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CAPM and Option Pricing with Elliptical Disbributions

Mahmoud Hamada and Emiliano Valdez ()

No 120, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper, we offer an alternative proof of the Capital Asset Pricing Model when the returns follow a multivariate elliptical distribution. Empirical studies continue to demonstrate the inappropriateness of the normality assumption in modelling asset returns. The class of elliptical distributions,which includes the more familiar Normal distribution, provides flexibility in modelling the thickness of tails associated with the possibility that asset returns take extreme values with non-negligible probabilities. Within this framework, we prove a new version of Stein's lemma for elliptical distribution and use this result to derive the CAPM when returns are elliptical. We also derive a closed form solution of call option prices when the underlying is elliptically distributed. We use the probability distortion function approach based on the dual utility theory of choice under uncertainty.

Pages: 33 pages
Date: 2004-02-01
New Economics Papers: this item is included in nep-fin and nep-fmk
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Published as: Hamada, M. and Valdez, E. A., 2008, "CAPM and Option Pricing with Elliptically Contoured Distributions", Journal of Risk and Insurance, 75, 387–409.

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