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

A quant calibrates a Ho-Lee-type model with time-dependent drift λ(t) to match today's term structure of zero-coupon bond prices exactly. She then raises the assumed future short-rate volatility and recalibrates to the same bond prices. What must happen to the fitted risk-neutral drift of the short rate at longer horizons?

The fitted risk-neutral drift must fall. Higher volatility increases the convexity benefit in bond prices, so to keep reproducing the same observed bond prices the model needs a lower drift at longer horizons, meaning drift and volatility are linked through the calibration.

  1. AIt must be lower, to offset the greater convexity value that higher volatility adds to bond pricesCorrect
  2. BIt must be higher, to compensate investors for the greater volatility
  3. CIt stays unchanged, because the bond prices fixed the drift independently of volatility
  4. DIt must be set equal to the forward-rate volatility so the model remains arbitrage-free

Explanation

Bond prices are convex in rates, so higher volatility raises model bond prices (convexity effect) if drift is unchanged. To keep matching the same observed prices, the fitted drift must be lower at longer horizons. Drift therefore depends on volatility, and a risk-premium argument is not how the calibration works.

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