FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at 100 on a two-step binomial tree. Each step has u = 1.10 and d = 0.90, and the gross risk-free return per step is 1.02. What is the value of a European call with a strike of 100 expiring after two steps?
The call is worth about 7.27. The risk-neutral up probability is 0.60. Only the double-up node, at 121, gives a payoff of 21, with probability 0.36. The expected payoff of 7.56 is discounted over two periods at 1.02 per period, giving 7.27.
- A7.27Correct
- B7.41
- C5.05
- D12.11
Explanation
p = (1.02 - 0.90)/0.20 = 0.60. The terminal prices are 121, 99 and 81, so only the uu node pays off, with a payoff of 21. Its probability is 0.36, so the value is 0.36 × 21/1.02² = 7.56/1.0404 = 7.27. Discounting only once gives 7.41, which is wrong.
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