Analysis of Financial Risks Interaction

Financial risk management requires adequate modeling of multivariate distributions that reflect non-linear and asymmetric dependence structures, especially in the tails of distributions. Traditional correlation-based approaches are insufficient for capturing complex risk interactions. Therefore, copula theory provides a flexible framework for separating marginal behavior from dependence structure. The purpose of the work is to investigate the applicability of special copula functions for constructing formal multivariate probabilistic models of interacting financial risks and to evaluate their effectiveness in practical risk problems. The methodology is based on applying copula theory to construct multivariate probabilistic models of interacting financial risks. Joint distributions are modeled using generated three-dimensional Cauchy, Student-t, and normal distributions, as well as empirical currency exchange rate data. Heavy-tailed marginal distributions are built using threshold-based approaches and then combined into joint models through Archimedean (Gumbel, Clayton, Frank) and elliptical (Gaussian, Student-t) copulas. Parameter estimation is carried out using a two-step maximum likelihood procedure. The proposed framework is validated through computational experiments with both theoretical and empirical data. The scientific novelty consists in developing an integrated approach to modeling financial risk interaction by combining heavy-tailed marginal distributions with flexible copula-based dependence structures. The study refines the two-step maximum likelihood estimation procedure for joint models constructed from marginals and copulas and provides a comparative analysis of several copula families for capturing complex, non-linear, and asymmetric dependence. The results support the integration of the proposed approach into intellectual decision support systems for financial risk management. Conclusions. The study confirms the effectiveness of copula-based modeling for describing complex dependence structures between financial risks. The proposed combined marginal modeling and two-step parameter estimation procedure allow accurate construction of multivariate distributions, including tail dependence effects. The computational experiments demonstrate practical applicability of the approach. Future research will focus on expanding copula families and developing methods for estimating portfolio risk measures within an intellectual decision support framework.