A Note on the Pricing of Multivariate Contingent Claims Under a Transformed-Gamma Distribution

18 Pages Posted: 28 Dec 2014

See all articles by Luiz Vitiello

Luiz Vitiello

University of Essex - Essex Business School

Ivonia Rebelo

London Metropolitan Business School

Date Written: December 27, 2014

Abstract

We develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy based on a multivariate transformed-gamma distribution. In our model, each transformed-gamma distributed underlying asset depends on two terms: a idiosyncratic term and a systematic term, where the latter is the same for all underlying assets and has a direct impact on their correlation structure. Given our distributional assumptions and the existence of a representative agent with a standard utility function, we apply equilibrium arguments and provide sufficient conditions for obtaining preference-free contingent claim pricing equations. We illustrate the applicability of our framework by providing examples of preference-free contingent claim pricing models. Multivariate pricing models are of particular interest when payoffs depend on two or more underlying assets, such as crack and crush spread options, options to exchange one asset for another, and options with a stochastic strike price in general.

Keywords: Multivariate Transformed-Gamma Distribution, Risk Neutral Valuation Relationship, Multivariate Contingent Claim, Stochastic Strike Price, General Equilibrium

JEL Classification: G13

Suggested Citation

Vitiello, Luiz and Rebelo, Ivonia, A Note on the Pricing of Multivariate Contingent Claims Under a Transformed-Gamma Distribution (December 27, 2014). Available at SSRN: https://ssrn.com/abstract=2543180 or http://dx.doi.org/10.2139/ssrn.2543180

Luiz Vitiello (Contact Author)

University of Essex - Essex Business School ( email )

Wivenhoe Park
Colchester, CO4 3SQ
United Kingdom

Ivonia Rebelo

London Metropolitan Business School ( email )

London Metropolitan University
Holloway Road 271-280
LONDON, London N7 8HN
United Kingdom

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