  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.
