The Wiener–Hopf Technique and Discretely Monitored Path-Dependent Option Pricing

30 Pages Posted: 29 Mar 2010

See all articles by Ross Green

Ross Green

affiliation not provided to SSRN

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Sir John Cass Business School - City, University of London

I. David Abrahams

affiliation not provided to SSRN

Date Written: 2008-06

Abstract

Fusai, Abrahams, and Sgarra (2006) employed the Wiener–Hopf technique to obtain an exact analytic expression for discretely monitored barrier option prices as the solution to the Black–Scholes partial differential equation. The present work reformulates this in the language of random walks and extends it to price a variety of other discretely monitored path-dependent options. Analytic arguments familiar in the applied mathematics literature are used to obtain fluctuation identities. This includes casting the famous identities of Baxter and Spitzer in a form convenient to price barrier, first-touch, and hindsight options. Analyzing random walks killed by two absorbing barriers with a modified Wiener–Hopf technique yields a novel formula for double-barrier option prices. Continuum limits and continuity correction approximations are considered. Numerically, efficient results are obtained by implementing Padé approximation. A Gaussian Black–Scholes framework is used as a simple model to exemplify the techniques, but the analysis applies to Lévy processes generally.

Suggested Citation

Green, Ross and Fusai, Gianluca and Abrahams, I. David, The Wiener–Hopf Technique and Discretely Monitored Path-Dependent Option Pricing (2008-06). Mathematical Finance, Vol. 20, Issue 2, pp. 259-288, April 2010. Available at SSRN: https://ssrn.com/abstract=1578537 or http://dx.doi.org/10.1111/j.1467-9965.2010.00397.x

Ross Green (Contact Author)

affiliation not provided to SSRN

No Address Available

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Sir John Cass Business School - City, University of London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

I. David Abrahams

affiliation not provided to SSRN

No Address Available

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