2. Which of the following GARCH models will take the shortest time to revert to its mean?

A. ht = 0.02 + 0.06r t-12 + 0.92 h t-1

B. ht  = 0.03 + 0.04r t-12  + 0.93 h t-1

C. ht = 0.04 + 0.05r t-12  + 0.94 h t-1

D. ht = 0.05 + 0.01r  t-12  + 0.95 h t-1

Correct answer is D

A is incorrect. The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by α 1  + ?. In this case the persistence factor is the second largest: α 1  + ?  = 0.06 + 0.92 = 0.98.

B is incorrect. The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by α 1  + ?. In this case the persistence factor is the second lowest: α 1  + ?  = 0.04 + 0.93 = 0.97.

C is incorrect. The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by α 1  + ?. In this case the persistence factor is the largest: α 1  + ?  = 0.05 + 0.94 = 0.99.

D is correct. The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by α 1  + ?. In this case the persistence factor is the lowest: α 1  + ?  = 0.01 + 0.95 = 0.96.

Reference:  Philippe Jorion, Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001), Chapter 8.

Type of Question: Quantitative Analysis

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