Financial risk analysis in multidimensional systems

Abstract

A new approach is proposed for modeling the interdependence among factors of multivariate risks, represented as matrices of interdependence measures for numerical description and a family of copulas with parameter estimates for analytical description. The approach proposed to construct a multivariate risk model in which, marginal distributions are modeled separately using elliptical distributions for measurements at the center of the samples and extreme distributions in the tails, while the dependencies between risks are modeled by copulas. The joint distribution is modeled using marginal distributions and copulas and can be applied to the analysis of risk characteristics. An approach to determining risk dependencies using the concept of mutual information within the framework of Bayesian networks has been developed. A computational experiment involving two generated, theoretically well-known three-dimensional distributions and one empirical three-dimensional distribution for exchange rates demonstrated the applicability of the proposed approach to modeling multidimensional risk.
The problem of identifying the optimal portfolio structure under active risk management and asset liquidity constraints, a multidimensional model for estimating tail risk measures is proposed. A computational experiment conducted to estimate risk measures by generating a sample yielded an estimation error of less than one percent for non-extreme quantiles. The quality of the estimation of risk deviation measures requires further refinement of the model. The quality of risk measure estimates for the tail regions of distributions indicates that the model based on a combination of marginal distributions using normal and Pareto distributions needs to be improved to describe central observations.