American Institute of Mathematical Sciences

Advanced
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)

[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)

[3]

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

[4]

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

[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)

[6]

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

[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)

[8]

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

[9]

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

[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)

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

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

[21]

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

[22]

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

[23]

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

[24]

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

[25]

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

[26]

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

[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)

[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)

[29]

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

[30]

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

[31]

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

[32]

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

[33]

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

[34]

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

[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)

[36]

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

[37]

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

[38]

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

[39]

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

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)

[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)

[3]

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

[4]

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

[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)

[6]

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

[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)

[8]

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

[9]

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

[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)

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

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

[21]

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

[22]

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

[23]

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

[24]

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

[25]

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

[26]

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

[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)

[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)

[29]

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

[30]

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

[31]

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

[32]

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

[33]

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

[34]

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

[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)

[36]

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

[37]

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

[38]

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

[39]

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

[1]

Shou Chen, Chen Xiao. Financial risk contagion and optimal control. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022070
[2]

Alireza Bahiraie, A.K.M. Azhar, Noor Akma Ibrahim. A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy. Journal of Industrial and Management Optimization, 2011, 7 (4) : 947-965. doi: 10.3934/jimo.2011.7.947
[3]

Qiong Liu, Ahmad Reza Rezaei, Kuan Yew Wong, Mohammad Mahdi Azami. Integrated modeling and optimization of material flow and financial flow of supply chain network considering financial ratios. Numerical Algebra, Control and Optimization, 2019, 9 (2) : 113-132. doi: 10.3934/naco.2019009
[4]

Alfredo Daniel Garcia, Martin Andrés Szybisz. Financial liquidity: An emergent phenomena. Journal of Dynamics and Games, 2020, 7 (3) : 209-224. doi: 10.3934/jdg.2020015
[5]

Reetabrata Mookherjee, Benjamin F. Hobbs, Terry L. Friesz, Matthew A. Rigdon. Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints. Journal of Industrial and Management Optimization, 2008, 4 (3) : 425-452. doi: 10.3934/jimo.2008.4.425
[6]

Jan Lorenz, Stefano Battiston. Systemic risk in a network fragility model analyzed with probability density evolution of persistent random walks. Networks and Heterogeneous Media, 2008, 3 (2) : 185-200. doi: 10.3934/nhm.2008.3.185
[7]

Ioannis Baltas, Anastasios Xepapadeas, Athanasios N. Yannacopoulos. Robust portfolio decisions for financial institutions. Journal of Dynamics and Games, 2018, 5 (2) : 61-94. doi: 10.3934/jdg.2018006
[8]

Robert Elliott, Dilip B. Madan, Tak Kuen Siu. Lower and upper pricing of financial assets. Probability, Uncertainty and Quantitative Risk, 2022, 7 (1) : 45-66. doi: 10.3934/puqr.2022004
[9]

P. Daniele, S. Giuffrè, S. Pia. Competitive financial equilibrium problems with policy interventions. Journal of Industrial and Management Optimization, 2005, 1 (1) : 39-52. doi: 10.3934/jimo.2005.1.39
[10]

Emmanuel Frénod, Jean-Philippe Gouigoux, Landry Touré. Modeling and solving alternative financial solutions seeking. Journal of Industrial and Management Optimization, 2015, 11 (1) : 145-170. doi: 10.3934/jimo.2015.11.145
[11]

Francesca Biagini, Jacopo Mancin. Financial asset price bubbles under model uncertainty. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 14-. doi: 10.1186/s41546-017-0026-3
[12]

Sergey V Lototsky, Henry Schellhorn, Ran Zhao. An infinite-dimensional model of liquidity in financial markets. Probability, Uncertainty and Quantitative Risk, 2021, 6 (2) : 117-138. doi: 10.3934/puqr.2021006
[13]

Ankhbayar Chuluunbaatar, Burmaa Galaa, Enkhbat Rentsen. Application of sphere packing theory in financial management. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022092
[14]

Dingjun Yao, Rongming Wang, Lin Xu. Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission. Journal of Industrial and Management Optimization, 2015, 11 (2) : 461-478. doi: 10.3934/jimo.2015.11.461
[15]

Pawan Lingras, Farhana Haider, Matt Triff. Fuzzy temporal meta-clustering of financial trading volatility patterns. Big Data & Information Analytics, 2018  doi: 10.3934/bdia.2017018
[16]

Qihong Chen. Recovery of local volatility for financial assets with mean-reverting price processes. Mathematical Control and Related Fields, 2018, 8 (3&4) : 625-635. doi: 10.3934/mcrf.2018026
[17]

Yingxu Tian, Junyi Guo, Zhongyang Sun. Optimal mean-variance reinsurance in a financial market with stochastic rate of return. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1887-1912. doi: 10.3934/jimo.2020051
[18]

Xiaoyu Xing, Caixia Geng. Optimal investment-reinsurance strategy in the correlated insurance and financial markets. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021120
[19]

Dimitra C. Antonopoulou, Marina Bitsaki, Georgia Karali. The multi-dimensional stochastic Stefan financial model for a portfolio of assets. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1955-1987. doi: 10.3934/dcdsb.2021118
[20]

Gonca Yıldırım, Ayyuce Aydemir-Karadag. Designing an annual leave scheduling policy: Case of a financial center. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2927-2958. doi: 10.3934/jimo.2021097

 Impact Factor: 

Tools

Metrics

  • PDF downloads (37)
  • HTML views (585)
  • Cited by (20)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy