Volatility modeling Flashcards
What stylized features of financial data cannot be explained using linear time series models?
Frequency, Non-stationarity, Linear Independence, Non-normality, Volatility clustering
What stylized feature of financial data are GARCH(1,1) models meant to capture?
Volatility clustering, and unconditional leptokurtosis.
What is leptokurtosis?
Having a higher peak than the normal distribution, and shallower tails.
Why do researchers prefer GARCH over ARCH?
ARCH uses a lot of parameters. GARCH can define an infinite ARCH model in just three. Because it can be written as an ARCH(inf) model, it can still capture all the dependence in the returns and thus volatility clustering.
What are the disadvantages of ARCH(q) overcome by GARCH?
How do we decide on q?
The required value of q can be very large.
Non-negativity constraints might be violated.
Name three extensions to the GARCH model
GJR-, E-, and -M.
What is a GJR-GARCH model?
GJR models add a part:
gamma * epsilont-1 ^ 2 * It-1
to the GARCH model. It makes sure that there is more volatility when the returns are negative.
What is an E-GARCH model?
The logged form of the GJR-GARCH model. It has the advantage that the volatility is always positive.
What is a GARCH-M model?
A term:
delta * sigmat-1
is added to the formula for returns. This means that the returns are higher when volatility becomes higher. This is because a risk premium is added.
When considering a GARCH(1,1) model for daily stock returns. What are likely values for the coefficients?
mu, being the average daily return, could be 0.05.
alpha0 could be 0.0001.
alpha1 and beta have to be close to 1 when added up, but beta has to be bigger. Thus alpha1 could be 0.15 and beta could be 0.8.
All three must be positive.
What is conditional variance?
The conditional variance is the a random variable at a particular point in time, conditional on previous data.
What is unconditional variance?
A random variable with a particular distribution.
When producing one-step ahead volatility forecast, would you be more likely to use conditional variance or unconditional variance?
Conditional variance. GARCH models are conditional models, and are most suited for such forecasts.
When producing twenty-step ahead volatility forecast, would you be more likely to use conditional variance or unconditional variance?
Unconditional variance. A conditional model such as GARCH could be used, but it converges on the historic mean anyway. When using another model such as EWMA, it doesn’t even do this and diverges more and more from the true 20-step ahead value. It is thus better to use and unconditional method such as measuring historic volatility.
What are the strengths and weaknesses of historical volatility models?
These models are very simple to calculate. The data however is unweighted which means the forecasts chance only slowly to chances in the economy. They also don’t take advantage of recent data to improve their forecasts. When there is a structural break, the forecast will be super high volatility for as long as the observation window.
