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Sensitivities under G2++ model of the yield curve

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  • H. Jaffal

    (Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université du Havre, 25 rue Philippe Lebon, B.P. 540, 76058 Le Havre cedex, France†Princess Nourah bint Abdulrahman University (PNU), Riyadh, Saudi Arabia)

  • Y. Rakotondratsimba

    (#x2021;ECE Paris Graduate School of Engineering, 37 quai de Grenelle CS71520 75 725 Paris 15, France)

  • A. Yassine

    (Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université du Havre, 25 rue Philippe Lebon, B.P. 540, 76058 Le Havre cedex, France§Institut Supérieur d’Etudes Logistiques (ISEL), Université du Havre, Quai Frissard, B.P. 1137, 76063 Le Havre cedex, France)

Abstract

The two-additive-factor Gaussian model G2++ is a famous stochastic model for the instantaneous short rate. It has functional qualities required in various practical purposes, as in Asset Liability Management and in Trading of interest rate derivatives. Though closed formulas for the prices of various main interest-rate instruments are known and used under the G2++ model, it seems that references for the corresponding sensitivities are not clearly presented over the financial literature. To fill this gap is one of our purposes in the present work. We derive here analytic expressions for the sensitivities of zero-coupon bond, coupon-bearing bonds, portfolio of coupon bearing bonds. The sensitivities under consideration here are those with respect to the shocks linked to the unobservable two-uncertainty shock risk/opportunity factors underlying the G2++ model. As a such, the hedging of a position sensitive to the interest rate by means of a portfolio (in accordance with the market participants practice) becomes easily transparent as just resulting from the balance between the various involved sensitivities.

Suggested Citation

  • H. Jaffal & Y. Rakotondratsimba & A. Yassine, 2017. "Sensitivities under G2++ model of the yield curve," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-38, March.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500086
    DOI: 10.1142/S2424786317500086
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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..
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    3. Frederick R. Macaulay, 1938. "Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856," NBER Books, National Bureau of Economic Research, Inc, number maca38-1.
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    5. 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.
    6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1979. "Duration and the Measurement of Basis Risk," The Journal of Business, University of Chicago Press, vol. 52(1), pages 51-61, January.
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    Keywords

    Interest rate; sensitivities; bonds; G2++;
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