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Risk Management of Interest Rate Derivative Portfolios: A Stochastic Control Approach

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  • Konstantinos Kiriakopoulos

    (Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, GR-157 04 Athens, Greece)

  • Alexandros Koulis

    (Department of Business Administration, Technological Educational Institute of Central Greece, GR-344 00 Psahna, Evia, Greece)

Abstract

In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The numerical approximation scheme is presented and applied using a single factor interest rate model. It is shown how the whole methodology works in practice, with the implementation of the algorithm for a specific interest rate portfolio. The recent financial crisis showed that risk management of derivatives portfolios especially in the interest rate market is crucial for the stability of the financial system. Modern Value at Risk (VAR) and Conditional Value at Risk (CVAR) techniques, although very useful and easy to understand, fail to grasp the need for on-line controlling and monitoring of derivatives portfolio. The portfolios should be designed in a way that risk and return be quantified and controlled in every possible state of the world. We hope that this methodology contributes towards this direction.

Suggested Citation

  • Konstantinos Kiriakopoulos & Alexandros Koulis, 2014. "Risk Management of Interest Rate Derivative Portfolios: A Stochastic Control Approach," JRFM, MDPI, vol. 7(4), pages 1-20, October.
    • Handle: RePEc:gam:jjrfmx:v:7:y:2014:i:4:p:130-149:d:41684
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. René M. Stulz, 2008. "Risk Management Failures: What Are They and When Do They Happen?," Journal of Applied Corporate Finance, Morgan Stanley, vol. 20(4), pages 39-48, September.
    3. Ralph C. Kimball, 2000. "Failures in risk management," New England Economic Review, Federal Reserve Bank of Boston, issue Jan, pages 3-12.
    4. Alexander, S. & Coleman, T.F. & Li, Y., 2006. "Minimizing CVaR and VaR for a portfolio of derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 583-605, February.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    7. Hilliard, Jimmy E, 1999. "Analytics Underlying the Metallgesellschaft Hedge: Short Term Futures in a Multi-period Environment," Review of Quantitative Finance and Accounting, Springer, vol. 12(3), pages 195-219, May.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    9. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
    10. Robert Jarrow & Stuart Turnbull, 1994. "Delta, gamma and bucket hedging of interest rate derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 21-48.
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