Stocks Paying Discrete Dividends

Abstract

In the Black–Scholes model, any dividends on stocks are paid continuously, but in reality dividends are always paid discretely, often after some announcement of the amount of the dividend. It is not entirely clear how such discrete dividends are to be handled; simple perturbations of the Black–Scholes model often fall into contradictions. The authors' approach here is to recognize the stock price as the net present value of all future dividends, and to model the (discrete) dividend process directly. The stock price process is then deduced and various option–pricing formulae derived. The Black–Scholes model with continuous dividend payments results as a limit as the time between dividend payments goes to zero.