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%.