Communications in Mathematical Finance

Immunization Theory Revisited: Convex Hedges and Immunization Bounds between Bonds and Swaps

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• Abstract

  We construct and calculate static immunization bounds for hedging a single swap liability with two bonds in order to control the interest rate risk of these fixed income securities. These bounds are based on two kinds of duration and convexity measures, namely the traditional Fisher-Weil measures and the more recent stochastic measures of duration and convexity associated to affine models of the term structure of interest rates (e.g. the Vasicek and Cox-Ingersoll-Ross models). The immunization bounds are described for arbitrary portfolios that have deterministic future cash-flows with vanishing present value and can hitherto be used in this more general setting.