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Measuring banks’ liquidity risk: An option-pricing approach

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  • Zhang, Jinqing
  • He, Liang
  • An, Yunbi

Abstract

This paper proposes a new approach to evaluating banks’ liquidity needs, which is not only well-grounded theoretically, but is also easy to apply practically. Within the framework of a global game with imperfect information, we first establish a boundary condition for bank runs and show that there exists a unique Nash equilibrium for bank runs. Using the option-pricing approach, we then obtain a closed-form formula for the value of bank equity with both run risk and insolvency risk. Finally, a bank's optimal liquidity ratio is derived by maximizing the value of bank equity. Using data on Chinese listed banks, we show that the deviation of the actual liquidity ratio from the optimal liquidity ratio in a bank represents a robust proxy for its liquidity risk. An increased liquidity shortfall leads to worsening liquidity problems, and this is particularly pronounced when the liquidity shortfall is high.

Suggested Citation

  • Zhang, Jinqing & He, Liang & An, Yunbi, 2020. "Measuring banks’ liquidity risk: An option-pricing approach," Journal of Banking & Finance, Elsevier, vol. 111(C).
    • Handle: RePEc:eee:jbfina:v:111:y:2020:i:c:s0378426619302778
    DOI: 10.1016/j.jbankfin.2019.105703
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    as
    1. Goodhart, Charles A.E. & Huang, Haizhou, 2005. "The lender of last resort," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1059-1082, May.
    2. Ricardo J. Caballero & Arvind Krishnamurthy, 2008. "Collective Risk Management in a Flight to Quality Episode," Journal of Finance, American Finance Association, vol. 63(5), pages 2195-2230, October.
    3. Hugonnier, Julien & Morellec, Erwan, 2017. "Bank capital, liquid reserves, and insolvency risk," Journal of Financial Economics, Elsevier, vol. 125(2), pages 266-285.
    4. Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
    5. Jean-Charles Rochet & Xavier Vives, 2004. "Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All?," Journal of the European Economic Association, MIT Press, vol. 2(6), pages 1116-1147, December.
    6. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    7. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    8. Douglas W. Diamond & Raghuram G. Rajan, 2011. "Fear of Fire Sales, Illiquidity Seeking, and Credit Freezes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 557-591.
    9. Postlewaite, Andrew & Vives, Xavier, 1987. "Bank Runs as an Equilibrium Phenomenon," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 485-491, June.
    10. Morris, Stephen & Shin, Hyun Song, 2004. "Coordination risk and the price of debt," European Economic Review, Elsevier, vol. 48(1), pages 133-153, February.
    11. Douglas W. Diamond & Raghuram G. Rajan, 2005. "Liquidity Shortages and Banking Crises," Journal of Finance, American Finance Association, vol. 60(2), pages 615-647, April.
    12. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    13. Mella-Barral, Pierre & Perraudin, William, 1997. "Strategic Debt Service," Journal of Finance, American Finance Association, vol. 52(2), pages 531-556, June.
    14. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    15. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    16. Brunnermeier, Markus K., 2001. "Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding," OUP Catalogue, Oxford University Press, number 9780198296980, Decembrie.
    17. Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," The Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
    18. Charitou, Andreas & Dionysiou, Dionysia & Lambertides, Neophytos & Trigeorgis, Lenos, 2013. "Alternative bankruptcy prediction models using option-pricing theory," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2329-2341.
    19. Diamond, D.W. & Kashyap, A.K., 2016. "Liquidity Requirements, Liquidity Choice, and Financial Stability," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 2263-2303, Elsevier.
    20. Merton, Robert C, 1987. "A Simple Model of Capital Market Equilibrium with Incomplete Information," Journal of Finance, American Finance Association, vol. 42(3), pages 483-510, July.
    21. Merton, Robert C., 1977. "An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory," Journal of Banking & Finance, Elsevier, vol. 1(1), pages 3-11, June.
    22. John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-1244, September.
    23. Gorton, Gary & Metrick, Andrew, 2012. "Securitized banking and the run on repo," Journal of Financial Economics, Elsevier, vol. 104(3), pages 425-451.
    24. Zhiguo He & Wei Xiong, 2012. "Dynamic Debt Runs," Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1799-1843.
    25. Iván Werning & George-Marios Angeletos, 2006. "Crises and Prices: Information Aggregation, Multiplicity, and Volatility," American Economic Review, American Economic Association, vol. 96(5), pages 1720-1736, December.
    26. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    27. Michael Ewens & Charles M. Jones & Matthew Rhodes-Kropf, 2013. "The Price of Diversifiable Risk in Venture Capital and Private Equity," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1854-1889.
    28. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    29. Robert F. Stambaugh & Jianfeng Yu & Yu Yuan, 2015. "Arbitrage Asymmetry and the Idiosyncratic Volatility Puzzle," Journal of Finance, American Finance Association, vol. 70(5), pages 1903-1948, October.
    30. Yorulmazer, Tanju, 2003. "Herd Behavior, Bank Runs and Information Disclosure," MPRA Paper 9513, University Library of Munich, Germany.
    31. Acharya, Viral & Naqvi, Hassan, 2012. "The seeds of a crisis: A theory of bank liquidity and risk taking over the business cycle," Journal of Financial Economics, Elsevier, vol. 106(2), pages 349-366.
    32. Cornett, Marcia Millon & McNutt, Jamie John & Strahan, Philip E. & Tehranian, Hassan, 2011. "Liquidity risk management and credit supply in the financial crisis," Journal of Financial Economics, Elsevier, vol. 101(2), pages 297-312, August.
    33. Nils Friewald & Christian Wagner & Josef Zechner, 2014. "The Cross-Section of Credit Risk Premia and Equity Returns," Journal of Finance, American Finance Association, vol. 69(6), pages 2419-2469, December.
    34. Gu, Chao, 2011. "Herding and bank runs," Journal of Economic Theory, Elsevier, vol. 146(1), pages 163-188, January.
    35. Tobias Adrian & Hyun Song Shin, 2009. "Money, Liquidity, and Monetary Policy," American Economic Review, American Economic Association, vol. 99(2), pages 600-605, May.
    36. Ronn, Ehud I & Verma, Avinash K, 1986. "Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model," Journal of Finance, American Finance Association, vol. 41(4), pages 871-895, September.
    37. Douglas W. Diamond & Raghuram G. Rajan, 2001. "Liquidity Risk, Liquidity Creation, and Financial Fragility: A Theory of Banking," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 287-327, April.
    38. Allen N. Berger & Christa H. S. Bouwman, 2009. "Bank Liquidity Creation," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3779-3837, September.
    39. Goodhart, Charles A E, 1999. "Myths about the Lender of Last Resort," International Finance, Wiley Blackwell, vol. 2(3), pages 339-360, November.
    40. Evan Gatev & Philip E. Strahan, 2006. "Banks' Advantage in Hedging Liquidity Risk: Theory and Evidence from the Commercial Paper Market," Journal of Finance, American Finance Association, vol. 61(2), pages 867-892, April.
    41. Dan Covitz & Chris Downing, 2007. "Liquidity or Credit Risk? The Determinants of Very Short‐Term Corporate Yield Spreads," Journal of Finance, American Finance Association, vol. 62(5), pages 2303-2328, October.
    42. Itay Goldstein & Ady Pauzner, 2005. "Demand–Deposit Contracts and the Probability of Bank Runs," Journal of Finance, American Finance Association, vol. 60(3), pages 1293-1327, June.
    43. C.A.E. Goodhart, 1999. "Myths about the Lender of Last Resort," International Finance, Wiley Blackwell, vol. 2(3), pages 339-360, November.
    44. Jan Ericsson & Olivier Renault, 2006. "Liquidity and Credit Risk," Journal of Finance, American Finance Association, vol. 61(5), pages 2219-2250, October.
    45. Tobias Adrian & Hyun Song Shin, 2008. "Liquidity, monetary policy, and financial cycles," Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 14(Jan).
    46. Fecht, Falko & Nyborg, Kjell G. & Rocholl, Jörg, 2011. "The price of liquidity: The effects of market conditions and bank characteristics," Journal of Financial Economics, Elsevier, vol. 102(2), pages 344-362.
    47. Wagner, Wolf, 2007. "The liquidity of bank assets and banking stability," Journal of Banking & Finance, Elsevier, vol. 31(1), pages 121-139, January.
    48. Tobias Adrian & Hyun Song Shin, 2008. "Liquidity and financial cycles," BIS Working Papers 256, Bank for International Settlements.
    49. Adrian, Tobias & Shin, Hyun Song, 2010. "Liquidity and leverage," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 418-437, July.
    50. Imbierowicz, Björn & Rauch, Christian, 2014. "The relationship between liquidity risk and credit risk in banks," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 242-256.
    51. Roberto Chang & Andres Velasco, 2001. "A Model of Financial Crises in Emerging Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 489-517.
    52. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    53. Viral V. Acharya & Hamid Mehran & Rangarajan K. Sundaram, 2016. "Cash holdings and bank compensation," Economic Policy Review, Federal Reserve Bank of New York, issue Aug, pages 77-83.
    54. Maria Vassalou & Yuhang Xing, 2004. "Default Risk in Equity Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 831-868, April.
    55. Ratnovski, Lev, 2009. "Bank liquidity regulation and the lender of last resort," Journal of Financial Intermediation, Elsevier, vol. 18(4), pages 541-558, October.
    56. Viral V. Acharya & Nada Mora, 2015. "A Crisis of Banks as Liquidity Providers," Journal of Finance, American Finance Association, vol. 70(1), pages 1-43, February.
    57. Nicholas Barberis & Ming Huang & Tano Santos, 2001. "Prospect Theory and Asset Prices," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(1), pages 1-53.
    58. Sreedhar T. Bharath & Tyler Shumway, 2008. "Forecasting Default with the Merton Distance to Default Model," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1339-1369, May.
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