Reducing approximation errors in LPI swaps

Brody, Crosby & Li (2008) introduced a quasi-analytical method to price limited price index (LPI) swaps with the Jarrow & Yildirim (2003) model. Their method works well for short-term contracts, but the approximation error for long maturities may be far from being negligible. In this article, Joshua Xingzhi Zhang and Fabio Mercurio modify the Brody, Crosby & Li method to reduce approximation error in the worst case to lower than 2 basis points

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. The most common values for x and y are 0% and 5%, respectively.

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Reducing approximation errors in LPI swaps

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