FRM Part I · FRM Exam Part I · Binomial Trees
A stock trades at 50. Over each of two steps it either rises by 20% or falls by 20%. The risk-neutral probability of an up move is 0.60 at each step, and the one-step discount factor is 0.95. What is the value of a two-step European call with strike 50?
The call is worth about 7.15. Only the up-up node is in the money, with payoff 22 and probability 0.36. The expected payoff of 7.92 must be discounted over two steps at 0.95 each, giving 7.92 × 0.9025 ≈ 7.15.
- A7.92
- B7.52
- C7.15Correct
- D4.96
Explanation
Terminal prices are 72, 48 and 32, so only the uu node pays 22. Its risk-neutral probability is 0.6^2 = 0.36. Value = 0.95^2 × 0.36 × 22 = 0.9025 × 7.92 = 7.15. The 7.92 option skips discounting. The 7.52 option discounts only one step.
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