FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
A risk analyst uses Model 1 with annualized basis-point volatility σ = 120 bps and drift λ = 0. The current short rate is 4.00%. What is the probability-weighted 1-in-20 (5% one-tailed) lowest short rate after 4 years, using a z-value of 1.645?
The 4-year standard deviation is 1.20% times 2, or 2.40%. At 1.645 standard deviations the shock is about 3.95%, giving a 5th percentile rate near 0.05%.
- A0.71%Correct
- B1.03%
- C2.03%
- D-0.71%
Explanation
Standard deviation over 4 years = 1.20% × √4 = 2.40%. Shock = 1.645 × 2.40% = 3.948%. Lowest rate = 4.00% − 3.948% = 0.052%, which rounds to about 0.05%. Recomputing: this does not match 0.71%, so check the options: none equals 0.05%.
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