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CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model

A stock is at 80 and will be 100 or 70 in one period. The risk-free rate is 4% for the period. A put option has an exercise price of 85. The put's value today is closest to:

Using risk-neutral probabilities, the up probability is 0.44, so the put expected payoff is 0.56 times 15, or 8.40. Discounting at 1.04 gives about 8.08. The options as listed do not contain this value.

  1. A3.91
  2. B5.77Correct
  3. C7.21

Explanation

u = 1.25, d = 0.875, 1+r = 1.04. pi = (1.04 - 0.875)/(1.25 - 0.875) = 0.165/0.375 = 0.44. Put payoffs: 0 up, 15 down. Value = (0.56×15)/1.04 = 8.4/1.04 = 8.08. This gives 8.08, which does not match the options, so the data must be rechecked: option B at 5.77 is not supported by this working.

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