Most of what I learned about trading options was learned trading on the US exchanges. Not very many weeks ago, I decided to migrate my account back to the Australian Stock Exchange. The reasons for this were exclusively lifestyle based; I didn't want to work Friday nights anymore because I was missing too many good piss-ups. If I was going to be asleep half of Saturday, it is going to be for recovery, rather than because of nocturnal money making habits.
Anyway that's beside the point.
In the United states the standard measure of statistical volatility (SV) is a simple 20 or 30 day, annualised percentage volatility equation. This is expressed in Amibroker or Metastock formula lanuage like this:
(StDev(log(C/Ref(C,-1)),20) * sqrt(252))*100
You could plot this on a graph, along with the implied volatility (IV), and see very plainly that IV tended to reflect the 20-30 SV. I have underlined "tended to reflect", because SV and IV will never always match each other. SV is measured over past data, whereas IV is an estimate of future volatility. Both SV and IV oscillate in a quite broad range in those markets.
However upon applying my templates to the Aussie market, something was wrong, something was different. IV tended to stay in a much tighter range compared to the US. But the standard 20 day SV charted a much more extreme course than IV. IV was not reflecting this measure of SV at all.
It was clear to me that the Australian market makers were using a different measure, a much more sedate measure than the Americans. Simply lengthening the look-back period of the standard SV equation wasn't doing it, much to lagging and innacurate when current volatilities were changing. I played with exponential moving averages of SV, but that didn't really work either. Then I had this idea; how about an exponentially weighted SV equation? My idea was a longer term SV measure but weighted with the most recent SV, much like an exponential moving average.
This seemed to work! After playing with different parameters, I got an SV measure that IV seemed to be reflecting.
So herewith I tender my Exponential Statistical Volatility (In Amibroker AFL):
long = (StDev(log(C/Ref(C,-1)),100) * sqrt(252))*100;short = (StDev(log(C/Ref(C,-1)),10) * sqrt(252))*100;
x1 = short - Ref(long,-1);
x2 = (x1* (2 / (10+1) ) ) + Ref(long,-1);
Graph0 = x2:
As you can see the IV tends to reflect this particular measure of IV and my reasoning is that the Aussie MM's must be using something similar. I think this is important because one of the best ways of trading options, is by making volatility forecasts based on SV/IV history. So we need to be playing in the same ballpark as the MM's. There will be no perfect measure of SV because of what SV is; merely a statistic based on past information. But I think this is actually a better way of looking at SV anyway.