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

A risk manager compares two Vasicek calibrations with the same σ and θ: Model A has k = 0.10 and Model B has k = 0.50. Which conclusion about the volatility of long-maturity spot rates is correct?

Model A, with k = 0.10, implies higher volatility of long-maturity rates. Slow mean reversion lets short-rate shocks persist across many years, so they move long rates more. Strong reversion in Model B dampens shocks quickly, so term volatility declines faster with maturity.

  1. AModel A implies higher long-maturity rate volatility, because slow mean reversion lets shocks persistCorrect
  2. BModel B implies higher long-maturity rate volatility, because strong reversion amplifies shocks
  3. CBoth imply the same volatility because σ is identical
  4. DNeither produces any long-rate volatility because rates revert to θ

Explanation

Shocks to the short rate decay at speed k, and long rates depend on the average expected short rate. With low k, shocks persist and move long rates more; with high k they fade quickly, damping long-rate volatility. Equal σ does not imply equal term volatility.

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