Bayesian Risk Measures for Derivatives via Random Esscher Transform

Tak Kuen Siu, Howell Tong and Hailiang Yang

North American Actuarial Journal, 2001, vol. 5, issue 3, 78-91

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.

Date: 2001
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DOI: 10.1080/10920277.2001.10596000

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