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Delta, gamma and bucket hedging of interest rate derivatives

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  • Robert Jarrow
  • Stuart Turnbull

Abstract

The paper describes a framework for delta and gamma hedging an interest rate portfolio using a multifactor form of the Heath et al. (1992) model. A formal description of bucket hedging is given along with a discussion of some of the issues surrounding the choice of bucket lengths. Given that a small number of factors can describe the evolution of the term structure, the bucket deltas are defined in terms of these factors. The hedging of corporate bonds is also addressed.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:21-48
    DOI: 10.1080/13504869400000002
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. 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..
    3. Ingersoll, Jonathan E. & Skelton, Jeffrey & Weil, Roman L., 1978. "Duration Forty Years Later," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(4), pages 627-650, November.
    4. 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.
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    Citations

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    Cited by:

    1. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    2. Elisa Luciano & Luca Regis & Elena Vigna, 2017. "Single- and Cross-Generation Natural Hedging of Longevity and Financial Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 961-986, September.
    3. Mozumder, Sharif & Dempsey, Michael & Kabir, M. Humayun & Choudhry, Taufiq, 2016. "An improved framework for approximating option prices with application to option portfolio hedging," Economic Modelling, Elsevier, vol. 59(C), pages 285-296.
    4. Jevtić, Petar & Regis, Luca, 2015. "Assessing the solvency of insurance portfolios via a continuous-time cohort model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 36-47.
    5. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    6. Luciano, Elisa & Regis, Luca, 2014. "Efficient versus inefficient hedging strategies in the presence of financial and longevity (value at) risk," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 68-77.
    7. Clemente De Rosa & Elisa Luciano & Luca Regis, 2017. "Basis risk in static versus dynamic longevity-risk hedging," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(4), pages 343-365, April.
    8. Clemente De Rosa & Elisa Luciano & Luca Regis, 2015. "Static versus dynamic longevity-risk hedging," Carlo Alberto Notebooks 403, Collegio Carlo Alberto.
    9. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736, August.
    10. Juraj Hruška, 2015. "Delta-gamma-theta Hedging of Crude Oil Asian Options," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(6), pages 1897-1903.
    11. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
    12. 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.
    13. Ballotta, Laura & Haberman, Steven, 2003. "Valuation of guaranteed annuity conversion options," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 87-108, August.
    14. Nawalkha, Sanjay K. & Soto, Gloria M. & Zhang, Jun, 2003. "Generalized M-vector models for hedging interest rate risk," Journal of Banking & Finance, Elsevier, vol. 27(8), pages 1581-1604, August.
    15. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
    16. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    17. Elisa Luciano & Luca Regis & Elena Vigna, 2012. "Natural delta gamma hedging of longevity and interest rate risk," ICER Working Papers - Applied Mathematics Series 21-2011, ICER - International Centre for Economic Research.

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