Rational Models for Inflation-Linked Derivatives

TL;DR

This paper introduces rational models for inflation-linked derivatives that enable closed-form pricing and risk management, incorporating inflation convexity adjustments and calibration to EUR data.

Contribution

It develops a novel class of rational pricing kernel models that facilitate closed-form solutions for a wide range of inflation-linked products and interest rate derivatives.

Findings

Closed-form pricing for vanilla inflation products

Inclusion of inflation convexity-adjustment term

Model calibration demonstrated with EUR data

Abstract

We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, year-on-year swaps, caps and floors, and the exotic limited-price-index swap. We study the conditions necessary for the multiplicative nominal pricing kernel to give rise to short rate models for the nominal interest rate process. The proposed class of pricing kernel models retains the attractive features of a nominal multi-curve interest rate model, such as closed-form pricing of nominal swaptions, and it isolates the so-called inflation convexity-adjustment term arising from the covariance between the underlying stochastic drivers. We conclude with examples of how the model can be calibrated to EUR data.