Risk Neutral Valuation of Inflation-Linked Interest Rate Derivatives

TL;DR

This paper develops a comprehensive stochastic model for jointly evolving inflation and interest rates, deriving a valuation framework for inflation-linked derivatives and providing an efficient numerical solution.

Contribution

It introduces a novel joint inflation-interest rate model and derives a PDE-based valuation method with a practical numerical scheme.

Findings

The valuation equation reduces to a finite set of PDEs.

The model accurately prices inflation-linked derivatives.

The numerical scheme efficiently computes prices in examples.

Abstract

We propose a model for the joint evolution of European inflation, the European Central Bank official interest rate and the short-term interest rate, in a stochastic, continuous time setting. We derive the valuation equation for a contingent claim depending potentially on all three factors. This valuation equation reduces to a finite number of Cauchy problems for a degenerate parabolic PDE with non-local terms. We show that the price of the contingent claim is the only viscosity solution of the valuation equation. We also provide an efficient numerical scheme to compute the price and implement it in an example.