Answer: $ h_t = 0.03 + 0.02r_{t-1}^2 + 0.95h_{t-1} $

## 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.

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