Interaction between Portfolios under G2++ Model

Abstract

The following paper will show an investigation regarding the hedging portfolios for the G2++ interest rate model which will be analyzed, in which a focus on the decomposition of its variations while using derived sensitivities from the instantaneous short-rate dynamics will also occur. Thus, this paper will provide the following information: a precise control of the associated approximation error, computed high-order sensitivities, an accurate polynomial approximation of the portfolio value variations with coefficients giving by the sensitives. The central aim of this paper is to provide a comprehensive, portfolio oriented presentation of the hedging methodology. Its structure will begin with defining the composition of the portfolios, bonds and swaps, to derive their decomposition in terms of sensitivities. Later, a clear presentation of the optimized problem that underlies the hedging strategy will be made, to end the work with a range of numerical experiments to demonstrate the efficiency of the proposed approach. Plenty of hedging methods exist in literature, however, our approach is more optimal in the sense, due to the way the hedger is determined based on an upper bound on the potential loss which is induced by the hedging strategy itself.