Inflation, ECB and short-term interest rates: A new model, with calibration to market data

TL;DR

This paper introduces a new stochastic model for European inflation, ECB interest rates, and short-term rates, providing improved market data fit and efficient numerical solutions with fewer parameters than existing models.

Contribution

A novel non-affine model for joint inflation and interest rate dynamics with a unique valuation solution and efficient calibration to market data.

Findings

Model outperforms benchmark on 2008-2015 data

Uses fewer parameters than existing models

Provides an efficient numerical algorithm for valuation

Abstract

We propose a new model for the joint evolution of the European inflation rate, 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 and show that it has a unique solution. The contingent claim payoff may depend on all three economic factors of the model and the discount factor is allowed to include inflation. Taking as a benchmark the model of Ho, H.W., Huang, H.H. and Yildirim, Y., Affine model of inflation-indexed derivatives and inflation risk premium, (European Journal of Operational Researc, 2014), we show that our model performs better on market data from 2008 to 2015. Our model is not an affine model. Although in some special cases the solution of the valuation equation might admit a closed form, in general it has to be solved numerically. This can be done efficiently by the algorithm that we provide. Our model uses many fewer parameters than the benchmark model, which partly compensates the higher complexity of the numerical procedure and also suggests that our model describes the behaviour of the economic factors more closely.