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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

Which statement about the market price of risk in term-structure modelling is correct?

The market price of risk shifts the short-rate drift when changing from the real-world measure to the risk-neutral measure. Bond prices are computed under the risk-neutral drift, and the adjustment is generally non-zero because investors demand compensation for interest-rate risk.

  1. AIt converts real-world drift of the short rate into the risk-neutral drift used for pricing bondsCorrect
  2. BIt is always zero in an arbitrage-free model
  3. CIt equals the standard deviation of the short rate
  4. DIt is only needed for coupon bonds, not for zero-coupon bonds
  5. It is observed directly as the yield on the longest-maturity bond

Explanation

By Girsanov's theorem the market price of risk adjusts the drift when moving from the real-world measure P to the risk-neutral measure Q. It is generally non-zero when investors demand compensation for interest-rate risk. It applies to all bonds and is not directly an observed yield.

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