wilmott.com

Hi Guys,I am wondering what is the difference in hedging options with implied volatility vs. realized. Let's assume the current realized volatility is a good proxy for the next move and implied is a value expected to materialize at soem point.What is the difference between the two hedging methods?Maybe as an example: Let's assume oil implied vola is very high 80%, which is a risk premium for a future move. The actual vola, however, is much lower, say 20% since -for now- nothing is happeneing. Which vola is the right one to use for my Greeks/hedging? What is teh difference?Thank you very much guysKim

This article by Paul and Riaz would be a good start.http://www.math.ku.dk/~rolf/Wilmott_WhichFreeLunch.pdf

thanks for that link - good article

QuoteOriginally posted by: SkogThis article by Paul and Riaz would be a good start.http://www.math.ku.dk/~rolf/Wilmott_Whi ... ch.pdfWhen they say actual vol, do they mean the empirical volatility calculated over their sample from 1999-2005? They say actual vol is 30 percent and I assume they use this in their calculations for delta hedging over a 1 year period. I don't really understand. If its empirical vol, say the option starts on 1st Jan 2004 and expires 1st Jan 2005, and empirical vol is 30 percent on 1st Jan 2004, calculated from data from 1st Jan 1999 until 1st of Jan 2004, wouldn't it not change say by the 1st Feb 2004 as one more months data is available so the empirical vol is then calculated from 1st Jan 1999 until 1st Feb 2004, so then the actual vol would be say 29.2 percent. I just get the impression that actual vol of 30 percent is then used throughout the whole years hedging strategy without it being updated as time goes by. And the same goes for Implied vol, which is said to be 20 percent, but again this would change on a daily basis, but it seems 20 percent is used for the whole years hedging?What am I missing?

QuoteOriginally posted by: sdlifeQuoteOriginally posted by: SkogThis article by Paul and Riaz would be a good start.http://www.math.ku.dk/~rolf/Wilmott_Whi ... ch.pdfWhen they say actual vol, do they mean the empirical volatility calculated over their sample from 1999-2005? They say actual vol is 30 percent and I assume they use this in their calculations for delta hedging over a 1 year period. I don't really understand. If its empirical vol, say the option starts on 1st Jan 2004 and expires 1st Jan 2005, and empirical vol is 30 percent on 1st Jan 2004, calculated from data from 1st Jan 1999 until 1st of Jan 2004, wouldn't it not change say by the 1st Feb 2004 as one more months data is available so the empirical vol is then calculated from 1st Jan 1999 until 1st Feb 2004, so then the actual vol would be say 29.2 percent. I just get the impression that actual vol of 30 percent is then used throughout the whole years hedging strategy without it being updated as time goes by. And the same goes for Implied vol, which is said to be 20 percent, but again this would change on a daily basis, but it seems 20 percent is used for the whole years hedging?What am I missing?They did not update the vol over the hedging period; the focus was in comparing the historical x implied approaches, and updating the estimates would make it harder to match theoretical results with the simulations.

correct me if i am wrong, but if you update the hedging volatility i think you'd have an additional term: vega.

A little off-topic but regarding the same article. When they consider the effect of skew (Figure 7) with constant negative slope, why does the expected profit increase whenever the strike is away from ATM? I don't seem to be able to reconcile this with the no-skew case (Figure 4 and 5).