Hedging with Portfolio of Bonds and Swaps Under the G2 Model

Abstract

The two-additive-factor Gaussian model G2 (which encompasses the famous twofactor Hull-White model) is a stochastic model which describes the instantaneous short rate dynamic. It has functional qualities required in various practical purposes as in Asset Liability Management and in Trading of interest rate derivatives. Recently the second author, has derived analytic expressions for the price sensitivities of zero-coupon bonds, coupon-bearing bonds and interest rate swap contracts. These sensitivities are those with respect to the shocks linked to the unobservable two-uncertainty factors underlying the G2 model. As a such, the hedging of a position sensitive to the interest rate by means of a portfolio by bonds or swaps (in accordance with the market participants practice) becomes easily transparent as resulting from the balance between the various sensitivities involved.Our main purpose here is to fully document this hedging approach portfolio oriented. This is done first by the presentation of the rationale behind the methodology, second by the derivation of the involved analytic tools (i.e. sensitivities), third by the proofs of theoretical foundations, and last by the display of various numerical illustrations showing the effectiveness of our approach. In contrast with various hedging results in the literature, our approach is optimal in the sense that the hedger may know or fix in advance the maximal loss amount which can occur from the hedging approach itself.