The subject of asset bubbles and market crashes has fascinated me for more than 20 years. As an options market maker for Susquehanna International Group (“SIG”), extreme price movements were a daily source of concern. I sat next to Jeff Yass for years and watched him manage option positions in thousands of different stocks. Almost daily he would be celebrating a big win in a stock that had an unusually large move (SIG loves to own the “teenie” puts).

At some point, a very interesting question popped into my head:

Why is it that 10-sigma events happen all the time?

Current risk models and option pricing models suggest that these events should happen almost never.(1)

The science of risk management and derivative pricing revolves around one thing: estimating future prices of assets. For over 50 years the world of finance has defaulted to using a normal distribution to estimate the probabilities of future price moves. Why? Is it a physical law of the universe that asset prices follow a normal distribution? There are plenty of other statistical distributions that asset prices could follow.

So, why use the Normal distribution?

Sadly, the answer is that the normal distribution is mathematically neat and easy to use. It doesn’t work, but it’s easy to use. Some of the smartest people in the world have lost billions of dollars because they wanted to use an easy formula (i.e. Long Term Capital Management).

Over the years people began to realize that the normal distribution does a terrible job in predicting future price moves. But, instead of trying to find a distribution that does work, people decided to try to mangle the normal into something useful. They squeezed and stretched the normal with intelligent sounding terms like leptokurtosis and skew. It does work better now, but still not great.

Is There A Better Model For Stocks Than the Normal Distribution?

For many years I have been using a different distribution that works much better, and has made a fortune for the companies in which I have worked. This formula is simple, easy to use, and has the added benefit of being able to arguably identify market bubbles before they burst. As you probably know, when an asset is in the midst of a bubble, the probability of an unusually large downside move is greatly increased. The good news is that the options world does not know how to identify bubbles, and often prices the out-of-the-money puts too low.