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