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...

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Bibliographic Details
Published in:Finance and stochastics 2006-01, Vol.10 (1), p.1-26
Main Authors: Fusai, Gianluca, Abrahams, I. David, Sgarra, Carlo
Format: Article
Language:English
Subjects:
Economic models
Evaluation
Financial economics
Integral equations
Mathematical economics
Monte Carlo simulation
Numerical analysis
Option pricing
Partial differential equations
Securities prices
Stochastic processes
Stock options
Stock prices
Studies
Valuation
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-005-0170-y