Parametric interest rate risk immunization

Abstract

In this chapter we develop a new immunization model based on a parametric specification of the term structure of interest rates. The model extends traditional duration analysis to account for both parallel and non-parallel term structure shifts that have an economic meaning. Contrary to most interest rate risk models, we formally analyse both first-order and second-order conditions for bond portfolio immunization, emphasizing that the key to successful immunization will be to build up a portfolio such that the gradient of its future value is zero, and such that its Hessian matrix is positive semidefinite. We provide explicit formulae for new parametric interest rate risk measures and present alternative approaches to implement the immunization strategy. Additionally, we develop a more accurate approximation for the price sensitivity of a bond based upon new parametric interest rate risk measures and revise both classic and modern approaches to convexity in order to highlight the risks of convexity when changes other than parallel shifts in the term structure are considered. Furthermore, we provide useful expressions for the sensitivity of interest rate risk measures to changes in term structure shape parameters.