IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.16494.html
   My bibliography  Save this paper

Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach

Author

Listed:
  • Deb Narayan Barik
  • Siddhartha P. Chakrabarty

Abstract

We present a novel approach for the bank's decision problem, incorporating Limited Liability in the objective function. Accordingly, we consider continuous time models, with and without Limited Liability. We compare the solutions of these two models to demonstrate the effect of inclusion of Limited Liability. To solve the problem with the objective function incorporating Limited Liability, we approximate the payoff function to another set of functions for which we have closed-form solutions. Then, we show that the solution with Limited Liability incorporates less risky assets, while simultaneously increasing the resilience of the bank. After that, we use the metric of $Distance~to~Default$, from the KMV Model, to analyze the bank's resiliency, by considering that the interest rate follows the Vasicek model. Finally, we illustrate the results obtained with a numerical example.

Suggested Citation

  • Deb Narayan Barik & Siddhartha P. Chakrabarty, 2025. "Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach," Papers 2507.16494, arXiv.org.
    • Handle: RePEc:arx:papers:2507.16494
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.16494
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blum, Jürg M., 2008. "Why 'Basel II' may need a leverage ratio restriction," Journal of Banking & Finance, Elsevier, vol. 32(8), pages 1699-1707, August.
    2. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2022. "Does limited liability reduce leveraged risk?: The case of loan portfolio management," Papers 2209.12636, arXiv.org.
    3. Munk, Claus & Sorensen, Carsten, 2004. "Optimal consumption and investment strategies with stochastic interest rates," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1987-2013, August.
    4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    6. Michael Puhle, 2008. "Bond Portfolio Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-76593-6, December.
    7. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    8. Hans-Werner Sinn, 2002. "Risktaking, Limited Liability, and the Competition of Bank Regulators," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 59(3), pages 305-329, August.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2022. "Does Limited Liability Reduce Leveraged Risk?: The Case of Loan Portfolio Management," JRFM, MDPI, vol. 15(11), pages 1-15, November.
    11. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2025. "Dynamic loan portfolio management in a three time step model," Papers 2501.07856, arXiv.org.
    2. Chenghu Ma, 2003. "Term Structure of Interest Rates in the Presence of Levy Jumps: The HJM Approach," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 401-426, November.
    3. Constantin Mellios, 2007. "Interest rate options valuation under incomplete information," Annals of Operations Research, Springer, vol. 151(1), pages 99-117, April.
    4. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    5. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    6. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2016. "Portfolio choice with stochastic interest rates and learning about stock return predictability," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 347-370.
    7. repec:dau:papers:123456789/5374 is not listed on IDEAS
    8. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    9. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2025. "Loan Portfolio Management and Liquidity Risk: The Impact of Limited Liability and Haircut," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 23(3), pages 713-734, September.
    10. Deb Narayan Barik & Siddhartha P. Chakrabarty, 2023. "Loan portfolio management and Liquidity Risk: The impact of limited liability and haircut," Papers 2308.06525, arXiv.org.
    11. Shao, Jia & Papaioannou, Apostolos D. & Pantelous, Athanasios A., 2017. "Pricing and simulating catastrophe risk bonds in a Markov-dependent environment," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 68-84.
    12. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    13. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    14. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    15. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    16. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    17. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    18. Sorwar, Ghulam & Barone-Adesi, Giovanni & Allegretto, Walter, 2007. "Valuation of derivatives based on single-factor interest rate models," Global Finance Journal, Elsevier, vol. 18(2), pages 251-269.
    19. Linnenluecke, Martina K. & Chen, Xiaoyan & Ling, Xin & Smith, Tom & Zhu, Yushu, 2017. "Research in finance: A review of influential publications and a research agenda," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 188-199.
    20. J. A. Nielsen & K. Sandmann, 1996. "The pricing of Asian options under stochastic interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 209-236.
    21. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," Working Papers 94-09, New York University, Leonard N. Stern School of Business, Department of Economics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2507.16494. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.