General equilibrium and risk neutral framework for option pricing with a mixture of distributions

This article develops a closed form risk-neutral valuation model for pricing European style options when the underlying has a mixture of transformed-normal distributions. Specifically, we introduce the mixture of g distributions which contains the mixture of normal and lognormal distributions as a special case. The risk neutral valuation relation is developed following Rubinstein [1976]; Brennan [1979] and Camara [2003] and is consistent with the framework of Heston [1993b] and Schroder [2004]. Our model encompasses several well known models and is particularly useful for pricing derivatives written on illiquid assets and derivatives that are themselves illiquid.