Part 8

Question 1

Volatility clustering

Answer 1

Large changes tend to follow large changes; small changes tend
to follow small changes

Question 2

Fat tails

Answer 2

Fat tails
▶ Excess kurtosis: more extremes than predicted by a normal
distribution

Question 3

Leverage effects

Answer 3

Assymetric effects: volatility tends to go up more after
negative returns

Question 4

Calculating ARCH-LM test

Answer 4

T (obvs) x R^2 - X^2 (q - restrictions)

Question 5

So if the test statistic is greater than the critical value here (ARCH-LM)

Answer 5

We reject the null that there are no arch effects and we insists that in fact there is

Question 6

Problems with ARCH-LM

Answer 6

Not obvious how to choose right q
Required q might be very large

Question 7

Unconditional variance formula (GARCH)

Answer 7

α0 /
1 − (α1 + β)

Question 8

For a to be well behaved, variance estimates are …

Answer 8

The variance estimates are always positive
▶ The variance estimates are stationary

Question 9

For E-GARCH, if If γ < 0 is there evidence of leverage

Answer 9

No

Question 10

For GJR Garch, If γ > 0 is there evidence of leverage?

Answer 10

No

Question 11

For GARCH-M (Garch in mean), what do you allow to enter equation and why?

Answer 11

Higher risk → higher return, so might make sense to include
estimate of volatility into mean equation

Question 12

Day and Lewis (1992) considered whether Implied Volatility or
GARCH do a better job at forecasting volatility. What did they conclude (2)

Answer 12

In sample: Both IV and GARCH / EGARCH contain unique
information.
▶ Out of sample: Neither really accurately predicts volatility