Despite the importance played by Interest Rate Swaps (IRS), it appears that sounding analyzes related to the hedging of portfolios made by swaps is not clear in the financial literature. We provide here the analysis corresponding to a parallel shift of the interest rate. The suitable swap sensitivities to make use in hedging and risk management obtained here may be seen as some generalization of the well known bond duration and convexity in the swap framework. Our present results might provide a support for practitioners, using portfolio of swaps and/or bonds, in their hedge decision-making.
The two-additive-factor Gaussian model G2[Formula: see text] 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[Formula: see text] 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[Formula: see text] 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.
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