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

Author(s):

João Amaro de Matos (Faculdade de Economia, Universidade Nova de Lisboa, Lisbon, Portugal)

Rui Dilão (Nonlinear Dynamics Group, Instituto Superior Técnico, Lisbon, Portugal)

Bruno Ferreira (Nonlinear Dynamics Group, Instituto Superior Técnico, Lisbon, Portugal)

Acknowledgements:

The authors would like to thank Faisal Al‐Sharji for the careful test of the results presented here. This work has been partially supported by Fundac˜ao para a Ciˆencia e a Tecnologia (Portugal), under a pluriannual funding grant.

Abstract:

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.

Keywords:

Europe, Dividends, Assets, Accuracy

Type:

Research paper

Publisher:

Emerald Group Publishing Limited

Copyright:

© Emerald Group Publishing Limited 2009
Published by Emerald Group Publishing Limited

Citation:

João Amaro de Matos, Rui Dilão, Bruno Ferreira, (2009) "On the value of European options on a stock paying a discrete dividend", Journal of Modelling in Management, Vol. 4 Issue: 3, pp.235-248, https://doi.org/10.1108/17465660911006468

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