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Multivariate Option Pricing With Time Varying Volatility and Correlations

  • Jeroen Rombouts
  • Lars Peter Stentoft

In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes to option pricing. Specifically, we derive the risk neutral dynamics for a general class of multivariate heteroskedastic models, and we provide a feasible way to price options in this framework. Our framework can be used irrespective of the assumed underlying distribution and dynamics, and it nests several important special cases. We provide an application to options on the minimum of two indices. Our results show that not only is correlation important for these options but so is allowing this correlation to be dynamic. Moreover, we show that for the general model exposure to correlation risk carries an important premium, and when this is neglected option prices are estimated with errors. Finally, we show that when neglecting the non-Gaussian features of the data, option prices are also estimated with large errors. Au cours des récentes années, les modèles multivariés utilisés pour évaluer les rendements de l'actif ont suscité beaucoup d'intérêt, plus particulièrement les modèles qui tiennent compte de la volatilité variant dans le temps. Dans le présent document, nous explorons les modèles de cette catégorie et examinons leur potentiel en matière de fixation du prix des options. Plus précisément, nous établissons la dynamique risque neutre pour une catégorie générale de modèles hétéroscédastiques à variables multiples et proposons un moyen réaliste de fixer le prix des options à l'intérieur de cette structure. Notre cadre de référence peut être utilisé sans égard à la distribution et la dynamique sous-jacentes possibles. Il prend également en compte de nombreux cas spéciaux importants. Nous proposons une application aux options selon un minimum de deux indices. Nos résultats révèlent non seulement l'importance de la corrélation en ce qui a trait à ces options, mais aussi l'importance d'une corrélation qui soit dynamique. De plus, nous illustrons, dans le cas du modèle général, que l'exposition au risque de corrélation comporte une prime importante et que, si cet aspect est négligé, l'évaluation du prix des options est alors erronée. Enfin, nous démontrons qu'en faisant peu de cas des caractéristiques non gaussiennes des données, l'évaluation du prix des options comporte des écarts importants.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2010s-23.

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Length: 40 pages
Date of creation: 01 May 2010
Date of revision:
Handle: RePEc:cir:cirwor:2010s-23
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