Path Integral and Asset Pricing

Quantitative Finance 15(11) (2015) 1759-1771, Featured Article

30 Pages Posted: 7 Oct 2014 Last revised: 11 Aug 2016

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Date Written: February 20, 2015

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.

Keywords: Path integral, asset pricing, short-rate models, Vasicek model, Hull-White model, Black-Karasinski model, pricing function, stochastic differential equation, quantum mechanics, perturbation theory, Feynman diagrams

JEL Classification: G00

Suggested Citation

Kakushadze, Zura, Path Integral and Asset Pricing (February 20, 2015). Quantitative Finance 15(11) (2015) 1759-1771, Featured Article. Available at SSRN: https://ssrn.com/abstract=2506430 or http://dx.doi.org/10.2139/ssrn.2506430

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

1127 High Ridge Road #135
Stamford, CT 06905
United States
6462210440 (Phone)
6467923264 (Fax)

HOME PAGE: http://www.linkedin.com/in/zurakakushadze

Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159
Georgia

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