FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at 100 and will move to either 110 or 90 in one period. The risk-free rate is 2% per period (simple). Investors believe the real-world probability of an up move is 0.70. What is the no-arbitrage value of a call with strike 100 expiring after one period?
The call is worth about 5.88. The real-world probability of 0.70 is irrelevant. The risk-neutral up probability is (1.02 - 0.90)/0.20 = 0.60, so the discounted expected payoff is 0.60 × 10 / 1.02 = 5.88.
- A5.88Correct
- B6.86
- C6.00
- D3.92
Explanation
The risk-neutral probability is p = (1.02 - 0.90)/0.20 = 0.60. Value = 0.60 × 10/1.02 = 5.88. Using the real-world 0.70 gives 6.86, which is wrong because arbitrage-free pricing does not depend on real-world probabilities. 6.00 omits discounting. 3.92 uses 0.40, the down probability.
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