Interconnected Risk Contributions: A Heavy-Tail Approach to Analyze U.S. Financial Sectors

Abstract

This paper investigates the dynamic evolution of tail risk interdependence among U.S. banks, financial services and insurance sectors. Life and non-life insurers have been considered separately to account for their different characteristics. The tail risk interdependence measurement framework relies on the multivariate Student-t Markov switching (MS) model and the multiple-conditional value-at-risk (CoVaR) (conditional expected shortfall (CoES)) risk measures introduced in Bernardi et al. (2013), accounting for both the stylized facts of financial data and the contemporaneous multiple joint distress events. The Shapley value methodology is then applied to compose the puzzle of individual risk attributions, providing a synthetic measure of tail interdependence. Our empirical investigation finds that banks appear to contribute more to the tail risk evolution of all of the remaining sectors, followed by the financial services and the insurance sectors, showing that the insurance sector significantly contributes as well to the overall risk. We also find that the role of each sector in contributing to other sectors' distress evolves over time according to the current predominant financial condition, implying different interdependence strength.

Switching generalized autoregressive score copula models with application to systemic risk

“…The dynamic conditional copula theory was first developed by Patton (), although the problem of modeling the joint comovement of stock returns was already present in Bollerslev, Engle, and Wooldridge () and Engle, Ng, and Rothschild (), among others. Furthermore, occasionally we observe breaks in the dependence structure, which are more evident during crisis periods and other infrequent events, as documented, for example, by Bernardi and Petrella () and Bernardi, Maruotti, and Petrella (). As regards dependence breaks, Markov switching (MS) models have been proven to effectively capture nonsmooth evolutions of the volatility and correlations dynamics.…”

“…In what follows, we apply the econometric framework and the methodology described in the previous sections to examine the evolution of the systemic risk in Europe over the past decade. As discussed in Billio, Getmansky, Lo, and Pelizzon (), and Bernardi and Petrella (), Bernardi, Maruotti, and Petrella (), the high level of interdependence and interconnection among financial institutions has been recognized as the main ingredient that facilitates the spread of adverse shocks affecting individual institutions (or countries) over the overall financial system. Systemic events are particularly relevant since they involve extreme losses for all the market participants threatening the stability of the entire economic and financial system.…”

Optimal Randomness for Stochastic Configuration Network (SCN) with Heavy-Tailed Distributions

“…Heavy-tailed distributions are widely used for modeling in different scenarios, such as finance [ 19 ], insurance [ 20 ], and medicine [ 21 ]. The distribution of a real-valued random variable X is said to have a heavy right tail if the tail probabilities decay more slowly than those of any exponential distribution if for every .…”

CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions

“…Using the same set of state factors and extending the idea of CoCDaR as a measure of systemic risk contribution, we propose a more comprehensive measure called multiple-CoCDaR, which measures the conditional drawdown-at-risk of the financial system conditioned on the distress levels of all I institutions being considered. The idea is an extension of the CoCDaR approach defined above by combining it with a generalization of the multiple-CoVaR method defined in Bernardi et al (2013) and Bernardi and Petrella (2014). In their paper, a similar approach was developed that defines conditional tail risk of a system/institution conditioned on the distress level of multiple institutions at the same time.…”

“…Bernardi et al (2013) noticed that the original ∆CoVaR sys|i is not a desirable risk distribution measure, because summing up ∆CoVaR sys|i for all institutions i does not generally equal their overall effect on the system. This issue is addressed in Bernardi et al (2013) and Bernardi and Petrella (2014) via the Shapley value, which transforms the calculated contribution using ∆Multiple − CoVaR to a Shapley value for each institution so that their contribution adds up to the joint contribution of all institutions together on the system. The Shapley value methodology was originally proposed to measure shared utility or cost among participants of a cooperative game.…”