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January  2017, 2: 9 doi: 10.1186/s41546-017-0020-9

The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks

Stefan Weber , and  Kerstin Weske

Institut für Mathematische Stochastik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Received  January 15, 2017 Revised  May 30, 2017 Published  December 2017

The paper presents a comprehensive model of a banking system that integrates network effects, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium. The number of defaults corresponding to the greatest price-payment equilibrium is analyzed in several comparative case studies. These illustrate the individual and joint impact of interbank liabilities, bankruptcy costs, fire sales and cross-holdings on systemic risk. We study policy implications and regulatory instruments, including central bank guarantees and quantitative easing, the significance of last wills of financial institutions, and capital requirements.
Keywords: Systemic risk, Financial contagion, Financial network, Cross-holdings, Fire sales, Bankruptcy costs.
Mathematics Subject Classification: G01;G21;D85.
Citation: Stefan Weber, Kerstin Weske. The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 9-. doi: 10.1186/s41546-017-0020-9
References:
[1]

Amini, H, Filipović, D, Minca, A:Systemic risk with central counterparty clearing. Swiss Finance Institute Research Paper No. 13-34 (2013) Google Scholar

[2]

Amini, H, Filipović, D, Minca, A:Uniqueness of equilibrium in a payment system with liquidation costs. Oper. Res. Lett 44(1), 1-5 (2016) Google Scholar

[3]

Boucinha, M, Holton, S, Tiseno, A:Bank equity valuations and credit supply. Working Paper (2017). Google Scholar

[4]

https://www.oenb.at/dam/jcr:c49e6115-3592-45fd-8416-6ed37332e201/4 paper bank equity valuations and credit supply boucinha.pdf Google Scholar

[5]

Brioschi, F, Buzzacchi, L, Colombo, MG:Risk capital financing and the separation of ownership and control in business groups. J. Bank. Finance 13(4), 747-772 (1989) Google Scholar

[6]

Brunnermeier, MK:Deciphering the liquidity and credit crunch 2007-2008. J. Econ. Perspect 23(1), 77-100 (2009) Google Scholar

[7]

Chen, N, Liu, X, Yao, DD:An optimization view of financial systemic risk modeling:Network effect and market liquidity effect. Oper. Res 64(5), 1089-1108 (2016) Google Scholar

[8]

Cifuentes, R, Ferrucci, G, Shin, HS:Liquidity risk and contagion. J. Eur. Econ. Assoc 3(2-3), 556-566(2005) Google Scholar

[9]

Cont, R, Wagalath, L:Fire sales forensics:Measuring endogenous risk. Math. Finance 26(4), 835-866(2016) Google Scholar

[10]

Cont, R, Moussa, A, Santos, EB:Network structure and systemic risk in banking systems. Handbook on Systemic Risk, pp. 327-368. Cambridge University Press (2013) Google Scholar

[11]

Coval, J, Stafford, E:Asset fire sales (and purchases) in equity markets. J. Financial Econ 86(2), 479-512(2007) Google Scholar

[12]

Craig, B, von Peter, G:Interbank tiering and money center banks. J. Financial Intermediation 23(3), 322-347 (2014) Google Scholar

[13]

Drehmann, M, Tarashev, N:Measuring the systemic importance of interconnected banks. BIS Working Paper 342, Bank for International Settlements (2011) Google Scholar

[14]

Eisenberg, L, Noe, TH:Systemic risk in financial systems. Manag. Sci 47(7), 236-249 (2001) Google Scholar

[15]

Elliott, M, Golub, B, Jackson, MO:Financial networks and contagion. Am. Econ. Rev 104(10), 3115-3153 (2014) Google Scholar

[16]

Elsinger, H:Financial networks, cross holdings, and limited liability. Working Papers 156, Österreichische Nationalbank (Austrian Central Bank) (2009) Google Scholar

[17]

Elsinger, H, Lehar, A, Summer, M:Risk assessment for banking systems. Manage. Sci 52(9), 1301-1314(2006) Google Scholar

[18]

Erdös, P, Rényi, A:On random graphs, I. Publicationes Mathematicae (Debrecen) 6, 290-297 ((1959)) Google Scholar

[19]

Fedenia, M, Hodder, JE, Triantis, AJ:Cross-holdings:Estimation issues, biases, and distortions. Rev.Financial Stud 7(1), 61-96 (1994) Google Scholar

[20]

Feinstein, Z:Financial contagion and asset liquidation strategies. Oper. Res. Lett 45(2), 109-114 (2017) Google Scholar

[21]

Feinstein, Z, Rudloff, B, Weber, S:Measures of systemic risk. SIAM J. Financial Math (2017) Google Scholar

[22]

Fischer, T:No-arbitrage pricing under systemic risk:Accounting for cross-ownership. Math. Finance 24(1), 97-124 (2014) Google Scholar

[23]

Föllmer, H, Schied, A Stochastic Finance-An Introduction in Discrete Time, 3rd edn. De Gruyter, Berlin (2011) Google Scholar

[24]

Föllmer, H, Weber, S:The Axiomatic Approach to Risk Measurement for Capital Determination. Ann. Rev. Financial Econ 7, 301-337 (2015) Google Scholar

[25]

Gai, P, Kapadia, S:Contagion in financial networks. Bank of England Working Papers 383, Bank of England (2010) Google Scholar

[26]

Glasserman, P, Young, HP:How likely is contagion in financial networks? J. Bank. Finance 50, 383-399(2015) Google Scholar

[27]

Jotikasthira, C, Lundblad, C, Ramadorai, T:Asset fire sales and purchases and the international transmission of funding shocks. J. Finance 67(6), 2015-2050 (2012) Google Scholar

[28]

Karl, S, Fischer, T:Cross-ownership as a structural explanation for over-and underestimation of default probability. Quant Finance 14(6), 1031-1046 (2014) Google Scholar

[29]

Khandani, AE, Lo, AW:What happened to the quants in August 2007? J. Financial Markets 14(1), 1-46(2011) Google Scholar

[30]

Nier, E, Yang, J, Yorulmazer, T, Alentorn, A:Network models and financial stability. J. Econ. Dynam.Control 31(6), 2033-2060 (2007) Google Scholar

[31]

Rogers, LCG, Veraart, LAM:Failure and rescue in an interbank network. Manag. Sci 59(4), 882-898(2013) Google Scholar

[32]

Shleifer, A, Vishny, RW:Liquidation values and debt capacity:A market equilibrium approach. J. Finance 47(4), 1343-1366 (1992) Google Scholar

[33]

Shleifer, A, Vishny, RW:Fire sales in finance and macroeconomics. J. Econ. Perspect 25(1), 29-48 (2011) Google Scholar

[34]

Staum, J:Counterparty contagion in context:Contributions to systemic risk. Handbook on Systemic Risk, pp. 512-548. Cambridge University Press (2013) Google Scholar

[35]

Suzuki, T:Valuing corporate debt:The effect of cross-holdings of stock and debt. J. Oper. Res. Soc. Japan 45(2), 123-144 (2002) Google Scholar

[36]

Tarski, A:A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math 5(2), 285-309 (1955) Google Scholar

[37]

Upper, C:Using counterfactual simulations to assess the danger of contagion in interbank markets. BIS Working Papers 234, Bank for International Settlements (2007) Google Scholar

[38]

Upper, C:Simulation methods to assess the danger of contagion in interbank markets. J. Financial Stab 7(3), 111-125 (2011) Google Scholar

[39]

van Lelyfeld, I, in't Veld, D:Finding the core:Network structure in interbank markets. J. Bank. Finance 49, 27-40 (2014) Google Scholar

show all references

References:
[1]

Amini, H, Filipović, D, Minca, A:Systemic risk with central counterparty clearing. Swiss Finance Institute Research Paper No. 13-34 (2013) Google Scholar

[2]

Amini, H, Filipović, D, Minca, A:Uniqueness of equilibrium in a payment system with liquidation costs. Oper. Res. Lett 44(1), 1-5 (2016) Google Scholar

[3]

Boucinha, M, Holton, S, Tiseno, A:Bank equity valuations and credit supply. Working Paper (2017). Google Scholar

[4]

https://www.oenb.at/dam/jcr:c49e6115-3592-45fd-8416-6ed37332e201/4 paper bank equity valuations and credit supply boucinha.pdf Google Scholar

[5]

Brioschi, F, Buzzacchi, L, Colombo, MG:Risk capital financing and the separation of ownership and control in business groups. J. Bank. Finance 13(4), 747-772 (1989) Google Scholar

[6]

Brunnermeier, MK:Deciphering the liquidity and credit crunch 2007-2008. J. Econ. Perspect 23(1), 77-100 (2009) Google Scholar

[7]

Chen, N, Liu, X, Yao, DD:An optimization view of financial systemic risk modeling:Network effect and market liquidity effect. Oper. Res 64(5), 1089-1108 (2016) Google Scholar

[8]

Cifuentes, R, Ferrucci, G, Shin, HS:Liquidity risk and contagion. J. Eur. Econ. Assoc 3(2-3), 556-566(2005) Google Scholar

[9]

Cont, R, Wagalath, L:Fire sales forensics:Measuring endogenous risk. Math. Finance 26(4), 835-866(2016) Google Scholar

[10]

Cont, R, Moussa, A, Santos, EB:Network structure and systemic risk in banking systems. Handbook on Systemic Risk, pp. 327-368. Cambridge University Press (2013) Google Scholar

[11]

Coval, J, Stafford, E:Asset fire sales (and purchases) in equity markets. J. Financial Econ 86(2), 479-512(2007) Google Scholar

[12]

Craig, B, von Peter, G:Interbank tiering and money center banks. J. Financial Intermediation 23(3), 322-347 (2014) Google Scholar

[13]

Drehmann, M, Tarashev, N:Measuring the systemic importance of interconnected banks. BIS Working Paper 342, Bank for International Settlements (2011) Google Scholar

[14]

Eisenberg, L, Noe, TH:Systemic risk in financial systems. Manag. Sci 47(7), 236-249 (2001) Google Scholar

[15]

Elliott, M, Golub, B, Jackson, MO:Financial networks and contagion. Am. Econ. Rev 104(10), 3115-3153 (2014) Google Scholar

[16]

Elsinger, H:Financial networks, cross holdings, and limited liability. Working Papers 156, Österreichische Nationalbank (Austrian Central Bank) (2009) Google Scholar

[17]

Elsinger, H, Lehar, A, Summer, M:Risk assessment for banking systems. Manage. Sci 52(9), 1301-1314(2006) Google Scholar

[18]

Erdös, P, Rényi, A:On random graphs, I. Publicationes Mathematicae (Debrecen) 6, 290-297 ((1959)) Google Scholar

[19]

Fedenia, M, Hodder, JE, Triantis, AJ:Cross-holdings:Estimation issues, biases, and distortions. Rev.Financial Stud 7(1), 61-96 (1994) Google Scholar

[20]

Feinstein, Z:Financial contagion and asset liquidation strategies. Oper. Res. Lett 45(2), 109-114 (2017) Google Scholar

[21]

Feinstein, Z, Rudloff, B, Weber, S:Measures of systemic risk. SIAM J. Financial Math (2017) Google Scholar

[22]

Fischer, T:No-arbitrage pricing under systemic risk:Accounting for cross-ownership. Math. Finance 24(1), 97-124 (2014) Google Scholar

[23]

Föllmer, H, Schied, A Stochastic Finance-An Introduction in Discrete Time, 3rd edn. De Gruyter, Berlin (2011) Google Scholar

[24]

Föllmer, H, Weber, S:The Axiomatic Approach to Risk Measurement for Capital Determination. Ann. Rev. Financial Econ 7, 301-337 (2015) Google Scholar

[25]

Gai, P, Kapadia, S:Contagion in financial networks. Bank of England Working Papers 383, Bank of England (2010) Google Scholar

[26]

Glasserman, P, Young, HP:How likely is contagion in financial networks? J. Bank. Finance 50, 383-399(2015) Google Scholar

[27]

Jotikasthira, C, Lundblad, C, Ramadorai, T:Asset fire sales and purchases and the international transmission of funding shocks. J. Finance 67(6), 2015-2050 (2012) Google Scholar

[28]

Karl, S, Fischer, T:Cross-ownership as a structural explanation for over-and underestimation of default probability. Quant Finance 14(6), 1031-1046 (2014) Google Scholar

[29]

Khandani, AE, Lo, AW:What happened to the quants in August 2007? J. Financial Markets 14(1), 1-46(2011) Google Scholar

[30]

Nier, E, Yang, J, Yorulmazer, T, Alentorn, A:Network models and financial stability. J. Econ. Dynam.Control 31(6), 2033-2060 (2007) Google Scholar

[31]

Rogers, LCG, Veraart, LAM:Failure and rescue in an interbank network. Manag. Sci 59(4), 882-898(2013) Google Scholar

[32]

Shleifer, A, Vishny, RW:Liquidation values and debt capacity:A market equilibrium approach. J. Finance 47(4), 1343-1366 (1992) Google Scholar

[33]

Shleifer, A, Vishny, RW:Fire sales in finance and macroeconomics. J. Econ. Perspect 25(1), 29-48 (2011) Google Scholar

[34]

Staum, J:Counterparty contagion in context:Contributions to systemic risk. Handbook on Systemic Risk, pp. 512-548. Cambridge University Press (2013) Google Scholar

[35]

Suzuki, T:Valuing corporate debt:The effect of cross-holdings of stock and debt. J. Oper. Res. Soc. Japan 45(2), 123-144 (2002) Google Scholar

[36]

Tarski, A:A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math 5(2), 285-309 (1955) Google Scholar

[37]

Upper, C:Using counterfactual simulations to assess the danger of contagion in interbank markets. BIS Working Papers 234, Bank for International Settlements (2007) Google Scholar

[38]

Upper, C:Simulation methods to assess the danger of contagion in interbank markets. J. Financial Stab 7(3), 111-125 (2011) Google Scholar

[39]

van Lelyfeld, I, in't Veld, D:Finding the core:Network structure in interbank markets. J. Bank. Finance 49, 27-40 (2014) Google Scholar

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