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

A desk calibrates a constant-drift model so that λ matches the market price of the 5-year zero-coupon bond. The model then misprices the 2-year and 10-year bonds. What is the best explanation and remedy?

A single constant drift has only one free parameter, so it can match just one point on the term structure. The remedy is a time-dependent drift, as in the Ho-Lee model, which can be chosen to fit prices at every maturity.

  1. AA single constant λ can fit only one point of the curve; use a time-dependent drift λ(t), as in the Ho-Lee model, to fit all maturities.Correct
  2. BVolatility is too high; setting σ to zero will fit all maturities.
  3. CThe mispricing arises because λ is a real-world drift; replacing it with the historical mean change fixes it.
  4. DConvexity is absent from the model; adding it will not change the fit, so the mispricing is unavoidable.

Explanation

One constant parameter λ can match only one maturity. A drift that varies with time lets the model fit the whole initial curve, which is the Ho-Lee approach. Setting σ to zero would remove convexity and distort prices, and the real-world drift is not what prices bonds.

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