Switching generalized autoregressive score copula models with application to systemic risk

Abstract

Recent financial disasters have emphasized the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme events strongly relies on their flexibility to account for the highly nonlinear and asymmetric dependence patterns observed in financial time series. In this paper, we develop a new class of flexible copula models where the dependence parameters evolve according to a Markov switching generalized autoregressive score (GAS) dynamics. Maximum likelihood estimation is performed using a two-step procedure where the second step relies on the expectation-maximization algorithm. The proposed switching GAS copula models are then used to estimate the conditional value at risk and the conditional expected shortfall, measuring the impact on an institution of extreme events affecting another institution or the market. The empirical investigation, conducted on a panel of European regional portfolios, reveals that the proposed model is able to explain and predict the evolution of the systemic risk contributions over the period 1999-2015.Recent financial disasters have emphasized the need to accurately predict extreme financial losses and their consequences for institutions' financial health and, more generally, for the safety of the broader economy. As a consequence of the ever increasing level of interconnection between economies, markets, and institutions, recent financial crises feature similar ingredients. Indeed, the recent global financial crisis of 2007-2008 and the European sovereign debt crisis of 2010-2011 have been characterized by the spread of the financial turmoil from the banking sector to the whole economy, leading to sharp economic downturns and recessions. A large empirical literature focusing on the propagation mechanisms provides evidence that, during huge crisis episodes, the failure of banks and financial institutions triggers other nonfinancial institutions through the balance sheet and liquidity channels, threatening the stability of real economy (see, e.g., (Adrian & Shin, 2010;Brunnermeier, 2009;Brunnermeier & Pedersen, 2009).The ability of econometric models to account for the negative consequences for the overall financial system of such extreme events strongly relies on their flexibility to feature the highly nonlinear and asymmetric dependence structures of financial returns. Over the years, the correlation coefficient has emerged as the most natural measure of dependence. However, despite its widespread use, the correlation fails to capture the important tails behavior of the joint probability distribution (see, e.g., Embrechts, McNeil, & Straumann, 1999, 2002. Hence modeling the tail dependence and the asymmetric dependence between pairs of assets has been becoming increasingly more important in today's financial markets. Furthermore, the linear correlation coefficient as a measure of dependence is usually associated with the assumption of J Appl Econ. 2019;34:43-65...

Allocation of risk capital in a cost cooperative game induced by a modified expected shortfall

“…Our aim is to assess how the events related to the European sovereign debt crisis impact the safety of the most important economy in the Euro area, using the provided risk measure and the associated risk measurement framework based on the cooperative game. A similar empirical investigation has been conducted by Bernardi and Catania (2015) using stock market data of the major European financial indexes, using dynamic Generalised Autoregressive Score (GAS) models on CDS, and Engle et al (2014) again using stock market data of European individual institutions, and Blasques et al (2014) using spatial GAS models on European sovereign debt CDS.…”

“…The Gaussian assumption is not only convenient but it represents also a common choice for practical applications, and it favours the interpretation of the estimation results as the output of a graphical model, see Koller and Friedman (2009). Nevertheless the Gaussian distribution can be easily replaced by either another parametric distribution or by more involved dynamic models that describe the evolution over time of the CDS, see, for example, Bernardi and Catania (2015). Proposition 16 in Appendix 6 provides the analytical formulas to calculate V aR, ES, SCoV aR and SCoES under the Gaussian assumption.…”

“…The assessment of financial risk in a multi-institution framework when some institutions are subject to systemic or non-systemic distress is one of the main topics of the latest years which received large attention from scholars in Mathematical Finance, Statistics, Management, see, e.g., Brunnermeier (2011, 2016), Billio et al (2012), Acharya et al (2012), Girardi and Ergün (2013), Hautsch et al (2014), Engle et al (2014), , Bernardi and Catania (2015), Sordo et al (2015), just to quote a few of the most relevant approaches. For an extensive and up to date survey on systemic risk measures, see Bisias et al (2012), while the recent literature on systemic risk is reviewed by Benoit et al (2016).…”

Portfolio optimisation under flexible dynamic dependence modelling

“…Time-varying copulas have been successfully employed in empirical works such as in Rodriguez (2007), De Lira Salvatierra and Patton (2015) and Bernardi and Catania (2015).…”

“…For this reason, we propose a new specification for the evolution of the conditional correlation matrix of elliptical copulas relying on the famous Dynamic Conditional Correlation (DCC) specification of Engle (2002a) and Tse and Tsui (2002), and the extension of Cappiello et al (2006). Moreover, as in Billio and Caporin (2005) and, more recently, Bernardi and Catania (2015), we also allow for the dynamic evolution of the conditional correlation matrix to depend upon the realisation of a first order Markovian process. More precisely, our model allows for different dynamic behaviours of the underlying dependence process in each specific state of the nature, as in Billio and Caporin (2005) and Bernardi and Catania (2015), but it additionally includes exogenous regressors in the dependence structure conditional to the latent state.…”