Background to question:
I was trying to fit a GARCH(1,1) model to the variance of log returns of a series, and ARMA(0,0) for the mean. I was using the
fGarch package in R to do this. The aim of the modeling is to generate a predicted volatility number to feed into the Black-Scholes model to an generate option price and therefore option deltas. I plan to backtest the delta from GARCH volatility to hedge my option positions (as opposed to deltas derived from implied vol prices).
A) I used the
predict function in the package to generate a 'n-day ahead' volatility forecast. As I understand GARCH, these numbers are annualized standard deviation numbers. To hedge a 1 month option I want to forecast 30 day volatility. I can simply put 'n-days ahead = 30 to get the numbers, but how do I combine those 30 numbers to get a annualized vol number?
B) Could anyone also please explain how to use the
nroll argument in the package? Basically I want rolling GARCH estimates of volatility. For example, at day 10, I want to use the past 10 days of data to get a vol prediction for day 11, at day 50 I want to use 50 days of data for vol prediction of day 51 etc.