Bayesian risk measures for derivatives via random Esscher transform

Abstract

This paper proposes a model for measuring risks for derivatives that is easy to implement and satisfies a set of four coherent properties introduced in Artzner et al. (1999). We construct our model within the context of Gerber-Shiu’s option-pricing framework. A new concept, namely Bayesian Esscher scenarios, which extends the concept of generalized scenarios, is introduced via a random Esscher transform. Our risk measure involves the use of the risk-neutral Bayesian Esscher scenario for pricing and a family of real-world Bayesian Esscher scenarios for risk measurement. Closed-form expressions for our risk measure can be obtained in some special cases.