Clustering of Volatility in Variable Diffusion Processes

Andrei Török∗ Department of Mathematics, University of Houston, and Institute of Mathematics of the Romanian Academy, Bucharest, Romania (Dated: March 9, 2009) Abstract Increments in financial markets have anomalous statistical properties including fat-tailed distributions and volatility clustering (i.e., the autocorrelation functions of return increments decay quickly but those of the squared increments decay slowly). One of the central questions in financial market analysis is to deduce the nature of the underlying stochastic process, given these statistical properties. We have proposed previously that financial markets evolve under a class of variable diffusion processes and have shown that these processes have fat-tailed distributions. Here we show analytically that such models also exhibit volatility clustering. To our knowledge, this is the first case where clustering of volatility is proven analytically in a model.