The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

Vitiello, Luiz and Rebelo, Ivonia (2011) The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy. Centre for EMEA Banking, Finance and Economics Working Paper Series, 2011 (21). pp. 1-24.

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Abstract

In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions, leading to preference-free contingent claim pricing equations. Multivariate contingent claim pricing models are of particular interest when payoffs depend on two or more stochastic variables, such as options to exchange one asset for another, options on mutual funds, and options with a stochastic strike price in general. In our model each underlying stochastic variable depends on a systematic gamma distributed term and on an idiosyncratic one, where the former has a direct impact on the correlation structure of the underlying variables. To illustrate the applicability of our framework, we present multivariate gamma distributed versions of well-known multivariate normally/lognormally distributed contingent claim pricing formulae. The gamma distribution is particularly suitable to price stochastic variables that present implied volatilities that are an increasing function of the strike price.

Item Type: Article
Uncontrolled Keywords: Centre for EMEA Banking, Finance and Economics Working Paper Series, Multivariate Gamma Distribution, Risk Neutral Valuation Relationship, Multivariate Contingent Claim, Stochastic Strike Price, General Equilibrium.
Subjects: 300 Social sciences > 330 Economics
Department: Guildhall School of Business and Law
Depositing User: David Pester
Date Deposited: 21 Apr 2015 09:08
Last Modified: 21 Apr 2015 09:08
URI: http://repository.londonmet.ac.uk/id/eprint/441

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