Path Integral and Asset Pricing

TL;DR

This paper introduces the use of Euclidean path integrals in asset pricing, demonstrating their application to short-rate models and providing explicit formulas and techniques for more complex models like Black-Karasinski.

Contribution

It presents a pragmatic approach to applying path integral methods in asset pricing, including explicit formulas and perturbative techniques for complex interest rate models.

Findings

Explicit formulas for bond pricing in short-rate models

Application of quantum mechanical semiclassical approximation

Outline of perturbative techniques using Feynman diagrams

Abstract

We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the Black-Karasinski model. We give explicit formulas for computing the bond pricing function in such models in the analog of quantum mechanical "semiclassical" approximation. We also outline how to apply perturbative quantum mechanical techniques beyond the "semiclassical" approximation, which are facilitated by Feynman diagrams.