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: enter image description here

Can anyone help to clarify if this is the best way, or if there is another way?

  • $\begingroup$ I am not sure what you try to do. Delta hedging would be buying the underlying to offset gains/losses in your option position (this needs to be done frequently, not set Up once for a 3m period. It also has nothing to do with ATM IVOL. Realized vol =historical vol. Setting up retrospectively a trade where you exploit that the market was underpricing actual vol isn't helpful as you don't know what hist vol is until the period is over. It can be calculated in many ways. Most frequently its standard deviation of log returns. $\endgroup$ – AKdemy May 9 at 21:14

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