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Risk management of a bond portfolio using options

Author

Listed:
  • J. ANNAERT
  • G. DEELSTRA
  • D. HEYMAN
  • M. VANMAELE

Abstract

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn et al. (1999), who consider the same problem for an investment in a share.

Suggested Citation

  • J. Annaert & G. Deelstra & D. Heyman & M. Vanmaele, 2007. "Risk management of a bond portfolio using options," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/465, Ghent University, Faculty of Economics and Business Administration.
    • Handle: RePEc:rug:rugwps:07/465
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    References listed on IDEAS

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    1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
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    3. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    4. 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.
    5. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Andrew K. Prevost & Lawrence C. Rose & Gary Miller, 2000. "Derivatives Usage and Financial Risk Management in Large and Small Economies: A Comparative Analysis," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(5‐6), pages 733-759, June.
    8. Gordon M. Bodnar & Gregory S. Hayt & Richard C. Marston, 1998. "1998 Wharton Survey of Financial Risk Management by US Non-Financial Firms," Financial Management, Financial Management Association, vol. 27(4), Winter.
    9. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    10. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    11. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    12. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    13. Andrew K. Prevost & Lawrence C. Rose & Gary Miller, 2000. "Derivatives Usage and Financial Risk Management in Large and Small Economies: A Comparative Analysis," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(5‐6), pages 733-759, June.
    14. Dong‐Hyun Ahn & Jacob Boudoukh & Matthew Richardson & Robert F. Whitelaw, 1999. "Optimal Risk Management Using Options," Journal of Finance, American Finance Association, vol. 54(1), pages 359-375, February.
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    Cited by:

    1. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2011. "Optimizing international portfolios with options and forwards," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3188-3201.
    2. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.
    3. Monika Harcarikova & Michal Soltes, 2016. "Risk Management in Energy Sector Using Short Call Ladder Strategy," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 12(3), pages 39-54.
    4. Alessandro Ramponi, 2012. "Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: a Fourier Transform Approach," Papers 1207.6759, arXiv.org.
    5. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2013. "Option-based risk management of a bond portfolio under regime switching interest rates," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 47-70, May.
    6. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 767-800, December.
    7. Griselda Deelstra & Ahmed Ezzine & Dries Heyman & Michèle Vanmaele, 2007. "Managing value-at-risk for a bond using bond put options," Computational Economics, Springer;Society for Computational Economics, vol. 29(2), pages 139-149, March.

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    More about this item

    Keywords

    (Tail) Value-at-Risk; bond hedging; affine term structure model;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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