City Research Online

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.

Publication Type:	Article
Additional Information:	This is the accepted version of the following article: Green, R., Fusai, G. and Abrahams, I. D. (2010), THE WIENER–HOPF TECHNIQUE AND DISCRETELY MONITORED PATH-DEPENDENT OPTION PRICING. Mathematical Finance, 20: 259–288., which has been published in final form at http://dx.doi.org/10.1111/j.1467-9965.2010.00397.x
Publisher Keywords:	Barrier, Discrete monitoring, Double-barrier, First-touch, Hindsight, Option pricing, Padé approximants, Wiener-Hopf technique
Subjects:	H Social Sciences > HG Finance Q Science > QA Mathematics
Departments:	Bayes Business School > Finance
SWORD Depositor:	Symplectic Administrator

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