In the Ho-Lee model, the discrete time evolution of the short-term rate on a binomial tree at step $n$ and node $j$ (where $j=0$ is the lowest node) is given by:

$r_{n,j} = r_0 + \sum_{i=1}^n \theta_i \Delta t + (2j - n)\sigma \sqrt{\Delta t}$

Given the problem data:

• Current rate $r_0 = 3.2\% = 0.032$
• Time step $\Delta t = 1/12 \text{ year}$
• Volatility $\sigma = 2.1\% = 0.021$
• Annualized drifts: $\theta_1 = 80 \text{ bps} = 0.0080$, $\theta_2 = 120 \text{ bps} = 0.0120$

We need to calculate the lowest node after 2 months ($n=2, j=0$): $r_{2,0} = r_0 + \theta_1 \Delta t + \theta_2 \Delta t - 2\sigma \sqrt{\Delta t}$

Plugging in the numbers: $\theta_1 \Delta t = 0.0080 \times \frac{1}{12} = 0.0006667$ $\theta_2 \Delta t = 0.0120 \times \frac{1}{12} = 0.0010000$ $2\sigma \sqrt{\Delta t} = 2 \times 0.021 \times \sqrt{\frac{1}{12}} = 2 \times 0.021 \times 0.288675 = 0.012124$

$r_{2,0} = 0.032 + 0.0006667 + 0.0010000 - 0.012124$ $r_{2,0} = 0.021542$

Converting to percentage, the rate is approximately $2.15%$.