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

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.

The proposed method is a computational method for the analytical solution of the problem.

It was found that the proposed method is computationally faster than any other exact computational available method, including Monte‐Carlo simulations.

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.

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.

The computing time in the approach is several orders of magnitude faster than with traditional Monte Carlo methods, for the same desired accuracy.