An exact analytical solution for discrete barrier options

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. Key words: Barrier options, discrete monitoring, Wiener-Hopf equation, BlackScholes, z-transform JEL Classification: G13, C63

• Type: Journal
• Year: 2006
• Where: FS
• Authors: Gianluca Fusai, I. David Abrahams, Carlo Sgarra
• Keywords: Barrier Options, Discrete Barrier Options, FS 2006, Wiener-Hopf Equation