Modeling financial data using the multivariate generalized hyperbolic distribution and copula.

Abstract

Financial data usually possess some characteristics, such as volatility clustering, asymmetry, heavy and semi-heavy tails thus, making it difficult, if not impossible, to use Normal distribution to model them. Statistical analyzis shows that the Generalized hyperbolic distribution is appropriate for capturing these characteristics. This research shows that the USD/ZAR, All shares, Gold mining as well as the the S&P 500 returns are best modeled with the Skew t, generalized hyperbolic, hyperbolic, generalized hyperbolic distributions respectively based on AIC and Value-at-Risk (VAR) backtesting. Further multivariate analyzis of these returns based on the kernel smoothing goodness of fit shows that; the multivariate affine normal inverse gaussian (MANIG) distribution provides the best fit for the affine models. Likewise, the multivariate normal inverse gaussian (MNIG) distribution based on AIC provides the best model for the four returns. Finally, the positive tail dependencies exhibited between the All shares and Gold mining returns as well as All shares and S&P 500 returns is best modeled with the Gumbel and Clayton copulas respectively. While the negative dependencies between the USD/ZAR returns and other returns is modeled with the Frank copula.