publication . Article . Preprint . 2018

Multivariate Shortfall Risk Allocation and Systemic Risk

Armenti, Yannick; Crépey, Stéphane; Drapeau, Samuel; Papapantoleon, Antonis;
Open Access
  • Published: 11 Apr 2018 Journal: SIAM Journal on Financial Mathematics, volume 9, pages 90-126 (eissn: 1945-497X, Copyright policy)
  • Publisher: Society for Industrial & Applied Mathematics (SIAM)
  • Country: France
Abstract
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance. We develop here a pragmatic approach to systemic risk measurement and allocation based on multivariate shortfall risk measures, where acceptable allocations are first computed and then aggregated so as to minimize costs. We analy...
Subjects
free text keywords: Finance, Applied Mathematics, Numerical Analysis, sensitivities, multivariate shortfall risk, Systemic risk, risk allocation, numerical methods, CCP default fund, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Quantitative Finance - Risk Management, Mathematics - Probability, 91G, 91B30, 91G60
26 references, page 1 of 2

[1] V. Acharya, T. P. L. Pedersen, and M. Richardson. Measuring systemic risk. SSRN 1573171, 2010.

[2] V. Acharya, R. Engle, and M. Richardson. Capital shortfall: A new approach to ranking and regulating systemic risks. American Economic Review: Papers & Proceedings, 102(3):59-64, 2012.

[3] T. Adrian and M. Brunnermeier. CoVaR. National Bureau of Economic Research Working Paper, 1745, 2011.

[4] P. Artzner, F. Delbaen, J. M. Eber, and D. Heath. Coherent measures of risk. Mathematical Finance, 9:203-228, 1999. [OpenAIRE]

[5] C. Bayer, H. Hoel, E. von Schwerin, and R. Tempone. On nonasymptotic optimal stopping criteria in Monte Carlo simulations. SIAM Journal on Scientific Computing, 36:A869-A885, 2014.

[6] A. Ben-Tal and M. Teboulle. An old-new concept of convex risk measures: the optimized certainty equivalent. Mathematical Finance, 17(3):449-476, 2007.

[7] F. Biagini, J.-P. Fouque, M. Frittelli, and T. Meyer-Brandis. A unified approach to systemic risk measures via acceptance sets. arXiv:1503.06354, 2015.

[8] C. Brownlees and R. Engle. Volatility, correlation and tails for systemic risk measurement. SSRN 1611229, 2012. [OpenAIRE]

[9] M. K. Brunnemeier and P. Cheridito. Measuring and allocating systemic risk. SSRN 2372472, 2014.

[10] I. Cascos and I. Molchanov. Multivariate risk measures: a constructive approach based on selections. Mathematical Finance, 2014. Forthcoming.

[11] P. Cheridito and T. Li. Risk measures on Orlicz hearts. Mathematical Finance, 19(2):189-214, 2009. [OpenAIRE]

[12] R. Cont, E. Santos, and A. Moussa. Network structure and systemic risk in banking systems. In J.-P. Fouque and J. Langsam, editors, Handbook of Systemic Risk. Cambridge University Press, 2013. [OpenAIRE]

[13] S. Drapeau and M. Kupper. Risk preferences and their robust representation. Mathematics of Operations Research, 28(1):28-62, 2013.

[14] S. Drapeau, M. Kupper, and A. Papapantoleon. A Fourier approach to the computation of CV@R and optimized certainty equivalents. Journal of Risk, 16(6):3-29, 2014.

[15] E. Eberlein, K. Glau, and A. Papapantoleon. Analysis of Fourier transform valuation formulas and applications. Applied Mathematical Finance, 17:211-240, 2010. [OpenAIRE]

26 references, page 1 of 2
Related research
Abstract
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance. We develop here a pragmatic approach to systemic risk measurement and allocation based on multivariate shortfall risk measures, where acceptable allocations are first computed and then aggregated so as to minimize costs. We analy...
Subjects
free text keywords: Finance, Applied Mathematics, Numerical Analysis, sensitivities, multivariate shortfall risk, Systemic risk, risk allocation, numerical methods, CCP default fund, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], Quantitative Finance - Risk Management, Mathematics - Probability, 91G, 91B30, 91G60
26 references, page 1 of 2

[1] V. Acharya, T. P. L. Pedersen, and M. Richardson. Measuring systemic risk. SSRN 1573171, 2010.

[2] V. Acharya, R. Engle, and M. Richardson. Capital shortfall: A new approach to ranking and regulating systemic risks. American Economic Review: Papers & Proceedings, 102(3):59-64, 2012.

[3] T. Adrian and M. Brunnermeier. CoVaR. National Bureau of Economic Research Working Paper, 1745, 2011.

[4] P. Artzner, F. Delbaen, J. M. Eber, and D. Heath. Coherent measures of risk. Mathematical Finance, 9:203-228, 1999. [OpenAIRE]

[5] C. Bayer, H. Hoel, E. von Schwerin, and R. Tempone. On nonasymptotic optimal stopping criteria in Monte Carlo simulations. SIAM Journal on Scientific Computing, 36:A869-A885, 2014.

[6] A. Ben-Tal and M. Teboulle. An old-new concept of convex risk measures: the optimized certainty equivalent. Mathematical Finance, 17(3):449-476, 2007.

[7] F. Biagini, J.-P. Fouque, M. Frittelli, and T. Meyer-Brandis. A unified approach to systemic risk measures via acceptance sets. arXiv:1503.06354, 2015.

[8] C. Brownlees and R. Engle. Volatility, correlation and tails for systemic risk measurement. SSRN 1611229, 2012. [OpenAIRE]

[9] M. K. Brunnemeier and P. Cheridito. Measuring and allocating systemic risk. SSRN 2372472, 2014.

[10] I. Cascos and I. Molchanov. Multivariate risk measures: a constructive approach based on selections. Mathematical Finance, 2014. Forthcoming.

[11] P. Cheridito and T. Li. Risk measures on Orlicz hearts. Mathematical Finance, 19(2):189-214, 2009. [OpenAIRE]

[12] R. Cont, E. Santos, and A. Moussa. Network structure and systemic risk in banking systems. In J.-P. Fouque and J. Langsam, editors, Handbook of Systemic Risk. Cambridge University Press, 2013. [OpenAIRE]

[13] S. Drapeau and M. Kupper. Risk preferences and their robust representation. Mathematics of Operations Research, 28(1):28-62, 2013.

[14] S. Drapeau, M. Kupper, and A. Papapantoleon. A Fourier approach to the computation of CV@R and optimized certainty equivalents. Journal of Risk, 16(6):3-29, 2014.

[15] E. Eberlein, K. Glau, and A. Papapantoleon. Analysis of Fourier transform valuation formulas and applications. Applied Mathematical Finance, 17:211-240, 2010. [OpenAIRE]

26 references, page 1 of 2
Related research
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