On Redington's theory of immunization

Abstract

In Redington's model of immunization, there is no distinction between short-term and long-term interest rates, i.e., all yield curves are assumed to be flat. This assumption gives rise to arbitrage opportunities. The model also assumes that the interest rate shocks are small. In this paper we generalize the theory to the case that interest rates are a function of time and the shock is of arbitrary magnitude. We also show that, for the single premium immediate annuity business, a duration-matching strategy may guarantee losses for the company under each and every parallel shift of the yield curve.