Efficient Option Pricing on Stocks Paying Discrete or Path-Dependent Dividends with the Stair Tree

Pricing options on a stock that pays discrete dividends has not been satisfactorily settled because of the conflicting demands of computational tractability and realistic modeling of the stock price process. Many papers assume that the stock price minus the present value of future dividends or the stock price plus the forward value of future div-idends follows a lognormal diffusion process; however, these assumptions might produce unreasonable prices for some exotic options and American options. It is more realistic to assume that the stock price decreases by the amount of the dividend payout at the ex-dividend date and follows a lognormal diffusion process between adjacent ex-dividend dates, but analytical pricing formulas and efficient numerical methods are hard to de-velop. This paper introduces a new tree, the stair tree, that faithfully implements the aforementioned dividend model without approximations. The stair tree uses extra nodes only when it needs to simulate the price jumps due to dividend payouts and return to a more economical, simple structure at all other times. Thus it is simple to construct, easy to understand, and efficient. Numerous numerical calculations confirm the stair tree’