Premium
CAPM and Option Pricing With Elliptically Contoured Distributions
Author(s) -
Hamada Mahmoud,
Valdez Emiliano A.
Publication year - 2008
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/j.1539-6975.2008.00265.x
Subject(s) - capital asset pricing model , class (philosophy) , econometrics , multivariate normal distribution , valuation of options , economics , financial economics , mathematical economics , multivariate statistics , mathematics , computer science , statistics , artificial intelligence
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.