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

## TL;DR

This paper introduces an effective-potential path-integral method, inspired by physics, to accurately approximate transition probabilities and Arrow-Debreu densities for diffusions, offering a computationally efficient alternative for derivatives pricing.

## Contribution

The paper develops a semi-analytical approximation method based on path-integral techniques for diffusions, demonstrating high accuracy and efficiency in derivatives pricing.

## Key findings

- Accurately approximates transition probabilities for complex models.
- Performs well even in high volatility regimes.
- Offers a computationally efficient alternative to numerical schemes.

## Abstract

We 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. We 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.