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. 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.