Interest Rate Sensitivities Under the G2&#43&#43 Model

Abstract

The two-factor Hull-White (2-HW) model is a famous stochastic model that describes 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. The 2-HW is actually a special case of a two-additive-factor Gaussian model G2&#43&#43, which despite of its unpleasant feature of theoretical possibility of negative rates, is quite analytically tractable in that explicit formulas for basic instruments can be readily available.Though closed-formulas for the prices of various main interest-rate instruments are known and used under the G2&#43&#43 model, it seems that references for the corresponding sensitivities are not clearly presented over the financial literature. To fill this gap is among of our purposes in the present work.So we derive here analytic expressions for the sensitivities of zero-coupon bond, coupon-bearing bonds, forward rate agreement and interest rate swap contracts. The sensitivities under consideration here are those with respect to the shocks linked to the unobservable two-uncertainty shocks risk/opportunity factors underlying the G2&#43&#43 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. MatLab codes of our results are also provided here.