CAPM and Option Pricing with Elliptical Disbributions
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.
|Date of creation:||01 Feb 2004|
|Publication status:||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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- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(01), pages 71-92, May.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
- Landsman, Zinoviy, 2002. "Credibility theory: a new view from the theory of second order optimal statistics," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 351-362, June.
- Mahmoud Hamada & Michael Sherris, 2003. "Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 19-47.
- N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.