrive at a hedging formula different from Duan's , although they concur on the pricing formula. In this note, we explain the difference by pointing out that the formula developped by Kallsen and Taqqu corresponds to the usual concept of hedging in the context of ARCH-type models. We argue however that Duan's formula has some appeal and propose a stochastic volatility model which ensures its validity. We conclude by a comparison of ARCH-type and stochastic volatility option pricing models.

Duan (1995) a proposé récemment une formule de valorisation d'option fondée sur un modèle GARCH ainsi que la formule de couverture correspondante. Dans un modèle similaire de type ARCH pour l'actif sous-jacent conduisant à la même formule de valorisation, Kallsen et Taqqu (1994) arrivent à une formule de couverture différente. Dans cette note, nous expliquons cette différence en soulignant que la formule de Kallsen et Taqqu correspond au concept usuel de couverture dans le cadre des modèles de type ARCH. Nous trouvons toutefois que la formule de couverture de Duan a un certain attrait et proposons un modèle de volatilité stochastique qui en assure la validité. Nous concluons par une comparaison des modèles ARCH et de volatilité stochastique pour la valorisation d'options.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 97s-13.

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Date of creation: 01 Apr 1997
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Handle: RePEc:cir:cirwor:97s-13

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G1 - Financial Economics - - General Financial Markets

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Marcel Boyer, 1997. "Competition and Access in Telecoms: ECPR, Global Price Cap, and Auctions," CIRANO Working Papers 97s-03, CIRANO. [Downloadable!]

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