An exact analytical solution for discrete barrier options

Fusai, Gianluca and Abrahams, David and Sgarra, Carlo (2006) An exact analytical solution for discrete barrier options. Finance and Stochastics, 10 (1). pp. 1-26. ISSN 1432-1122

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Abstract

In the present paper we provide an analytical solution for pricing discrete barrier options in the Black-Scholes framework.We reduce the valuation problem to a Wiener-Hopf equation that can be solved analytically. We are able to give explicit expressions for the Greeks of the contract. The results from our formulae are compared with those from other numerical methods available in the literature. Very good agreement is obtained, although evaluation using the present method is substantially quicker than the alternative methods presented.

Item Type: Article
Uncontrolled Keywords: Barrier options, discrete monitoring, Wiener-Hopf equation, Black- Scholes, z-transform
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus
MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 03 Jan 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/683

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