FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 50. Over one period it will rise to 60 or fall to 40. The gross risk-free return for the period is 1.05. The real-world probability of an up move is 0.50. What is the value of a European call option with a strike of 50 expiring at the end of the period?
The call is worth about 5.95. The risk-neutral up probability is 0.625, the expected payoff is 6.25, and discounting at the 1.05 gross risk-free return gives 5.95. The real-world probability of 0.50 is irrelevant to the no-arbitrage price.
- A5.95Correct
- B4.76
- C6.25
- D3.57
Explanation
u = 1.2 and d = 0.8, so p = (1.05 - 0.8)/0.4 = 0.625. The payoffs are 10 and 0, so the value is 0.625 × 10/1.05 = 5.95. Using the real-world probability of 0.5 gives 4.76, which is wrong because valuation requires risk-neutral probabilities.
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