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Q.2857 A dataset has a mean-reverting parameter of 0.37 and a volatility of 197 basis points. We are also informed that the short-term rate is normally distributed. Use the Vasicek model to determine the standard deviation of the terminal distribution of the short rate after 5 years. | Financial Risk Manager Part 2 Quiz - LeetQuiz

Explanation:

Recall that the standard deviation of the terminal distribution of the short rate after T years is:

\sqrt{\frac{\sigma^2(1 - \mathrm{e}^{-2kT})}{2k}} = \sqrt{\frac{0.0197^2(1 - \mathrm{e}^{-2 \times 0.37 \times 5})}{2 \times 0.37}} = 0.02261

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Q.2857 A dataset has a mean-reverting parameter of 0.37 and a volatility of 197 basis points. We are also informed that the short-term rate is normally distributed. Use the Vasicek model to determine the standard deviation of the terminal distribution of the short rate after 5 years.