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

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.

Comment added pertaining to volatility autocorrelation, clarifying approximation used in calculation

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Cited by in corpus (5)

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• A Dynamic Bayesian Model for Interpretable Decompositions of Market Behaviour
• Nonlinear Stochastic Model of Return matching to the data of New York and Vilnius Stock Exchanges
• Minding impacting events in a model of stochastic variance