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

A stock is at 50 and can move to 60 or 40 after one period. The risk-free rate is 5% per period and the risk-neutral up probability is 0.625. The value today of a European call option with a strike of 50 is closest to:

The call is worth about 5.95. The risk-neutral expected payoff is 0.625 times 10, or 6.25, and discounting one period at 5% gives 5.95. Leaving out the discounting step gives the incorrect 6.25.

  1. A3.57
  2. B5.95Correct
  3. C6.25

Explanation

Payoffs: up = 10, down = 0. Expected payoff = 0.625 x 10 = 6.25. Discounting at 1.05 gives 5.95. The 6.25 option omits discounting; 3.57 wrongly uses 0.375 as the up probability and then discounts (3.75/1.05).

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