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

TL;DR

This paper introduces a non-Gaussian stochastic model for stock returns that captures key features like volatility clustering and heavy tails using a single Brownian noise source with multi-scale feedback.

Contribution

It presents a novel multi-time scale model that explains non-Gaussian features of stock returns with a unified stochastic process.

Findings

Model reproduces volatility clustering observed in real data.

Captures slow decay of kurtosis over time.

Fits well with empirical volatility correlation decay.

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.