Bayesian Risk Measures for Derivatives via Random Esscher Transform |
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Authors: | Tak Kuen Siu PhD Howell Tong FIA PhD Hailiang Yang ASA PhD |
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Institution: | Department of Statistics and Actuarial Science , University of Hong Kong , Pokfulam Road , Hong Kong |
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Abstract: | 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. |
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