Statistical Volatility


OptionVue’s method for computing statistical volatility (SV) is the "extreme value method".  Using just daily high and low prices, the extreme value method is roughly five times more precise than the more common "close-to-close" estimator.  And the extreme value method has the further advantage of being unaffected by any possibly missing days.  You can go away for a week or two, and come back and pick up where you left off.  (The SV number might be a little bit "stale", but the formula deals with the gap just fine.)


Truthfully, the calculation of SV involves more than just the basic ”r;extreme value formula”.  There is an algorithm involving several steps. These steps represent refinements made over the years.  The heart of the algorithm, is this ”extreme value” formula: SV = .627 * sqrt(365.25) * ln( H / L )


where:


SV = statistical volatility


sqrt = the square root function


ln = the natural logarithm function


H = the high of the day


L = the low of the day


This formula gives you the statistical volatility number for one trading day, normalized to a year (all volatility numbers are normalized to one year).


The result of using the above formula on each of ”n” trading days is ’n’ different SV numbers.  These may then be combined by averaging. In OptionVue we use 20 trading days,  We use an exponential averaging method to give the most weight to the SV of the most recent trading day, and successively less weight to the other days as you go back in time.


Here is the exponential averaging algorithm as used in OptionVue.


a = 1.0


alpha = 0.92


numer = 0.0


denom = 0.0


For each trading day, do the following three instructions:


   number = number + (a * daily volatility)


   denom = denom + a


   a = a * alpha


Then the final step is: Average SV = number / denom


In this algorithm, ”a” represents the progressively smaller weight, and is used as a multiplier against each daily SV reading.  You can see that ”a” starts out at 1.0, and becomes smaller as it is multiplied by 0.92 repeatedly.