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

The gamma class of distributions encompasses several important distributions, either as special or limiting cases or through simple transformations. Here we derived closed form and preference free European option pricing formulae for various (transformed) gamma distributions under the general equilibrium RNVR framework. The gamma class of distributions is used historically in hydrology for modelling natural events. Our models can be used to price derivatives associated with these natural phenomena, which will help to encourage greater risk sharing through financial securitization. Our pricing formulae are theoretically sound even if the underlyings and the derivative instruments are not (frequently) traded.