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Financial Risk Manager Part 2

Financial Risk Manager Part 2

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A quantitative analyst on the fixed-income desk of an investment bank is applying the Vasicek model to estimate future short-term interest rates. The model is given below:

dr=k∗(Θ−r)∗dt+σ∗dwdr = k * (\Theta - r) * dt + \sigma * dwdr=k∗(Θ−r)∗dt+σ∗dw

where drdrdr is the change in the short-term interest rate, Θ\ThetaΘ is the estimated long-run value of the short-term interest rate, kkk is the mean reversion rate, rrr is the current level of the short-term interest rate, σ\sigmaσ is the annual basis-point volatility of the short-term interest rate, dtdtdt is the time interval measured in years, and dwdwdw is a normally distributed random variable with mean zero and standard deviation equal to the square root of dtdtdt.

The analyst gathers the following information:

  • Current short-term interest rate (rrr): 3.35%
  • Long-run value of short-term interest rate (Θ\ThetaΘ): 4.55%
  • Mean reversion rate (kkk): 0.06
  • Annual basis-point volatility (σ\sigmaσ): 120 bps

The analyst then creates an interest rate tree, determines the expected short-term interest rate after 8 years, and calculates how long it will take the short-term interest rate to revert halfway to the long-run value. Which of the following statements would be correct for the analyst to make?*

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