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A computational technique borrowed from the physical sciences is introducedto obtain accurate closed-form approximations for the transition probability ofarbitrary diffusion processes. Within the path integral framework the sametechnique allows one to obtain remarkably good approximations of the pricingkernels of financial derivatives. Several examples are presented, and theapplication of these results to increase the efficiency of numerical approachesto derivative pricing is discussed.

THE EXPONENT EXPANSION: AN EFFECTIVE APPROXIMATION OF TRANSITION PROBABILITIES OF DIFFUSION PROCESSES AND PRICING KERNELS OF FINANCIAL DERIVATIVES