Sensitivities under G2++ model of the yield curve

Abstract

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.

Sensitivities of Interest Rate Swaps Under the G2++ Model

“…In order to make a decomposition for the IRS value change (which is useful for the hedging purpose) we are lead to introduce sensitivities of order k, for all non negative integers k. Under the G2++ model for the short interest rate, a decomposition for the zero-coupon bond change, as stated in [10] is ready to be used in the IRS decomposition part. The Residual term of IRS which represent the sensitivity of order 0 is defined by the expression Res Swap(t, T ; Υ) ≡ Res Swap t, T ; notional; rate Swap; Υ ≡ notional× − y(t 0 , t 1 ) − rate Swap P (0, t 1 )t…”