Copula Measures and Option-Pricing Models

(Jointly with Hemantha Herath and Amin Amershi)

Copulas C(u,v) are joint probability distribution functions on IxI, with u and v in the unit interval I:[0,1]. Since Sklar (1959), a large statistical literature on copulas has developed (see e.g. surveys by Nelsen (1995, 1999), Fisher(1997), Schweizer (1991)). Numerous recent "real-world" applications are in actuarial sciences (Frees and Valdez (1995)); option pricing (Cherubini, Luciano and Vecchiato (2004)); real options (Herath, Kumar and Amershi (2005)), risk analysis (Clemen and Reilly (1999)). A parallel, active literature, starting from Strassen's (1965) seminal paper, has emerged in the mainstream probability literature(see, e.g, Dudley (2002)). Strassen employed Markov Kernels(MK) that are a dominant theme in Bayesian Decision Theory and the associated Blackwell (1951)- Le Cam(1964) Theory of Informativeness of Experiments(see e.g. Torgerson (1991) and Shirayev and Spokiny(2001), Amershi (1988, 2005)). Our research program aims at the explorative survey of possible interrelationships among the three literatures, investigation of features related to applications and the theory and design of real financial options with a more powerful unified theory.

[7] Herath, Hemantha S. B. and P. Kumar.,“On Simple Binomial Approximation for Pricing Options,” Advances in Investment Analysis and Portfolio Management, “forthcoming”. ( pdf )

[6] Herath, H. S. B. and Kumar, P.. “Multinomial Approximation Models for Options”, Advances in Investment Analysis and Portfolio Management (New Series). Volume 2, 2005 (To appear). ( pdf )

[5] Herath, Hemantha S. B. and P. Kumar, “The Jackknife Estimator for Estimating the Volatility of Volatility of a Stock,” Corporate Finance Review, Volume 7, No. 3, Nov/Dec, 2002, pp. 13-21. (pdf)

[4] Herath, Hemantha S. B., P. Kumar, and C. Park, “Real Options: Further Results for a Two State Variable Approximation Model,” Proceedings of Industrial Engineering Research Conference, Portland, Oregon, May 18-21,2003.

[3] Herath, H.S.B. and Kumar, P.. “On Simple Binomial Approximations for Options”, Pacific BasinFinance Economics and Accounting Conference, Thailand, August, 2004.

[2] Herath, H.S.B., Kumar, P. and Park, C.. “Real Options: Further Results for a Two State VariableApproximation Model”, Industrial Engineering Research Conference, Portland, Oregon, May, 2003.

[1] Herath Hemantha S. B. and Pranesh Kumar, “External Audit Requirements of Banking Systems around the World,” 10th Pacific Basin Finance, Economics and Accounting (PBFEA) Annual Conference, Singapore, August 7 – 8, 2002. ( pdf )