CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model
A stock is at 40 and will be either 48 or 32 after one period. The risk-free rate is 5% per period. A one-period European put has an exercise price of 40. The value of the put today is closest to:
The put is worth about 2.86 using risk-neutral valuation: a 0.375 down probability times an 8 payoff gives 3.00, discounted at 5%. Among the choices, 2.38 is the nearest.
- A1.43
- B2.38Correct
- C3.57
Explanation
Risk-neutral up probability is (1.05 − 0.8)/0.4 = 0.625, so down probability is 0.375. Put payoffs: 0 up, 8 down. Expected payoff = 0.375 × 8 = 3.00. Discounted: 3/1.05 = 2.86. Closest listed value is 2.38 versus 3.57; 2.86 is nearer 2.38 (0.48 vs 0.71).
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