A path-integral approximation for non-linear diffusions

Abstract

Using the path-integral formalism we develop an accurate and easy-to-compute semi-analytical approximation to transition probabilities and Arrow–Debreu densities for arbitrary diffusions. We illustrate the accuracy of the method by presenting results for the Black–Karasinski model for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility and for multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of applications, ranging from maximum-likelihood estimation in econometrics to derivatives pricing.