Modeling stylized facts for financial time series

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). The model is tested successfully to fit joint distributions of the 100+ years of daily price returns of the Dow Jones 30 Industrial Average.