19. The payment of a dividend on the underlying stock increases the value of a put option since it "lowers" the stock price distribution at maturity. This question provides a numerical illustration.
Let a two-period binomial tree be given with the following parameters: S = 100, u = 1.10, d = 0.90, and R = 1.05. Consider a two-period American put option with a strike of 90. Note that this put is quite deep out-of-the-money at inception.
(a) What is the value of the American put given these parameters?
(b) Now suppose a dividend of $4 is paid at the end of the first period. What is the new price of the put?
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