The Path Integral Approach to Financial Modeling and Options Pricing

Vadim Linetsky

Computational Economics, 1998, vol. 11, issue 1-2, 129-63

Abstract: In this paper we review some applications of the path integral methodology of quantum mechanics to financial modeling and options pricing. A path integral is defined as a limit of the sequence of finite-dimensional integrals, in much the same way as the Riemannian integral is defined as a limit of the sequence of finite sums. The risk-neutral valuation formula for path-dependent options contingent upon multiple underlying assets admits an elegant representation in terms of path integrals (Feynman-Kac formula). The path integral representation of transition probability density (Green's function) explicitly satisfies the diffusion PDE. Gaussian path integrals admit a closed-form solution given by the Van Vleck formula. Analytical approximations are obtained by means of the semiclassical (moments) expansion. Difficult path integrals are computed by numerical procedures, such as Monte Carlo simulation or deterministic discretization schemes. Several examples of path-dependent options are treated to illustrate the theory (weighted Asian options, floating barrier options, and barrier options with ladder-like barriers). Citation Copyright 1998 by Kluwer Academic Publishers.

Date: 1998
References: Add references at CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://journals.kluweronline.com/issn/0927-7099/contents (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:11:y:1998:i:1-2:p:129-63

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().