Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
The authors show how effective-potential path-integrals methods, stemming from 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 semianalytical 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 multiyear time horizons. The accuracy and the computational efficiency of the proposed approximation make 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 semianalytical approximations of transition probabilities and Arrow-Debreu prices for nonlinear 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.