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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:
where is the change in the short-term interest rate, is the estimated long-run value of the short-term interest rate, is the mean reversion rate, is the current level of the short-term interest rate, is the annual basis-point volatility of the short-term interest rate, is the time interval measured in years, and is a normally distributed random variable with mean zero and standard deviation equal to the square root of .
The analyst gathers the following information:
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?*