Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities

Abstract

The authors show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities and Arrow-Debreu densities for arbitrary diffusions. The authors illustrate the accuracy of the method by presenting results for the Black-Karasinski and the GARCH linear models, 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 derivatives pricing applications.

TOPICS: Derivatives, options, credit default swaps

Key Findings

• • The connection between Feynman’s path-integrals and the formalism of derivatives pricing provides powerful computational tools for financial applications.

• • An ‘effective potential’ path-integral formalism of quantum statistical mechanics, employed over the years for the study of a number quantum systems, can be employed to develop semi-analytical approximations of transition probabilities and Arrow-Debreu prices for non-linear diffusion.

• • The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of derivatives pricing applications.