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Strategies & Market Trends : Options 201: Beyond Obi-Wan-Kenobe
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To: tyc:> who wrote (774)2/25/2003 1:02:24 AM
From: Dan Duchardt  Read Replies (1) of 1064
 
BBs are a useful indication of the expected range of price movement over any time period. You seem to have a pretty good handle on what the BBs are telling you. To the extent that price follows a "normal" distribution, the standard deviation or its multiples relate to the probability of price diverging from the average during the period. For your purposes of trying to estimate the likelihood of price reaching some level within the life of an option, the BBs are meaningful indicators

If you think about the definition of "average" and "standard deviation" for a set of data, you realize that the order of the data within the set is of no consequence. What that means for today's average and today's BBs is that the preceding daily prices could have been in any order and the average and BB width would still be the same.

For that same set of data, volatility is a measure of the typical day to day fluctuations of price change. You could take the same set of 50 prices and come up with very different HVs depending on how you order the prices within the set. If they are arranged sequentially from highest to lowest or lowest to highest, the day to day changes will be minimized and the volatility will be relatively small compared to a random ordering of the same prices. A contrived arrangement of alternating high and low prices would yield a much higher volatility.

I can't find any links to a definition of historical volatility. I remember If found one a couple of years ago, and found a spreadsheet for a Black Scholes calculator that worked with raw price data to find the HV component. What I described for calculating HV is based on my recollection of the old source, confirmed by the spreadsheet calculation. Based on that definition, it becomes clear that volatility is a measure of deviation from LINEARITY of price movement, or more correctly from log-linear movement. You might try to play around with a set of 50 numbers to see how different HV can be when the order is changed.
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