# Variants of the Smith-Wilson method with a view towards applications

## TL;DR

This paper introduces two innovative variants of the Smith-Wilson method tailored for insurance industry applications, enhancing data integration and convergence to the ultimate forward rate.

## Contribution

It presents novel modifications to the Smith-Wilson method that allow for weighted data incorporation and explicit convergence to the ultimate forward rate.

## Key findings

- First variant enables partial weighting of market data.
- Second variant ensures convergence to the ultimate forward rate.
- Both variants improve practical applicability in insurance contexts.

## Abstract

We propose two variants of the Smith-Wilson method for practical application in the insurance industry. Our first variant relaxes the Smith-Wilson energy and can be used to incorporate less reliable market data with a certain weight rather than disregarding it completely. This is particularly useful for deriving yield curves in the IFRS 17 accounting regime, where there is a mandate to incorporate all available market data. A second variant incorporates the requirement to reach the ultimate forward rate at a prescribed term into the problem formulation. This provides a natural way to fulfil the Solvency II convergence requirement and is more elegant than the current methodology adapting the term-scale parameter to control convergence.