FRM Part II · FRM Exam Part II · The Art of Term Structure Models: Drift
Under Model 1 (dr = σ dw), the annualized volatility of the short rate is 120 basis points per year. Time steps are monthly (dt = 1/12). The current short rate is 4.00%. What is the standard deviation of the one-month change in the rate, in basis points (to one decimal)?
The one-month standard deviation is σ√dt, which is 120 × √(1/12) ≈ 34.6 basis points. Volatility scales with the square root of time, so dividing by 12 to get 10 basis points would be incorrect.
- A10.0 bp
- B34.6 bpCorrect
- C120.0 bp
- D8.3 bp
Explanation
The standard deviation of the change over dt is σ√dt = 120 × √(1/12) = 120 × 0.28868 = 34.64 bp. Using 120/12 = 10 bp is wrong because it scales volatility linearly with time rather than with the square root.
Did you get it right without looking?
One question tells you little. A timed set on The Art of Term Structure Models: Drift shows your real accuracy, how long you take and where you lose marks.
More The Art of Term Structure Models: Drift questions
- A trader calibrates a constant-drift model to the market and obtains a positive λ, because the yield curve slopes upward. The trader conclud…
- A Vasicek model has k = 0.40 per year. Approximately how long is the half-life of a deviation of the short rate from θ, and what does the ha…
- A bank's treasury is calibrating a short-rate model for an environment in which rates are close to zero. Which statement about the models is…
- Under Model 1 with zero drift and σ = 100 bp per year, the current short rate is 3.00%. Using a monthly-step tree with normal shocks, what i…
- In a Model 2 setting, a trader observes that the market 10-year spot rate is below the model's value computed with the historical (real-worl…
- In a lognormal short-rate model, dr = a·r·dt + σ·r·dw, with a = 3% and σ = 20%, what is the drift of ln(r) per year, after applying Ito's le…