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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift

A trader notes that, in a no-arbitrage model with a normally distributed short rate, the model-implied price of a long-dated zero-coupon bond is higher than the price obtained by discounting at the expected path of the short rate. Which feature explains this?

The convex relationship between rates and bond prices (Jensen's inequality) means the expected discount factor exceeds the discount factor at the expected rate. Volatility therefore raises bond prices, and the effect grows with maturity and with variance, which is the convexity effect in no-arbitrage term structure models.

  1. AConvexity: the convex relationship between rates and bond prices means that volatility raises the expected discount factor above the discount factor at the expected rateCorrect
  2. BLiquidity premium that always reduces bond prices
  3. CCredit spread embedded in the risk-free curve
  4. DNegative mean reversion in the short rate

Explanation

By Jensen's inequality, E[exp(-integral r)] exceeds exp(-E[integral r]) because exp is convex. Hence volatility increases bond prices relative to the expected-rate discounting, and this effect grows with maturity and sigma squared. This is the convexity effect, not a liquidity or credit effect.

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