General equilibrium and preference free model for pricing options under transformed gamma distribution

Abstract

. Luiz Vitiello is at London Metropolitan Business School, London Metropolitan University. We are grateful to Michael Brennan, Richard Stapleton and Konstantinos Vonatsos for valuable insights. We would like to thank the seminar participants at Singapore Management University for helpful comments.

The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy

“…The gamma distribution may be particularly useful for pricing agricultural commodities, as it captures the increasing implied volatility of contingent claims as a function of the strike price (see Zhou (1998), Vitiello and Poon (2010)). Thus one could price an option on a basket of agricultural commodities using the framework developed here, which also allows the impact of a systematic variable on option prices to be considered.…”

“…It is interesting to note that, as in the univariate gamma models of Heston (1993) and Vitiello and Poon (2010), the preference parameter has a direct impact on the scale parameter. This contrasts, for instance, with the multivariate (transformed) normal economies of Stapleton and Subrahmanyam (1984) and Camara (2005), in which the preference parameter impacts on the location parameter only.…”

“…While the idiosyncratic terms are, of course, independent of each other, the systematic term has a direct impact on all underlying stochastic variables and on their correlation structure. As our framework is developed in a multivariate setting, it extends previous contingent claim pricing models which are based on only one gamma distributed underlying stochastic variable (see for instance Heston (1993), Schroder (2004, Vitiello and Poon (2010)). …”

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

“…The framework developed here could help the pricing of contingent claims on such situations, for instance. 4 Also, it could also be useful for pricing multivariate commodity options, as it can capture the increasing implied volatility pattern of such assets (see Vitiello and Poon, 2010;Zhou, 1998). Thus one could price an option written several agricultural commodities, such as crush spread options.…”

Asset Pricing under Information with Stochastic Volatility

“…Other authors (e.g. Câmara, 2003;Schroder, 2004;Vitiello and Poon, 2006) recently also extended their approaches to alternative distributions and utility functions, where they focus on preferences and distributions which yield risk neutral valuation relationships, i.e. pricing formulas without any preference parameter.…”