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FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution

Two Ho-Lee models are calibrated to the same initial term structure. Model A uses σ = 0.80% and Model B uses σ = 1.20%. Which statement is correct?

Because both are calibrated to the same initial term structure, they price today's zero-coupon bonds identically. The higher-volatility Model B generates greater dispersion of future rates and therefore higher option values. Both models produce normally distributed rates.

  1. ABoth will price the underlying zero-coupon bonds identically today, but Model B will give higher prices for options on those bondsCorrect
  2. BModel B will give lower prices for today's zero-coupon bonds than Model A
  3. CModel A will have a higher λ(t) at every maturity because its volatility is lower
  4. DThe models differ in the distribution of rates: Model A is normal and Model B is lognormal

Explanation

Both are fitted to the same curve via λ(t), so today's bond prices match. Higher σ increases the dispersion of future bond prices and so raises option values. λ(t) includes a σ²t term, so it is larger in Model B, not A, and both models are normal.

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