A European option on a stock with known dollar dividend is valued by setting the stock price variable equal to the stock price minus the present value of the dividend in the Black-Scholes-Merton formula. A second price can be obtained using the tree building procedure in the chapter. Which of the following is true when a very large number of time steps are used in the tree?
A) The first price is higher than the second price
B) The first price is lower than the second price
C) The first price is sometimes higher and sometimes lower than the second price
D) The two prices are almost exactly the same

Question

Quizplus · Accepted Answer

When a very large number of time steps are used in the tree, the tree model will converge to the Black-Scholes-Merton model, which means the two prices will become very close to each other. Therefore, the correct choice is D, where the two prices are almost exactly the same.

A European Option on a Stock with Known Dollar Dividend