@article {Capriottijod.2020.1.107, author = {Luca Capriotti and Ruggero Vaia}, title = {Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities}, elocation-id = {jod.2020.1.107}, year = {2020}, doi = {10.3905/jod.2020.1.107}, publisher = {Institutional Investor Journals Umbrella}, 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 swapsKey Findings{\textbullet} The connection between Feynman{\textquoteright}s path-integrals and the formalism of derivatives pricing provides powerful computational tools for financial applications.{\textbullet} An {\textquoteleft}effective potential{\textquoteright} 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.{\textbullet} 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.}, issn = {1074-1240}, URL = {https://jod.pm-research.com/content/early/2020/04/25/jod.2020.1.107}, eprint = {https://jod.pm-research.com/content/early/2020/04/25/jod.2020.1.107.full.pdf}, journal = {The Journal of Derivatives} }