Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T01:03:09.716Z Has data issue: false hasContentIssue false

ASYMPTOTICS FOR SYSTEMIC RISK WITH DEPENDENT HEAVY-TAILED LOSSES

Published online by Cambridge University Press:  29 April 2021

Jiajun Liu*
Affiliation:
Department of Statistics and Actuarial Science, Xi’an Jiaotong-Liverpool University, E-Mail: [email protected]
Yang Yang
Affiliation:
Department of Statistics, Nanjing Audit University, E-Mail: [email protected]

Abstract

Systemic risk (SR) is considered as the risk of collapse of an entire system, which has played a significant role in explaining the recent financial turmoils from the insurance and financial industries. We consider the asymptotic behavior of the SR for portfolio losses in the model allowing for heavy-tailed primary losses, which are equipped with a wide type of dependence structure. This risk model provides an ideal framework for addressing both heavy-tailedness and dependence. As some extensions, several simulation experiments are conducted, where an insurance application of the asymptotic characterization to the determination and approximation of related SR capital has been proposed, based on the SR measure.

Type
Research Article
Copyright
© 2021 by Astin Bulletin. All rights reserved

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acharya, V.V. A theory of systemic risk and design of prudential bank regulation, Journal of Financial Stability 5 (2009), 224255.CrossRefGoogle Scholar
Acharya, V.V.; Engle, R.; Richardson, M. Capital shortfall: A new approach to ranking and regulating systemic risks, American Economic Review 102 (2012), 5964.CrossRefGoogle Scholar
Acharya, V.V.; Pedersen, L.H.; Philippon, T.; Richardson, M. Measuring Systemic Risk, The Review of Financial Studies 30 (2017), 247.CrossRefGoogle Scholar
Adrian, T.; Brunnermeier, M.K. CoVaR, American Economic Review 106 (2016), 17051741.CrossRefGoogle Scholar
Asimit, A. V; Furman, E.; Tang, Q.; Vernic, R. Asymptotics for risk capital allocations based on conditional tail expectation, Insurance: Mathematics and Economics 49 (2011), 310324.Google Scholar
Asimit, A.V. ; Li, J. Extremes for coherent risk measures, Insurance: Mathematics and Economics 71 (2016) 332341.Google Scholar
Asimit, A.V.; Li, J. Systemic risk: an asymptotic evaluation, ASTIN Bulletin 48 (2018), 673698.CrossRefGoogle Scholar
Asimit, A.V.; Gerrard, R.; Hou, Y.; Peng, L. Tail dependence measure for examining financial extreme co-movements, Journal of Econometrics 194 (2016), 330348.CrossRefGoogle Scholar
Balla, E.; Ergen, I.; Migueis, M. Tail dependence and indicators of systemic risk for large US depositories, Journal of Financial Stability 15 (2014), 195209.CrossRefGoogle Scholar
Bingham, N.H.; Goldie, C.M.; Teugels, J.L. Regular Variation. Cambridge University Press, Cambridge, 1987.CrossRefGoogle Scholar
Bluhm, C.; Overbeck, L.; Wagner, C. An Introduction to Credit Risk Modeling. Boca Raton, FL: CRC Press/Chapman & Hall., 2006.Google Scholar
Breiman, L. On some limit theorems similar to the arc-sin law, Theory of Probability and Its Applications 10 (1965) 323331.CrossRefGoogle Scholar
Brownlees, C.; Engle, R.F. SRISK: A conditional capital shortfall measure of systemic risk, The Review of Financial Studies 30 (2017), 4879.CrossRefGoogle Scholar
Cai, J.-J.; Einmahl, J.H.J; de Haan, L.; Zhou, C. Estimation of the marginal expected shortfall: the mean when a related variable is extreme, Journal of the Royal Statistical Society: Series B Statistical Methodology 77 (2015), 417442.CrossRefGoogle Scholar
Chen, Y.; Yuen, K.C. Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stochastic Models 25 (2009), 7689.CrossRefGoogle Scholar
Das, B.; Embrechts, P.; Fasen, V. Four theorems and a financial crisis, International Journal of Approximate Reasoning 54 (2013), 701716.CrossRefGoogle Scholar
Das, B.; Fasen, V. Risk contagion under regular variation and asymptotic tail independence, Journal of Multivariate Analysis 165 (2018), 194215.CrossRefGoogle Scholar
De Haan, L.; Zhou, C. Extreme residual dependence for random vectors and processes, Advances in Applied Probability 43 (2011), 217242.CrossRefGoogle Scholar
De Jonghe, O. Back to the basics in banking? A micro-analysis of banking system stability, Journal of Financial Intermediation 19 (2010), 387417.CrossRefGoogle Scholar
Dhaene, J.; Tsanakas, A.; Valdez, E.A.; Vanduffel, S. Optimal capital allocation principles, Journal of Risk and Insurance 79 (2012), 128.CrossRefGoogle Scholar
Embrechts, P.; Klüppelberg, C; Mikosch, T. Modelling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin, 1997.CrossRefGoogle Scholar
Erel, I.; Myers, S.C.; Read, J.A. Capital allocation. Working Paper (2013), Fisher College of Business, Ohio State University.Google Scholar
Gabaix, X. Power laws in economics and finance, Annual Review of Economics 1 (2009), 255293.CrossRefGoogle Scholar
Gabaix, X.; Gopikrishnan, P.; Plerou, V.; Stanley, H.E. Institutional investors and stock market volatility, Quarterly Journal of Economics 121 (2006), 461504.CrossRefGoogle Scholar
Geluk, J.; Tang, Q. Asymptotic tail probabilities of sums of dependent subexponential random variables, Journal of Theoretical Probability 22 (2009), 871882.CrossRefGoogle Scholar
Gravelle, T.; Li, F. Measuring systemic importance of financial institutions: An extreme value theory approach, Journal of Banking and Finance 37 (2013), 21962209.CrossRefGoogle Scholar
Gray, D.F.; Robert, C.M.; Zvi, B. Measuring and Managing Macrofinancial Risk and Financial Stability: A New Framework, ch. 05, p. 125157 in Alfaro, Rodrigo eds., Financial Stability, Monetary Policy, and Central Banking, vol. 15, Central Bank of Chile, 2011.Google Scholar
Hua, L.; Joe, H. Tail order and intermediate tail dependence of multivariate copulas, Journal of Multivariate Analysis 102 (2011), 14541471.CrossRefGoogle Scholar
Hua, L.; Joe, H. Strength of tail independence based on conditional tail expectation, Journal of Multivariate Analysis 123 (2014), 143159.CrossRefGoogle Scholar
Hyung, N.; de Vries, C.G. Portfolio diversification effects and regular variation in financial data, Allgemeines Statistiches Archiv 86 (2002), 6982.CrossRefGoogle Scholar
Hyung, N.; de Vries, C.G. Portfolio diversification effects of downside risk, Journal of Financial Econometrics 3 (2005), 107125.CrossRefGoogle Scholar
Hyung, N.; de Vries, C.G. Portfolio selection with heavy tails, Journal of Empirical Finance 14 (2007), 383400.CrossRefGoogle Scholar
Idierb, J.; Laméa, G.; Mésonnierb, J.-S. How useful is the marginal expected shortfall for the measurement of systemic exposure? A practical assessment, Journal of Banking and Finance 47 (2014), 134146.CrossRefGoogle Scholar
Kalkbrener, M. An axiomatic approach to capital allocation, Mathematical Finance 15 (2005), 425437.CrossRefGoogle Scholar
Kley, O.; Klüppelberg, C. Bounds for randomly shared risk of heavy-tailed loss factors, Extremes 19 (2016), 719733.CrossRefGoogle Scholar
Kley, O.; Klüppelberg, C.; Reinert, G. Risk in a large claims insurance market with bipartite graph structure, Operations Research 64 (2016), 11591176 CrossRefGoogle Scholar
Ledford, A.W.; Tawn, J.A. Statistics for near independence in multivariate extreme values, Biometrika 83 (1996), 169187.CrossRefGoogle Scholar
Lehar, A. Measuring systemic risk: A risk management approach, Journal of Banking and Finance 29 (2005), 25772603.CrossRefGoogle Scholar
Lehmann, E. L. Some concepts of dependence, Annals of Mathematical Statistics 37 (1966), 11371153.CrossRefGoogle Scholar
Li, J. On the joint tail behavior of randomly weighted sums of heavy-tailed random variables, Journal of Multivariate Analysis 164 (2018), 4053.CrossRefGoogle Scholar
McNeil, A.J.; Frey, R.; Embrechts, P. Quantitative Risk Management. Concepts, Techniques and Tools (revised edition). Princeton University Press, Princeton, NJ, 2015.Google Scholar
Moore, K.; Sun, P.; de Vries, C.G.; Zhou, C. The cross-section of tail risks in stock returns, MPRA Paper 45592 (2013), University Library of Munich, Germany.CrossRefGoogle Scholar
Reiss, R. Approximate Distributions of Order Statistics. Springer-Verlag, New York, 1989.CrossRefGoogle Scholar
Resnick, S.I. Extreme Values, Regular Variation, and Point Processes. Springer-Verlag, New York, 1987.CrossRefGoogle Scholar
Tang, Q.; Tang, Z.; Yang, Y. Sharp asymptotics for large portfolio losses under extreme risks, European Journal of Operational Research 276 (2019), 710722.CrossRefGoogle Scholar
Tang, Q.; Yuan, Z. Asymptotic analysis of the loss given default in the presence of multivariate regular variation, North American Actuarial Journal 17 (2013) 253271.CrossRefGoogle Scholar
Tang, Q.; Yuan, Z. Randomly weighted sums of subexponential random variables with application to capital allocation, Extremes 17 (2014), 467493.CrossRefGoogle Scholar
Tang, Q.; Yuan, Z. Interplay of insurance and financial risks with bivariate regular variation. Contribution to Extreme Value Modeling and Risk Analysis: Methods and Applications (edited by Dey, Dipak K. and Yan, Jun), 419438, CRC Press, Boca Raton, FL, 2015.Google Scholar
Yuan, Z. An asymptotic characterization of hidden tail credit risk with actuarial applications, European Actuarial Journal 7 (2017), 165192.CrossRefGoogle Scholar
Zhang, Y.; Shen, X.; Weng, C. Approximation of the tail probability of randomly weighted sums and applications, Stochastic processes and their applications 119 (2009), 655675.CrossRefGoogle Scholar
Zhou, C. Are banks too big to fail? Measuring systemic importance of financial institutions, International Journal of Central Banking 6 (2010), 205250.Google Scholar