Answer: 4.63%

## Explanation This question involves modeling spot rate changes using a short rate term structure model, specifically what appears to be the Vasicek model or similar mean-reverting model. **Given:** - Current short-term interest rate (r₀) = 5% - Volatility (σ) = 80 bps = 0.80% - Time period = 1 month = 1/12 year - Random variable realization (dW) = -0.5 - Constant drift (λ) = 0.36% **Calculation:** The general form for the short rate evolution is: dr = λdt + σdW Where: - dr is the change in interest rate - λ is the drift term - dt is the time increment - σ is the volatility - dW is the random shock Plugging in the values: - dt = 1/12 = 0.08333 - λdt = 0.36% × 0.08333 = 0.03% - σdW = 0.80% × (-0.5) = -0.40% Total change: dr = 0.03% + (-0.40%) = -0.37% New spot rate = r₀ + dr = 5% + (-0.37%) = 4.63% **Verification:** - Option A (5.37%): This would result from ignoring the negative shock - Option B (4.63%): Correct calculation - Option C (5.76%): This would result from adding the shock instead of subtracting - Option D (4.24%): This would result from overestimating the negative impact The negative dW value (-0.5) creates a downward shock to the interest rate, which combined with the small positive drift, results in a net decrease to 4.63%.

Author: LeetQuiz .