Scaling and multiscaling in financial series: a simple model

TL;DR

This paper introduces a simple, analytically tractable stochastic volatility model that captures key stylized facts of financial time series, including scaling, multiscaling, and crossover behaviors, with high accuracy.

Contribution

The paper presents a new simple stochastic volatility model that effectively reproduces complex scaling and multiscaling phenomena observed in financial data.

Findings

Model captures crossover from power-law to Gaussian tails

Reproduces slow decay in volatility autocorrelation

Fits key features of financial index time series accurately

Abstract

We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments. Despite its few parameters, the model is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with a remarkable accuracy.