FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models
A risk analyst calibrates a Vasicek model under the risk-neutral measure with k = 0.25, long-run risk-neutral mean rate of 6.00% and σ = 2.00%. What is the limiting yield on an infinitely long-maturity zero-coupon bond?
The limiting long-maturity yield is 5.68%. It equals the risk-neutral mean rate minus the convexity term σ²/(2k²). Here that term is 0.0004/0.125 = 0.32%, so the yield is 6.00% − 0.32% = 5.68%, below the long-run mean rate.
- A5.68%Correct
- B6.00%
- C5.92%
- D5.36%
Explanation
The long-maturity yield limit is θ* − σ²/(2k²). σ² = 0.0004 and 2k² = 0.125, so the adjustment is 0.0032, or 0.32%. The limit is 6.00% − 0.32% = 5.68%. Using 2k in the denominator gives 5.92%, and using k² only gives 5.36%. Ignoring convexity gives 6.00%.
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…
- In a two-factor Gaussian model the short rate is r = x1 + x2, where x1 has volatility 80 bps per year and x2 has volatility 60 bps per year,…
- 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 …