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CAPM and Option Pricing With Elliptically Contoured Distributions

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  • Mahmoud Hamada
  • Emiliano A. Valdez

Abstract

This article offers an alternative proof of the capital asset pricing model (CAPM) when asset returns follow a multivariate elliptical distribution. Empirical studies continue to demonstrate the inappropriateness of the normality assumption for modeling asset returns. The class of elliptically contoured distributions, which includes the more familiar Normal distribution, provides flexibility in modeling the thickness of tails associated with the possibility that asset returns take extreme values with nonnegligible probabilities. As summarized in this article, this class preserves several properties of the Normal distribution. Within this framework, we prove a new version of Stein's lemma for this class of distributions and use this result to derive the CAPM when returns are elliptical. Furthermore, using the probability distortion function approach based on the dual utility theory of choice under uncertainty, we also derive an explicit form solution to call option prices when the underlying is log-elliptically distributed. The Black-Scholes call option price is a special case of this general result when the underlying is log-normally distributed. Copyright (c) The Journal of Risk and Insurance, 2008.

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Bibliographic Info

Article provided by The American Risk and Insurance Association in its journal Journal of Risk & Insurance.

Volume (Year): 75 (2008)
Issue (Month): 2 ()
Pages: 387-409

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Handle: RePEc:bla:jrinsu:v:75:y:2008:i:2:p:387-409

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Cited by:
  1. Lundtofte, Frederik & Wilhelmsson, Anders, 2011. "Idiosyncratic Risk and Higher-Order Cumulants," Working Papers 2011:33, Lund University, Department of Economics.
  2. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
  3. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Analytical solution for the constrained Hansen-Jagannathan distance under multivariate ellipticity," Working Paper 2012-18, Federal Reserve Bank of Atlanta.
  4. Francisco Blasques, 2013. "Stationarity and Ergodicity Regions for Score Driven Dynamic Correlation Model," Tinbergen Institute Discussion Papers 13-097/IV, Tinbergen Institute.

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