Conditional Extremes in Asymmetric Financial Markets

ABSTRACT

The global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative.

KEY WORDS:

• Asymmetry
• Backtesting
• Bivariate skew-t distribution
• Bivariate skew-elliptical distribution
• Conditional extremes
• CoVaR
• Heavy tails
• Multivariate regular variation
• Risk contagion
• Systemic risk.

ACKNOWLEDGMENTS

We are grateful to the editor and two referees for many useful suggestions, which lead to a substantial improvement of the manuscript. The project was supported through the Discovery Grant of the Natural Sciences and Engineering Research Council of Canada.