The binomial model has proved to be an efficient technique for approximating the value of an option on a zero-dividend or fixed-yield-dividend stock. With some small modifications, this model can also be used to approximate the value of an option on a stock that pays fixed-cash dividends. If one assumes ex-dividend stock prices to be lognormally distributed, stock price can be partitioned into two parts—a riskless part representing the present value of all dividends to be paid over the option’s life and a risky part representing the remaining net assets of the firm. The stock price net of the present value of the escrowed dividends is used as the starting point of the binomial process. Then, a small number of formulas are used recursively to compute option prices at all nodes.
It may be more realistic, however, to assume lognormal cum-dividend prices with known but uncertain dividends. Dividends, which are not escrowed, may not be paid in full if the value of the firm falls far enough. In this case, one can construct the binomial tree ignoring dividends and interpolating option prices at ex-dividend dates.
Previously, solutions to the fixed-cash-dividend problem could be obtained only by using a cumbersome and computationally expensive version of the binomial model, or by using more complicated finite-difference techniques. The proposed binomial models offer good results from much less complex computations. Furthermore, the binomial models cost little more (and in some cases cost even less) than the fixed-yield-dividend binomial model.
