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CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

Which statement about risk-neutral probabilities used to price derivatives is most accurate?

Risk-neutral probabilities are those under which the underlying's expected future price, discounted at the risk-free rate, equals its current price. They are a pricing tool derived from no-arbitrage, not real-world forecasts, and they do not vary with investors' risk aversion.

  1. AThey are the actual probabilities of up and down moves estimated from historical data.
  2. BThey are the probabilities that make the discounted expected underlying price at the risk-free rate equal to its current price.Correct
  3. CThey depend on the risk aversion of the investor holding the derivative.

Explanation

Risk-neutral probabilities are constructed so the underlying earns the risk-free rate in expectation, which makes the derivative's expected payoff discountable at the risk-free rate. They are not real-world probabilities and do not depend on investor risk preferences.

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