Monday, September 12, 2011

Volatility clustering and characteristic of distribution

Benoit Mandelbrot observed that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes", what was named volatility clustering.

This behavior is not clearly visible in relation between single day changes, where randomness keeps the picture fuzzy:

Fig. Absolute one day change vs next day absolute change (S&P500)

It becomes more visible when one analyzes relations between cumulative changes over n days (say: 5-10-20-30) and the identical proceeding period:

Fig. Absolute cumulative change over n days against previous n days period (S&P500)

Hence we can assume that the distribution of expected price changes for a given period is not a constant, but depends on the previous volatility.

Volatility clustering is also the basis of the family of ARCH volatility models, used with varying successes in VaR calculation. 

So what can be done to improve the performance of volatility modeling?

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