IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v28y2011i1p390-395.html
   My bibliography  Save this article

The calculation of capital requirement using Extreme Value Theory

Author

Listed:
  • Tsai, Ming-Shann
  • Chen, Lien-Chuan

Abstract

The Basel Committee has suggested some formulas for calculating capital requirement using the Advanced Internal Ratings-Based Approach. However, these formulas were derived under the assumption of a normal distribution. Thus, the capital requirement estimated by the Basel formula may be incorrect when the asset distributions are not normal. Using an analysis of qualifying revolving retail exposures as an example, this paper introduces a formula based on the Extreme Value Theory to calculate the capital requirement. This formula is more general and accurate than its predecessors, because it can be used with any type of distribution. Numerical examples are provided to demonstrate that the capital requirement estimated by the Basel formula is less than by our formula when the asset distribution has a heavy tail, and more than by our formula when the distribution has a short tail. Our formula is also more sensitive to risk than competing models in the context of the recent financial crisis.

Suggested Citation

  • Tsai, Ming-Shann & Chen, Lien-Chuan, 2011. "The calculation of capital requirement using Extreme Value Theory," Economic Modelling, Elsevier, vol. 28(1), pages 390-395.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1:p:390-395
    DOI: 10.1016/j.econmod.2010.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999310001616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2010.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Edward I. Altman & Andrea Resti & Andrea Sironi, 2002. "The link between default and recovery rates: effects on the procyclicality of regulatory capital ratios," BIS Working Papers 113, Bank for International Settlements.
    2. Tor Jacobson & Jesper Lindé & Kasper Roszbach, 2005. "Credit Risk Versus Capital Requirements under Basel II: Are SME Loans and Retail Credit Really Different?," Journal of Financial Services Research, Springer;Western Finance Association, vol. 28(1), pages 43-75, October.
    3. Grané, A. & Veiga, H., 2008. "Accurate minimum capital risk requirements: A comparison of several approaches," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2482-2492, November.
    4. Gatzert, Nadine & Schmeiser, Hato, 2008. "Combining fair pricing and capital requirements for non-life insurance companies," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2589-2596, December.
    5. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    6. Perli, Roberto & Nayda, William I., 2004. "Economic and regulatory capital allocation for revolving retail exposures," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 789-809, April.
    7. Carey, Mark & Hrycay, Mark, 2001. "Parameterizing credit risk models with rating data," Journal of Banking & Finance, Elsevier, vol. 25(1), pages 197-270, January.
    8. Repullo, Rafael & Suarez, Javier, 2004. "Loan pricing under Basel capital requirements," Journal of Financial Intermediation, Elsevier, vol. 13(4), pages 496-521, October.
    9. Allen, Linda & DeLong, Gayle & Saunders, Anthony, 2004. "Issues in the credit risk modeling of retail markets," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 727-752, April.
    10. Johnston, Mark, 2009. "Extending the Basel II approach to estimate capital requirements for equity investments," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1177-1185, June.
    11. Brooks, C. & Clare, A. D. & Persand, G., 2000. "A word of caution on calculating market-based minimum capital risk requirements," Journal of Banking & Finance, Elsevier, vol. 24(10), pages 1557-1574, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shu Ling Chiang & Ming Shann Tsai, 2019. "The Valuation of Deposit Insurance Premiums Based on a Specific Bank's Official Default Probability," Multinational Finance Journal, Multinational Finance Journal, vol. 23(3-4), pages 141-167, September.
    2. Barbagli, Matteo & François, Pascal & Gauthier, Geneviève & Vrins, Frédéric, 2024. "The role of CDS spreads in explaining bond recovery rates," LIDAM Discussion Papers LFIN 2024002, Université catholique de Louvain, Louvain Finance (LFIN).
    3. Gander, James P., 2013. "Integrating bank profit and risk-avoidance decisions for selected European countries: A micro–macro analysis," Economic Modelling, Elsevier, vol. 31(C), pages 717-722.
    4. Barbagli, Matteo & Vrins, Frédéric, 2023. "Accounting for PD-LGD dependency: A tractable extension to the Basel ASRF framework," Economic Modelling, Elsevier, vol. 125(C).
    5. Frontczak, Robert & Rostek, Stefan, 2015. "Modeling loss given default with stochastic collateral," Economic Modelling, Elsevier, vol. 44(C), pages 162-170.
    6. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.

    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. Tsai, Ming-Shann & Chen, Lien-Chuan, 2011. "The calculation of capital requirement using Extreme Value Theory," Economic Modelling, Elsevier, vol. 28(1-2), pages 390-395, January.
    2. Simone Varotto, 2007. "Tests on the Accuracy of Basel II," ICMA Centre Discussion Papers in Finance icma-dp2007-09, Henley Business School, University of Reading.
    3. Grané, Aurea & Veiga, Helena, 2010. "Outliers in Garch models and the estimation of risk measures," DES - Working Papers. Statistics and Econometrics. WS ws100502, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Fenech, Jean-Pierre & Yap, Ying Kai & Shafik, Salwa, 2014. "Can the Chinese banking system continue to grow without sacrificing loan quality?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 31(C), pages 315-330.
    5. Hui, C.H. & Lo, C.F. & Wong, T.C. & Man, P.K., 2006. "Measuring provisions for collateralised retail lending," Journal of Economics and Business, Elsevier, vol. 58(4), pages 343-361.
    6. Aurea Grané & Helena Veiga, 2012. "Asymmetry, realised volatility and stock return risk estimates," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(2), pages 147-164, August.
    7. Simone Varotto, 2008. "An Assessment of the Internal Rating Based Approach in Basel II," ICMA Centre Discussion Papers in Finance icma-dp2008-04, Henley Business School, University of Reading.
    8. Clara Cardone-Riportella & Antonio Trujillo-Ponce & Anahí Briozzo, 2013. "Analyzing the role of mutual guarantee societies on bank capital requirements for small and medium-sized enterprises," Journal of Economic Policy Reform, Taylor & Francis Journals, vol. 16(2), pages 142-159, June.
    9. DAVID G. McMILLAN & ALAN E. H. SPEIGHT, 2007. "Value‐at‐Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long‐Memory GARCH Models," International Review of Finance, International Review of Finance Ltd., vol. 7(1‐2), pages 1-19, March.
    10. Jacobson, Tor & Linde, Jesper & Roszbach, Kasper, 2006. "Internal ratings systems, implied credit risk and the consistency of banks' risk classification policies," Journal of Banking & Finance, Elsevier, vol. 30(7), pages 1899-1926, July.
    11. Matthew C. Chang & Jui-Cheng Hung, 2012. "Can VAR Be Predictive for Regulation? Evidence from the Futures Industry in Taiwan," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 147-162, December.
    12. Edward Altman & Gabriele Sabato, 2005. "Effects of the New Basel Capital Accord on Bank Capital Requirements for SMEs," Journal of Financial Services Research, Springer;Western Finance Association, vol. 28(1), pages 15-42, October.
    13. Tor Jacobson & Jesper Lindé & Kasper Roszbach, 2005. "Credit Risk Versus Capital Requirements under Basel II: Are SME Loans and Retail Credit Really Different?," Journal of Financial Services Research, Springer;Western Finance Association, vol. 28(1), pages 43-75, October.
    14. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    15. Dinh, K. & Kleimeier, S., 2006. "Credit scoring for Vietnam's retail banking market : implementation and implications for transactional versus relationship lending," Research Memorandum 012, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. repec:zbw:bofrdp:2004_010 is not listed on IDEAS
    17. Dimitrakopoulos, Dimitris N. & Kavussanos, Manolis G. & Spyrou, Spyros I., 2010. "Value at risk models for volatile emerging markets equity portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 515-526, November.
    18. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    19. Luo, Weiwei & Brooks, Robert D. & Silvapulle, Param, 2011. "Effects of the open policy on the dependence between the Chinese 'A' stock market and other equity markets: An industry sector perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 21(1), pages 49-74, February.
    20. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    21. Ibrahim Ergen, 2014. "Tail dependence and diversification benefits in emerging market stocks: an extreme value theory approach," Applied Economics, Taylor & Francis Journals, vol. 46(19), pages 2215-2227, July.

    More about this item

    Keywords

    Basel accord; Extreme Value Theory; Capital requirement;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

    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:eee:ecmode:v:28:y:2011:i:1:p:390-395. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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.