Issues with the Smith-Wilson method

TL;DR

This paper critically examines the Smith-Wilson method used for discounting in Solvency II, highlighting issues with hedging, negative discount factors, and model singularities, and proposing conditions for alternative hedgeable curves.

Contribution

It introduces a novel stochastic representation of the Smith-Wilson method and identifies key issues affecting hedging and model calibration.

Findings

Key rate duration hedges beyond the Last Liquid Point are peculiar.

Negative discount factors are linked to singularities in the calibration criterion.

Necessary conditions for constructing hedgeable discount curves are provided.

Abstract

The objective of the present paper is to analyse various features of the Smith-Wilson method used for discounting under the EU regulation Solvency II, with special attention to hedging. In particular, we show that all key rate duration hedges of liabilities beyond the Last Liquid Point will be peculiar. Moreover, we show that there is a connection between the occurrence of negative discount factors and singularities in the convergence criterion used to calibrate the model. The main tool used for analysing hedges is a novel stochastic representation of the Smith-Wilson method. Further, we provide necessary conditions needed in order to construct similar, but hedgeable, discount curves.