Multivariate distribution of returns in financial time series

TL;DR

This paper develops multivariate probability density functions to model empirical features of financial returns, including heavy tails, volatility clustering, and leverage effects, based on over a century of Dow Jones data.

Contribution

It introduces a novel multivariate distribution model that captures key empirical behaviors of financial returns and is applicable for derivative pricing and risk management.

Findings

Model accurately describes heavy tails and volatility clustering.

Parameters fixed using 100+ years of data.

Applicable for derivative pricing and risk management.

Abstract

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Free parameters of the model are fixed over the long term by fitting 100+ years of daily prices of the Dow Jones 30 Industrial Average. The multivariate probability density functions which we have constructed can be used for pricing derivative securities and risk management.