# A copula based Markov Reward approach to the credit spread in European Union

## TL;DR

This paper introduces a novel copula-based Markov Reward methodology to analyze credit spread risks in the European Union, assessing risk distribution, total risk evolution, and contagion effects among countries.

## Contribution

It develops a new multivariate model combining Markov chains and copulas to evaluate credit spread risks and contagion in the EU, applied to real data from major rating agencies.

## Key findings

- Risk inequality and total risk increase over time with different rates per agency.
- Strong correlation observed among European countries' credit spreads.
- Dependence structure indicates significant contagion effects.

## Abstract

In this paper, we propose a methodology based on piece-wise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries' total spread allows understand any contagions in EU. The methodology is applied to real data of 24 countries for the three major agencies: Moody's, Standard and Poor's, and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency and that the dependence structure is characterized by a strong correlation between most of European countries.