Contingent Claim Pricing using Probability Distortion Operators: Methods from Insurance Risk Pricing and their Relationship to Financial Theory¤

This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and signi...cance because of the increased integration of insurance and ...nancial markets and also because insurance related risks are trading in ...nancial markets as a result of securitisation and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in ...nancial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on ...nancial theory. The theory underlying the approaches is set out and limitations on the use of the insurance based approach are illustrated. We extend the probability distortion approach to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.