FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 100 and can move to 125 or 75 over one year. The risk-free rate is 10% per year with annual compounding. What is the value of a one-year American put option with strike 110 in a one-step binomial tree?
The American put is worth 10.00. Holding it as a European option is worth only 9.55, from 0.30 × 35 / 1.10. Immediate exercise pays 110 - 100 = 10, which is larger, so early exercise is optimal and the value is the greater of the two.
- A10.00Correct
- B9.55
- C22.27
- D12.73
Explanation
The risk-neutral up probability is p = (1.10 - 0.75)/0.50 = 0.70, so the down probability is 0.30. The put pays 35 in the down state and 0 in the up state. The continuation value is 0.30 × 35 / 1.10 = 9.55. Immediate exercise today gives 110 - 100 = 10, which is higher, so the American put is worth 10.00. The 9.55 option is the European value, and 12.73 uses a down probability of 0.40.
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