FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 100. In a two-step binomial tree each step is one year, with u = 1.10 and d = 0.90. The risk-free rate is 5% per year, compounded annually. What is the value of a two-year European call option with strike 100?
The call is worth about 10.71. Only the up-up node (121) pays 21, with risk-neutral probability 0.75 squared, or 0.5625. The expected payoff of 11.8125 is discounted two periods at 5%, giving 10.71.
- A10.71Correct
- B11.81
- C11.25
- D4.76
Explanation
The risk-neutral probability is p = (1.05 - 0.90)/0.20 = 0.75. The only in-the-money terminal node is uu, where S = 121 and the payoff is 21. Its probability is 0.5625, so the expected payoff is 11.8125. Discounting over two steps gives 11.8125/1.1025 = 10.71. Failing to discount gives 11.81, and discounting only once gives 11.25.
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