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

Which of the following is the most appropriate description of the role of the risk-neutral probability in a one-period binomial model?

The risk-neutral probability is a mathematical weight chosen so that the expected derivative payoff, discounted at the risk-free rate, equals the no-arbitrage value. It is not the real-world probability of an up move and does not reflect investors' forecasts.

  1. AIt is the real-world chance that the underlying price rises
  2. BIt is the probability that makes the expected discounted payoff equal the no-arbitrage valueCorrect
  3. CIt is the investor's estimate of the option's chance of expiring in the money

Explanation

The risk-neutral probability is a device chosen so that discounting expected payoffs at the risk-free rate gives the arbitrage-free price. It is not the actual probability of an up move and does not depend on investor forecasts or risk preferences.

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