Thursday, August 16, 2012

A simple way to simulate volatility clustering

Nearly a year ago I have mentioned an important characteristic of financial markets returns, i.e. volatility clustering.

This phenomenon was analyzed by Benoit Mandelbrot and presented in a work he co-authored: "A Multifractal Model of Asset Returns".

Volatility clustering is closely connected with heteroscedasticity (existence of periods of different variance) of financial times series. It can be said that volatility clustering is a special case of heteroscedasticity of time series. In presence of volatility clustering, variance is not only variable, but tends to cluster in time.

As I've mentioned in my previous post, volatility clustering needs to be addressed by risk management. But that's not all. It is also important in development of quantitative investment models, which should recognize and adapt to changes in volatility.

The simplest solution is to get rid of hetorscedasticity by normalizing the data:

But is is even more important, to understand what is really going on under the hood. For that you can generate a time series demonstrating volatility clustering behavior. Since you have full control over the simulated data, you can easily experiment with it and look for effects you can trade on.

MMAR is definitely a superior approach to simulate behavior of financial data, but sometimes a much simpler approach may be enough:

[ R code ]