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

In this paper, we propose a new model for the joint evolution of the inflation rate, the Central Bank official interest rate and the short-term interest rate. Our model takes into account the fact that the Central Bank interest rate changes at random times, inflation is measured at fixed, regular times, while the short-term interest rate evolves essentially continuously. We derive the valuation equation for a contingent claim and show that it has a unique solution. The payoff may depend on all three economic factors of the model and the discount factor is allowed to include inflation. 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. Taking as a benchmark the model of [H. W. Ho, H. H. Huang & Y. Yildirim (2014) Affine model of inflation-indexed derivatives and inflation risk premium, European Journal of Operational Research 235, 159–169], we show that our model performs better on European market data from 2008 to 2015. Our model uses many fewer parameters than the benchmark model: This is advantageous from the numerical point of view and suggests that our model describes the behavior of the economic factors more closely.