Synthetic Data: Considering Volatility And Drift

I have continued to work on the question of changing volatility in the futures markets over time, for the purposes of attempting to build realistic synthetic data series.

It is my intention to mimic each class or sector separately and to have many different series for each "asset class" which try to incorporate typical volatilities for the underlying instruments.

I will program series for stock market indices, grains, metals (precious and industrial) and so on in an effort to introduce as much realism as possible.

In that regard I am taking a closer look at the entire history of each of the instruments in my portfolio. I set out on my website a few charts for Comex Silver.

What has happened over time? Has the frequency in any particular "bin" of daily return ranges changed over time? Has there been a trend up or down? If so, will this trend continue or will it revert to some sort of mean? Fruitless to speculate perhaps but interesting to see nonetheless what has occurred since volume built up by around 1967 in the newly created Comex Silver contract.

Again, I used a CSI Pertpetual contract and the log normal of daily price change. If you look at a price chart perhaps the most notable features are the huge spikes in 1979 (the Hunt cornering episode I think?) and again the gigantic run up in 2011.

In terms of short term measures of volatility (3, 7 and 14 days rolling annualised standard deviation of daily returns), these two periods alone do not really stand out: there are many peaks in very short term measures of volatility and these peaks seem to have been increasing in magnitude in recent years. The longer term picture seems more moot and the picture less clear: the trend in the 100 day rolling average seems to have trended up over time, but the same can not really be said for the 500 day. And in all cases the period from 1989 to 2002 shows a lowering of volatility over all time frames.

What of the future? Who knows? In may be safest to assume that volatility over the very long term is mean reverting. No doubt greater volatility has followed increased volumes, but what of volume? If silver is less traded for any reason in the future we might reasonably expect volume and volatility to drop off.

Where does this leave us? Back where we started: we must probably rely on a "close to random walk" in terms of volume, price and volatility if we want to cover all possibilities. But there again we should probably combine such series with different assumptions in other series for the same class: assumptions that volatility will trend upwards perhaps, as will volume.

And what of price? Certainly in terms of stock indices it may be reasonable to include both scenarios: price series where a continuation of the Enlightenment continues to drive economies and hence stock markets upwards. And price series which include no inherent return or "drift" - where stock indices remain stagnant and move sideways, perhaps over many, many years.

The same with commodities. Oil and gas may be scarce resources but who says their price has to move up forever? Perhaps man will cease to rely on oil as nuclear fusion becomes a reality.

My object in investigating synthetic data is to test trend following on as wide a range of possible future conditions as I can imagine.