The wiener-hopf technique and discretely monitored path-dependent option pricing

Green, R., Fusai, G. & Abrahams, I. D. (2010). The wiener-hopf technique and discretely monitored path-dependent option pricing. Mathematical Finance, 20(2), pp. 259-288. doi: 10.1111/j.1467-9965.2010.00397.x

[img]
Preview
PDF - Accepted Version
Download (241kB) | Preview

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.

Item 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
Uncontrolled 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
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/5994

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics