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Bayesian inference for CoVaR

Author

Listed:
  • Mauro Bernardi
  • Ghislaine Gayraud
  • Lea Petrella

Abstract

Recent financial disasters emphasised the need to investigate the consequence associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting market participants' risk capital. Commonly used risk management tools fail to account for potential spillover effects among institutions because they provide individual risk assessment. We contribute to analyse the interdependence effects of extreme events providing an estimation tool for evaluating the Conditional Value-at-Risk (CoVaR) defined as the Value-at-Risk of an institution conditioned on another institution being under distress. In particular, our approach relies on Bayesian quantile regression framework. We propose a Markov chain Monte Carlo algorithm exploiting the Asymmetric Laplace distribution and its representation as a location-scale mixture of Normals. Moreover, since risk measures are usually evaluated on time series data and returns typically change over time, we extend the CoVaR model to account for the dynamics of the tail behaviour. Application on U.S. companies belonging to different sectors of the Standard and Poor's Composite Index (S&P500) is considered to evaluate the marginal contribution to the overall systemic risk of each individual institution

Suggested Citation

  • Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
  • Handle: RePEc:arx:papers:1306.2834
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    References listed on IDEAS

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    1. Julia Schaumburg, 2010. "Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory," SFB 649 Discussion Papers SFB649DP2010-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    6. Adams, Zeno & Füss, Roland & Gropp, Reint, 2014. "Spillover Effects among Financial Institutions: A State-Dependent Sensitivity Value-at-Risk Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(03), pages 575-598, June.
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    8. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
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    11. Richard H. Gerlach & Cathy W. S. Chen & Nancy Y. C. Chan, 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 481-492, October.
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    Cited by:

    1. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    2. Gabriela Anghelache & Dumitru-Cristian Oanea, 2014. "Main Romanian Commercial Banks’ Systemic Risk during Financial Crisis: a CoVar Approach," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 6(2), pages 069-080, December.

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