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

A risk manager increases the mean-reversion speed k in a Vasicek model while holding σ and θ constant. What is the most likely effect on long-maturity zero-coupon yield volatility?

Long-maturity yield volatility falls. A higher mean-reversion speed makes short-rate shocks decay faster, so they have less persistent impact on long-term rates, which reduces the volatility of long yields relative to short yields.

  1. AIt rises, because rates reach θ faster
  2. BIt falls, because shocks to the short rate decay faster and affect long yields lessCorrect
  3. CIt is unchanged, because only σ drives yield volatility
  4. DIt becomes zero for all maturities

Explanation

Higher k makes shocks die out faster, so changes in the short rate have less influence on long-maturity rates. Volatility of long yields therefore declines relative to short yields, flattening the volatility term structure. It does not vanish because σ is still positive.

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