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Bayesian inference for CoVaR

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Author Info

  • 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

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File URL: http://arxiv.org/pdf/1306.2834
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1306.2834.

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Date of creation: Jun 2013
Date of revision: Nov 2013
Handle: RePEc:arx:papers:1306.2834

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Web page: http://arxiv.org/

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  1. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, October.
  2. Bernardi, Mauro, 2012. "Risk measures for Skew Normal mixtures," MPRA Paper 39828, University Library of Munich, Germany.
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  8. 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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  18. Bernardi, Mauro & Maruotti, Antonello & Lea, Petrella, 2012. "Skew mixture models for loss distributions: a Bayesian approach," MPRA Paper 39826, University Library of Munich, Germany.
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