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On deposit volumes and the valuation of non-maturing liabilities

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  • Nyström, Kaj
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    Abstract

    In this paper we propose a framework for the modelling of non-maturing liabilities, the latter referring to deposits without a specific maturity or deposits whose actual time horizon significantly differs from their contractual maturity. The set of non-maturing liabilities include most of the traditional deposit accounts like demand deposits and savings accounts and form the basis of the funding for depository institutions. Our framework consists of three pieces: models for market rates, deposit rates and deposit volumes. For the market rate an extended one-factor Vasicek model is used but the framework developed is general and any other and potentially more sophisticated and accurate model for the market rate can be applied. Deposit rates are modelled using policy functions which are allowed to depend on the current market rate and the volume deposited. Concerning deposit volumes we develop a framework in which models for deposit volumes can be derived in theoretically sound way. This is done in two steps. In the first step we propose reasonable rules or strategies based on which we attempt to capture the behaviour of the individual customer. In the second step we then define notions of homogeneity in customer behaviour and use these to derive models for the behaviour of the 'average customer' and for the volumes deposited by the 'average customer'. Finally, the pieces of the framework are integrated in a valuation formula, we here use the approach of Jarrow and Van Deventer [1998. The arbitrage-free valuation and hedging of demand deposits and credit card loans. Journal of Banking and Finance 22, 249-272], and a value is assigned to a portfolio of demand deposits. This valuation formula also forms the basis for the risk management of the interest rate risk embedded in the demand deposits.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 32 (2008)
    Issue (Month): 3 (March)
    Pages: 709-756

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    Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:709-756

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    Web page: http://www.elsevier.com/locate/jedc

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    1. Kalkbrener, Michael & Willing, Jan, 2004. "Risk management of non-maturing liabilities," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1547-1568, July.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    3. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    4. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-76.
    5. 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 449-70, May.
    6. Marie-Paule Laurent, 2004. "Non-maturity deposits with a fidelity premium," Working Papers CEB 04-016.RS, ULB -- Universite Libre de Bruxelles.
    7. 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 637-54, May-June.
    8. M. Kijima & T. Suzuki, 2001. "A jump-diffusion model for pricing corporate debt securities in a complex capital structure," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 611-620.
    9. Frauendorfer, Karl & Schurle, Michael, 2003. "Management of non-maturing deposits by multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 151(3), pages 602-616, December.
    10. Hayne E. Leland., 1998. "Agency Costs, Risk Management, and Capital Structure," Research Program in Finance Working Papers RPF-278, University of California at Berkeley.
    11. 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.
    12. 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(03), pages 399-417, September.
    13. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    14. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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