FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 50. In a two-step tree each step has u = 1.20 and d = 0.80, and the risk-free rate is 5% per step. What is the value of a European put with strike 52 and two steps to expiry?
The put is worth about 4.25. With p = 0.625, terminal payoffs of 0, 4 and 20 have probabilities 0.390625, 0.46875 and 0.140625. The expected payoff of 4.6875 is discounted over two periods at 5%, giving 4.25.
- A4.69
- B4.25Correct
- C4.46
- D6.35
Explanation
The risk-neutral probability is p = (1.05 - 0.80)/0.40 = 0.625. The terminal prices are 72, 48 and 32, so the put payoffs are 0, 4 and 20. The ud probability is 2(0.625)(0.375) = 0.46875 and the dd probability is 0.140625. The expected payoff is 1.875 + 2.8125 = 4.6875. Discounting by 1.05^2 gives 4.25. Using p = 0.5 instead gives 6.35.
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