Financial Risk Manager Part 2

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Explanation:

B is correct. The interest rate in the lowest node based on the Ho-Lee model is:

r_0 + (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}

= 3.2\% + \frac{(0.8\% + 1.2\%)}{12} - 2 \times 2.1\% \times \sqrt{\frac{1}{12}}

= 0.021542 = 2.15\%

A is incorrect. This uses the incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}$ to calculate the interest rate, subtracting instead of adding the second term in the formula.

C is incorrect. This uses the incorrect formula $r_0 + (\lambda_1 + \lambda_2)dt - \sigma\sqrt{dt}$ to calculate the interest rate, forgetting to multiply by 2 in the third term.

D is incorrect. This uses the incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt$ to calculate the interest rate, omitting the third term entirely.

Explanation:

B is correct. The interest rate in the lowest node based on the Ho-Lee model is:

r_0 + (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}

= 3.2\% + \frac{(0.8\% + 1.2\%)}{12} - 2 \times 2.1\% \times \sqrt{\frac{1}{12}}

= 0.021542 = 2.15\%

A is incorrect. This uses the incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}$ to calculate the interest rate, subtracting instead of adding the second term in the formula.

C is incorrect. This uses the incorrect formula $r_0 + (\lambda_1 + \lambda_2)dt - \sigma\sqrt{dt}$ to calculate the interest rate, forgetting to multiply by 2 in the third term.

D is incorrect. This uses the incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt$ to calculate the interest rate, omitting the third term entirely.

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Question A risk analyst constructs a binomial interest rate tree by using the Ho-Lee model. The time step is monthly and the annualized drift is 80 bps in the first month and 120 bps in the second month. Assuming the current annualized short-term rate is 3.2% and the annual basis point-volatility is 2.1%, what is the interest rate at the lowest node after 2 months?

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Last updated: July 5, 2026 at 07:29

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