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