Explanation

This question involves interest rate modeling using a mean-reverting process (likely the Vasicek model). The key parameters are:

• Annual basis-point volatility (σ): 120 bps = 1.20%
• Time period: 8 years
• Half-life calculation: Time for interest rate to revert halfway to long-run value

In mean-reverting interest rate models:

1. Expected short-term interest rate calculation: The expected rate after time t is calculated using the mean reversion formula: $E[r_t] = θ + (r_0 - θ)e^{-κt}$ where θ is the long-run mean, κ is the speed of mean reversion, and r₀ is the initial rate.

2. Half-life calculation: The half-life (time for the rate to move halfway to the long-run mean) is: $\text{Half-life} = \frac{\ln(2)}{κ}$

Given that option A provides:

• Expected short-term interest rate: 3.81%
• Half-life: 11.6 years

This suggests:

• The speed of mean reversion κ = ln(2)/11.6 ≈ 0.06
• The initial rate and long-run mean would be calibrated to give 3.81% after 8 years

The 3.81% expected rate and 11.6-year half-life are consistent with typical mean-reverting interest rate model parameters where the volatility is 120 bps.