The Exponent Expansion: An Effective Approximation of Transition Probabilities of Diffusion Processes and Pricing Kernels of Financial Derivatives

Details The Exponent Expansion: An Effective Approximation of Transition Probabilities of Diffusion Processes and Pricing Kernels of Financial Derivatives The Exponent Expansion: An Effective Approximation of Transition Probabilities of Diffusion Processes and Pricing Kernels of Financial Derivatives

2006-02-15

arxiv.org/abs/physics/0602107v1

International Journal of Theoretical and Applied Finance, Vol. 9, No. 7 (2006) 1179-1199

Physics

Physics and Society

21 pages, 5 figures, to appear in the International Journal of Theoretical and Applied Finance

Scientific paper

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of financial derivatives. Several examples are presented, and the application of these results to increase the efficiency of numerical approaches to derivative pricing is discussed.

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