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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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    Keywords

    Interest rate; sensitivities; bonds; G2++;
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