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 significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial 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 financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.

[1]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[2]  S. Beckers The Constant Elasticity of Variance Model and Its Implications For Option Pricing , 1980 .

[3]  S. Ross SOME STRONGER MEASURES OF RISK AVERSION IN THE SMALL AND THE LARGE WITH APPLICATIONS , 1981 .

[4]  M. Yaari The Dual Theory of Choice under Risk , 1987 .

[5]  A. Röell Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty , 1987 .

[6]  Mark Schroder Computing the Constant Elasticity of Variance Option Pricing Formula , 1989 .

[7]  J. Cox,et al.  Optimal consumption and portfolio policies when asset prices follow a diffusion process , 1989 .

[8]  Shaun S. Wang Premium Calculation by Transforming the Layer Premium Density , 1996, ASTIN Bulletin.

[9]  S. Pliska Introduction to Mathematical Finance: Discrete Time Models , 1997 .

[10]  Ken Seng Tan,et al.  Financial Economics: With Applications to Investments, Insurance and Pensions , 1999, British Actuarial Journal.

[11]  Joanne E. Kennedy,et al.  Financial Derivatives in Theory and Practice , 2000 .

[12]  J. Bohn,et al.  A Survey of Contingent‐Claims Approaches to Risky Debt Valuation , 2000 .

[13]  Shaun S. Wang A CLASS OF DISTORTION OPERATORS FOR PRICING FINANCIAL AND INSURANCE RISKS , 2000 .

[14]  M. Sherris,et al.  A class of non-expected utility risk measures and implications for asset allocations , 2001 .

[15]  Zinoviy Landsman,et al.  Risk measures and insurance premium principles , 2001 .

[16]  M. Sherris,et al.  Martingale Methods in Dynamic Portfolio Allocation with Distortion Operators-Proceedings AFIR 2001-Toronto, Canada , 2001 .

[17]  Shaun S. Wang A Universal Framework for Pricing Financial and Insurance Risks , 2002, ASTIN Bulletin.

[18]  Emiliano A. Valdez,et al.  CAPM and Option Pricing with Elliptical Disbributions , 2004 .