PT - JOURNAL ARTICLE
AU - Capriotti, Luca
AU - Vaia, Ruggero
TI - Physics and Derivatives: <em>Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities</em>
AID - 10.3905/jod.2020.1.107
DP - 2020 Apr 28
TA - The Journal of Derivatives
PG - jod.2020.1.107
4099 - http://jod.pm-research.com/content/early/2020/04/28/jod.2020.1.107.short
4100 - http://jod.pm-research.com/content/early/2020/04/28/jod.2020.1.107.full
AB - 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 swapsKey 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.