FRM Part I · FRM Exam Part I · Binomial Trees
A stock is priced at 80 and will move to either 100 or 60 over one period. The gross risk-free return is 1.05, and the real-world probability of an up move is 0.70. What is the value of a European put with a strike of 90?
The put is worth about 11.43. The risk-neutral up probability is 0.60, so the down probability is 0.40. The expected payoff is 0.40 times 30, or 12, and discounting at 1.05 gives 11.43. The real-world probability of 0.70 plays no role in the price.
- A11.43Correct
- B17.14
- C12.00
- D8.57
Explanation
The risk-neutral up probability is p = (80 × 1.05 - 60)/(100 - 60) = 24/40 = 0.60. The put pays 0 in the up state and 30 in the down state. Its value is 0.40 × 30/1.05 = 11.43. Using the real-world down probability of 0.30 gives 8.57, which is wrong.
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