How to hedge extrapolated yield curves

TL;DR

This paper develops a mathematical framework using functional analysis to hedge interest rate risk for liabilities based on extrapolated yield curves, with applications to Smith-Wilson and Swedish methods.

Contribution

It introduces a novel approach to hedge interest rate sensitivity by analyzing the yield curve as a functional and applying Gâteaux variation, specifically for Smith-Wilson and Swedish extrapolation methods.

Findings

Framework effectively captures yield curve sensitivities.

Application to Smith-Wilson method demonstrates practical hedging strategies.

Analysis of Swedish method shows similar sensitivity structure.

Abstract

We present a framework on how to hedge the interest rate sensitivity of liabilities discounted by an extrapolated yield curve. The framework is based on functional analysis in that we consider the extrapolated yield curve as a functional of an observed yield curve and use its G\^ateaux variation to understand the sensitivity to any possible yield curve shift. We apply the framework to analyse the Smith-Wilson method of extrapolation that is proposed by the European Insurance and Occupational Pensions Authority (EIOPA) in the coming EU legislation Solvency II, and the method recently introduced, and currently prescribed, by the Swedish Financial Supervisory Authority.