Explanation

In GARCH(1,1) models, the persistence parameter (β) determines how quickly volatility reverts to its long-run mean. The half-life of volatility shocks is calculated as:

Half-life = ln(0.5)/ln(β)

Where β is the coefficient on the lagged variance term (h_{t-1}).

Let's calculate the persistence (β) for each model:

• Option A: β = 0.96
• Option B: β = 0.95
• Option C: β = 0.97
• Option D: β = 0.98

Lower β values mean faster mean reversion. Therefore:

• Option B (β = 0.95) has the lowest persistence and will revert to the mean fastest
• Option D (β = 0.98) has the highest persistence and will take the longest to revert

Correct Answer: B - This model has the lowest persistence parameter (0.95), meaning volatility shocks dissipate most quickly.