I am working with a dataset from: http://web.math.ku.dk/~rolf/Svend/
named data 1.
I'm currently setting up a delta hedge for periods of 3 months. So currently we are starting at the start data of the data 29/january, hedging with the ATM implied volatiltiy, going 3 months forward and repeating.
I have noticed from papers that one can assume the historical volatility is approximately a good measure for the realized volatility, and that if realized volatilty > implied volatility the most beneficial way to set up your portfolio is by going long in the call option and short in the stock (Vice versa for realized<Implied)((Willmot and Ahmad)).
I want to embed this setup into my expirement. However, I'm not to sure how to calculate the historical/realized volatility, that is to be compared with the implied volatility.
My initial though was, as the historical volatility is a measure of historical deviations in the price process. I would scratch the starting 2 portfolios (from Jan 2004 - June 2004).
Then going setting a timer interval of 1 week, calculating the mean of the portfolio from the previous 6 months, and using the formula:
Can anyone help to clarify if this is the best way, or if there is another way?