On the value of European options on a stock paying a discrete dividend

Purpose - The purpose of this paper is to present an arbitrarily accurate approximation for the value of European options written on a Black-Scholes stock paying a discrete dividend.Design methodology approach - The proposed method is a computational method for the analytical solution of the problem...

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Bibliographic Details
Published in:Journal of modelling in management 2009-10, Vol.4 (3), p.235-248
Main Authors: Amaro de Matos, João, Dilão, Rui, Ferreira, Bruno
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Assets
Brownian motion
Dividends
Europe
Monte Carlo simulation
Partial differential equations
Present value
Put & call options
Securities markets
Stochastic models
Stock options
Studies
Volatility
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Summary:Purpose - The purpose of this paper is to present an arbitrarily accurate approximation for the value of European options written on a Black-Scholes stock paying a discrete dividend.Design methodology approach - The proposed method is a computational method for the analytical solution of the problem.Findings - It was found that the proposed method is computationally faster than any other exact computational available method, including Monte-Carlo simulations.Research limitations implications - The method is applied for a single dividend payment, but can be extended for several payments. The exact amount of the dividend must be known ex-ante, as well as the precise date of payment.Practical implications - The paper provides the most efficient way to compute with absolute precision the value of European options on dividend-paying assets, under the Black-Scholes assumption.Originality value - The computing time in the approach is several orders of magnitude faster than with traditional Monte Carlo methods, for the same desired accuracy.
ISSN:1746-5664
1746-5672
DOI:10.1108/17465660911006468