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

A risk manager compares valuing a bond via real-world expected cash flows discounted at the risk-free rate versus risk-neutral expected cash flows discounted at the risk-free rate. Which conclusion is correct for a risky, rate-sensitive bond?

Discounting real-world expected cash flows at the risk-free rate ignores the compensation investors require for bearing risk, so it misprices the bond. Risk-neutral probabilities embed that premium, allowing risk-free discounting to match no-arbitrage prices without assuming investors are actually risk neutral.

  1. AUsing real-world probabilities with the risk-free rate would ignore the risk premium and misprice the bondCorrect
  2. BBoth approaches always give the same price
  3. CRisk-neutral pricing requires investors to be indifferent to risk in reality
  4. DReal-world probabilities are required to avoid arbitrage

Explanation

Risk-neutral pricing adjusts probabilities to include risk compensation so risk-free discounting works. Real-world probabilities with risk-free discounting omit the premium, giving a wrong price. Investors need not actually be risk neutral; the method is a pricing device consistent with no arbitrage.

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