Answer: 2.15%

## Explanation The correct answer is **B (2.15%)**. Using the Ho-Lee model formula for the interest rate at the lowest node after 2 months: $$r_0 + (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}$$ Where: - $r_0 = 3.2\%$ (current annualized short-term rate) - $\lambda_1 = 0.8\%$ (annualized drift in first month) - $\lambda_2 = 1.2\%$ (annualized drift in second month) - $\sigma = 2.1\%$ (annual basis point volatility) - $dt = \frac{1}{12}$ (monthly time step) Calculation: $$= 3.2\% + \frac{(0.8\% + 1.2\%)}{12} - 2 * 2.1\% * \sqrt{\frac{1}{12}}$$ $$= 0.032 + \frac{0.02}{12} - 2 * 0.021 * \sqrt{\frac{1}{12}}$$ $$= 0.032 + 0.001667 - 2 * 0.021 * 0.288675$$ $$= 0.032 + 0.001667 - 0.012124$$ $$= 0.021543 = 2.15\%$$ **Why other options are incorrect:** - **A (1.82%)**: Uses incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt - 2\sigma\sqrt{dt}$, subtracting instead of adding the drift terms - **C (2.76%)**: Uses incorrect formula $r_0 + (\lambda_1 + \lambda_2)dt - \sigma\sqrt{dt}$, forgetting to multiply by 2 in the volatility term - **D (3.03%)**: Uses incorrect formula $r_0 - (\lambda_1 + \lambda_2)dt$, omitting the volatility term entirely

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