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

Which of the following conditions is most likely required for the one-period binomial model to give a valid no-arbitrage derivative value?

The model requires that the risk-free return lies between the down and up returns, meaning d is less than 1 plus r, which is less than u. This keeps the risk-neutral probability between zero and one and rules out arbitrage between the asset and the risk-free bond.

  1. AThe risk-free rate lies between the down and up returnsCorrect
  2. BThe up and down moves are equally likely
  3. CThe underlying pays a dividend in each period

Explanation

For the risk-neutral probability to lie between 0 and 1, the gross risk-free return must lie between d and u. Otherwise an arbitrage exists. Equal real-world probabilities and dividends are not required.

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