A multi-time scale non-Gaussian model of stock returns

Lisa Borland

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arXiv · cond-mat/0412526

A multi-time scale non-Gaussian model of stock returns

Lisa Borland

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Abstract

We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock returns. These include volatility clustering, a kurtosis which decreases slowly over time together with a close to log-normal distribution of instantaneous volatility. We calculate the rate of decay of volatility-volatility correlations, which depends on the strength of the memory in the system and fits well to empirical observations.

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Lisa Borland. 2005-01-24. A multi-time scale non-Gaussian model of stock returns. https://arxiv.org/abs/cond-mat/0412526

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