A Continuous-Time Inequality Measure Applied to Financial Risk: The Case of the European Union

Abstract

In this paper, we apply information theory measures and Markov processes in order to analyse the inequality in the distribution of the financial risk in a pool of countries. The considered financial variables are sovereign credit ratings and interest rates of sovereign government bonds of European countries. This paper extends the methodology proposed in our previous work, by allowing the possibility to consider a continuous time process for the credit rating evolution so that complete observations of rating histories and credit spreads can be considered in the analysis. Obtained results suggest that the continuous time model fits real data better than the discrete one and confirm the existence of a different risk perception among the three main rating agencies: Fitch, Moody's and Standard & Poor's. The application of the model has been performed by a software we developed, the full code is available on-line allowing the replication of all results.

Randentropy: a software to measure inequality in random systems

“…This application was originally considered by D'Amico, Scocchera, and Storchi (2018b) and D'Amico, Regnault, Scocchera, and Storchi (2018a) and successively in a more comprehensive way in D' Amico et al (2019). In this framework we have a meta-community that coincides with a given set of countries all belonging to a given Economic area.…”

On the Sensitivity of a Dynamic Measure of Financial Inequality

“…The implication of a country's default and generally, of an increase of the sovereign credit risk is of crucial importance concerning both its effects on the domestic economy but also on the neighborhood economies. We have focused our attention on the financial risk in European Union by applying dynamic measure of inequality to evaluate how the financial risk is distributed among countries and to assess its behavior over time (D'Amico et al, 2018a;2018b;2019). The financial risk of a country refers to the ability to cope with its financial commitments and it is expressed by the amount of credit spread that the country has to pay on its debt.…”

“…In the present work, we are interested in gaining more insight on the influence played by rating dynamics on the evolution of the inequality process and on the sensitivity of the measure of financial risk when estimation errors occur. Thus, starting from our previous work, (D'Amico et al, 2018b), a sensitivity analysis is carried out by adding a perturbation to the generator of the CTMC, in such a way to be able to depict the possible evolution of the inequality considering the uncertainty in the specification of the generator of the Markov process. The introduction of a perturbation for Markov process has been studied in several works.…”

“…We instead rely on the continuous time homogeneous Markov chain to model the rating dynamics. The advantages of working within a continuous-time framework are well known and documented in literature (Christensen et al, 2004;Lando and Skødeberg, 2002;Jarrow et al, 1997) and for the financial problem we posed (D'Amico et al, 2018b). Applications of information theory for economic and financial problems have been advanced in (D'Amico and Regnault, 2018) where the authors proposed a dynamic extension of common poverty indices.…”