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Interest rate risk in the banking book: A closed-form solution for non-maturity deposits

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  • Blöchlinger, Andreas

Abstract

I present an analytical valuation framework for the management of fixed-income instruments traded in imperfectly competitive markets, like demand deposits and credit card loans in the banking book, inter alia, to stabilize the abnormal profit margin. Banking book instruments contain embedded options such as withdrawal rights, discretionary pricing, rate clustering and zero-based floors. Analytical solutions speed up computation time to calculate valuations, earnings and risk measures like closed-form expressions for margin spreads, hedge ratios and parameter sensitivities. Asymptotically, according to martingale central limit theorems and thanks to the long-term nature of the banking book, Gaussian approximations can be applied.

Suggested Citation

  • Blöchlinger, Andreas, 2021. "Interest rate risk in the banking book: A closed-form solution for non-maturity deposits," Journal of Banking & Finance, Elsevier, vol. 125(C).
  • Handle: RePEc:eee:jbfina:v:125:y:2021:i:c:s0378426621000388
    DOI: 10.1016/j.jbankfin.2021.106080
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    1. Charles Kahn & George Pennacchi & Ben Sopranzetti, 1999. "Bank Deposit Rate Clustering: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 54(6), pages 2185-2214, December.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Steven Heston & Saikat Nandi, 2000. "Derivatives on volatility: some simple solutions based on observables," FRB Atlanta Working Paper 2000-20, Federal Reserve Bank of Atlanta.
    4. Longstaff, Francis A., 1990. "The valuation of options on yields," Journal of Financial Economics, Elsevier, vol. 26(1), pages 97-121, July.
    5. Rubinstein, Mark, 1976. "The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets," Journal of Finance, American Finance Association, vol. 31(2), pages 551-571, May.
    6. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    7. Jarrow, Robert A. & van Deventer, Donald R., 1998. "The arbitrage-free valuation and hedging of demand deposits and credit card loans," Journal of Banking & Finance, Elsevier, vol. 22(3), pages 249-272, March.
    8. Robert Jarrow & Haitao Li & Feng Zhao, 2007. "Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?," Journal of Finance, American Finance Association, vol. 62(1), pages 345-382, February.
    9. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    10. Kwangwoo Park & George Pennacchi, 2009. "Harming Depositors and Helping Borrowers: The Disparate Impact of Bank Consolidation," Review of Financial Studies, Society for Financial Studies, vol. 22(1), pages 1-40, January.
    11. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    12. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    15. Kalkbrener, Michael & Willing, Jan, 2004. "Risk management of non-maturing liabilities," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1547-1568, July.
    16. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    17. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.
    18. Alj, Abdelkamel & Azrak, Rajae & Mélard, Guy, 2014. "On conditions in central limit theorems for martingale difference arrays," Economics Letters, Elsevier, vol. 123(3), pages 305-307.
    19. Hutchison, David E. & Pennacchi, George G., 1996. "Measuring Rents and Interest Rate Risk in Imperfect Financial Markets: The Case of Retail Bank Deposits," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(3), pages 399-417, September.
    20. 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.
    21. Lee, O., 2013. "The functional central limit theorem for ARMA–GARCH processes," Economics Letters, Elsevier, vol. 121(3), pages 432-435.
    22. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    More about this item

    Keywords

    Basel committee on banking supervision (BCBS); Asset and liability management (ALM); Fourier-stieltjes transform analysis; Martingale central limit theorem; Zero lower bound;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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