GSH Dependence Modeling with an Application to Risk Management

Abstract

The generalized secant hyperbolic distribution (GSH) can be used to represent financial data with heavy tails as an alternative to the Student-t, because it guarantees the existence of all moments, also with a high kurtosis value. In order to obtain a multivariate extension of the GSH distribution, in this article we present two approaches to model the dependence, the copula approach and independent component analysis. Since the methodologies considered allow to simulate the GSH dependence, we show also the empirical results obtained in the estimation of risk of a financial portfolio by the Monte Carlo method.

Keywords:

• Copula approach
• Generalized secant hyperbolic (GSH) distribution
• Independent component analysis
• Risk measures

Mathematics Subject Classification:

• Primary 91B25
• Secondary 62E17
• 62H12
• 91G70

Notes

See http://mathworld.wolfram.com/Polylogarithm.html

Source: http://finance.yahoo.com

(*denotes significance at the 5% level at least).