I'm currently working on a dataset containing data from the 29 January till the 29 July 2009. In the dataset I have prices of the S&P 500 index for all days. Furthermore, I have the implied volatilities and prices of ATM option with 3 month to expiry.
I have read in Awartani and Corradi from 2005, that EGARCH(1,1) is particularly useful in estimating volatily from this index.
However, I want to test this statement and see if I can find a better model EGARCH(p,q) model. My setup in the expirement is as following: I have set up 20 non-overlapping portfolios (starting 125 days in the dataset) with 3 month to expiry options. From these 20 non-overlapping portfolios, I want to test what EGARCH(p,q) model is the best to forecast the portfolios volatilities (Delta-hedge portfolio).
I have 2 questions)
- What is the best method in figuring out the (p,q). I have read that AIC or FIC are the best methods in doing so, can anybody elaborate if this is true? Or are easier methods preferred?
- Deciding what (p,q) to choose, should I perform the test on the whole dataset, or fractions of the dataset. Example) The first portfolio starting the 28/7-2004, then find the optimal (p,q) from 29 January 2004 til 27 July 2004?