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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

Which statement about risk-neutral probabilities in a binomial term structure model is correct?

Risk-neutral probabilities are those that, with discounting at the short rate, reproduce observed benchmark security prices. They embed risk premiums, differ from real-world probabilities, need not be 0.5, and apply to all securities consistently.

  1. AThey equal the real-world probabilities of the rate moving up or down.
  2. BThey are the probabilities that make the model price of benchmark securities equal their market prices when payoffs are discounted at the short rate.Correct
  3. CThey must be 0.5 for the model to be arbitrage free.
  4. DThey are determined by the investor's risk aversion for each individual security.

Explanation

Risk-neutral probabilities are implied by no-arbitrage: they are chosen so that expected discounted payoffs under them reproduce observed prices. They need not equal real-world probabilities or 0.5, and they are not security-specific preferences; a single measure prices all securities.

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