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

摘要

Purpose - The purpose of this paper is to present an arbitrarily accurate approximation for the valuernof European options written on a Black-Scholes stock paying a discrete dividend.rnDesign/methodology/approach - The proposed method is a computational method for thernanalytical solution of the problem.rnFindings - It was found that the proposed method is computationally faster than any other exactrncomputational available method, including Monte-Carlo simulations.rnResearch limitations/implications - The method is applied for a single dividend payment, butrncan be extended for several payments. The exact amount of the dividend must be known ex-ante, asrnwell as the precise date of payment.rnPractical implications - The paper provides the most efficient way to compute with absoluternprecision the value of European options on dividend-paying assets, under the Black-Scholesrnassumption.rnOriginality/value - The computing time in the approach is several orders of magnitude faster thanrnwith traditional Monte Carlo methods, for the same desired accuracy.