A Note on the Pricing of Contingent Claims with a Mixture of Distributions in a Discrete-Time General Equilibrium Framework

This paper presents a framework for the pricing of contingent claims based on the assumption that the underlying asset has a mixture of transformed normal distributions. Speci...cally, the framework presented (i) can deliver risk neutral contingent claim pricing formulae, (ii) widens the set of distributions used in the mixture by assuming that the terminal price of the underlying security has a mixture of transformed-normal distributions, which contains the normal and lognormal distributions as special cases, and (iii) does not require the components of the mixture to have the same density as long as they belong to the family of transformed-normal distributions. An interesting aspect of mixtures of distributions, and in particular of the framework developed here, is that the actual and the risk neutral distributions may not have the same shape, which can lead to a non-monotonic pricing kernel.