FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Volatility and Distribution
In a lognormal short-rate model, dr = a r dt + σ r dw with σ = 20% (annual proportional volatility). The current short rate is 5.00%. What is the approximate basis-point volatility of the short rate per year implied by the model?
The basis-point volatility is the proportional volatility multiplied by the rate level: 20% times 5.00% equals 1.00%, or 100 basis points per year. The other values come from ignoring the multiplication by the rate level or mixing up the inputs.
- A20 bps
- B100 bpsCorrect
- C200 bps
- D500 bps
Explanation
Basis-point volatility equals σ × r = 0.20 × 5.00% = 1.00% = 100 bps per year. Choosing 20 bps ignores the rate level, and 500 bps misuses the rate level instead of the product.
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