FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A risk manager calibrates a Vasicek model with k = 0.25 per year. Approximately how long is the half-life of a deviation of the expected short rate from θ? Use ln 2 = 0.6931.
The half-life is ln2 divided by k, which is 0.6931/0.25 = 2.77 years. This is the time for the expected gap between the short rate and the long-run mean θ to halve.
- A0.69 years
- B1.39 years
- C2.77 yearsCorrect
- D5.54 years
Explanation
The expected deviation decays as e^(−kt). Half-life = ln2/k = 0.6931/0.25 = 2.77 years. Using ln2 alone gives 0.69, and 1.39 results from ln2 × 2 mistakenly, which is not valid.
Did you get it right without looking?
One question tells you little. A timed set on The Vasicek and Gauss+ Models shows your real accuracy, how long you take and where you lose marks.
More The Vasicek and Gauss+ Models questions
- A risk manager is choosing between a one-factor Vasicek model and a Gauss+ model with three Gaussian factors to price and hedge a book of sw…
- A risk manager compares hedging a bond portfolio using a one-factor Vasicek model versus a Gauss+ style multi-factor model. The portfolio is…
- A model validation team reviews a one-factor Vasicek implementation used to price zero-coupon bonds in a low-rate environment. Which stateme…
- A desk calibrates a Vasicek model and then re-estimates it with a higher σ, leaving k, the risk-neutral long-run mean rate and the current s…
- In a Vasicek model, k = 0.25, θ = 6.00%, σ = 1.00%, and the current short rate is 4.00%. What is the expected change in the short rate over …
- A desk calibrates a Gauss+ model by fitting model-implied swap rates to the market curve and fitting volatilities to historical rate changes…