Answer: The expected short-term interest rate is 3.81% and the half-life is 11.6 years.

## 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.

Author: LeetQuiz .