A Path-Integral Approximation for Non-Linear Diffusions

7 Pages Posted: 18 Nov 2018

See all articles by Luca Capriotti

Luca Capriotti

University College London; NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Date Written: October 27, 2018

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 applications, ranging from maximum-likelihood estimation in econometrics to derivatives pricing.

Keywords: Path integrals; Stochastic processes; Maximum-likelihood estimation; Arrow-Debreu pricing; Zero-coupon bonds; Derivative pricing; Black-Karasinski model

Suggested Citation

Capriotti, Luca, A Path-Integral Approximation for Non-Linear Diffusions (October 27, 2018). Available at SSRN: https://ssrn.com/abstract=3274004 or http://dx.doi.org/10.2139/ssrn.3274004

Luca Capriotti (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

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