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

A desk calibrates a Ho-Lee model with σ = 1.0% per year. Using the standard result that the convexity effect lowers the zero-coupon bond yield by σ²T²/6 in the Ho-Lee model's continuously compounded yield relative to the expected-rate path, what is the approximate convexity term for T = 10 years?

The convexity term is σ²T²/6 = 0.0001 × 100 / 6 ≈ 0.001667, or about 16.7 basis points. It grows with the square of maturity, so it matters far more for long-dated zero-coupon bonds than for short ones.

  1. A0.1667% (about 16.7 bp)Correct
  2. B1.67%
  3. C0.0167% (about 1.7 bp)
  4. D0.6000%

Explanation

σ²T²/6 = (0.01)² × 100 / 6 = 0.01/6 = 0.001667, i.e. 0.1667% or about 16.7 bp. Using T instead of T² gives 1.7 bp; omitting the division by 6 gives 1%.

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