Conditional risk measures in a bipartite market structure

Abstract In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations.

[1]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[2]  C. Brownlees,et al.  SRISK: A Conditional Capital Shortfall Measure of Systemic Risk , 2015 .

[3]  Oliver Kley,et al.  Bounds for randomly shared risk of heavy-tailed loss factors , 2015, 1503.03726.

[4]  Nizar Touzi,et al.  Vector-valued coherent risk measures , 2002, Finance Stochastics.

[5]  Ludger Overbeck,et al.  Systemic Risk Measures on General Measurable Spaces , 2016 .

[6]  Chen Chen,et al.  An Axiomatic Approach to Systemic Risk , 2013, Manag. Sci..

[7]  Kevin R. James,et al.  Model Risk of Risk Models , 2014 .

[8]  Markus K. Brunnermeier,et al.  Federal Reserve Bank of New York , 2009 .

[9]  Bojan Basrak.  The sample autocorrelation function of non-linear time series , 2000 .

[10]  Goetz von Peter,et al.  Natural Catastrophes and Global Reinsurance – Exploring the Linkages , 2012 .

[11]  Richard A. Davis,et al.  Regular variation of GARCH processes , 2002 .

[12]  A. Lo,et al.  A Survey of Systemic Risk Analytics , 2012 .

[13]  L. Pedersen,et al.  Measuring Systemic Risk , 2010 .

[14]  R. Ibragimov.  Portfolio diversification and value at risk under thick-tailedness , 2004 .

[15]  Xin Huang,et al.  Systemic Risk Contributions , 2011 .

[16]  Marco Frittelli,et al.  A unified approach to systemic risk measures via acceptance sets , 2015, 1503.06354.

[17]  C. Klüppelberg,et al.  Risk in a Large Claims Insurance Market with Bipartite Graph Structure , 2014, Oper. Res..

[18]  Nicole A. Lazar,et al.  Statistics of Extremes: Theory and Applications , 2005, Technometrics.

[19]  Ron Goldman,et al.  Poisson approximation , 2000, Proceedings Geometric Modeling and Processing 2000. Theory and Applications.

[20]  Stefan Weber,et al.  Measures of Systemic Risk , 2015, SIAM J. Financial Math..

[21]  Chen Zhou,et al.  Dependence Structure of Risk Factors and Diversification Effects , 2009 .

[22]  Haijun Li,et al.  Asymptotic Analysis of Multivariate Tail Conditional Expectations , 2012 .

[23]  Gregor Svindland,et al.  Risk-consistent conditional systemic risk measures , 2016, 1609.07897.

[24]  Robert F. Engle,et al.  Volatility, Correlation and Tails for Systemic Risk Measurement , 2012 .