  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.
