Reducing approximation errors in LPI swaps

Abstract

A limited price index (LPI) is a UK inflation index used to define typical payout structures of UK pension plans. By definition, LPIs have annual returns that are equal to the corresponding annual UK inflation rates capped at y and floored at x, for some strikes x and y. In this short article, the authors will first modify the Brody, Crosby & Li (2008) method and show that a simple change in their algorithm can improve the approximation result for long-term swaps. The authors' procedures can significantly reduce the approximation errors of the original method. Therefore, the resulting formulas can safely be applied in practice even for pricing long-term LPI swaps.