  In this paper, we establish a market model for the term structure of forward
inflation rates based on the risk-neutral dynamics of nominal and real
zero-coupon bonds. Under the market model, we can price inflation caplets as
well as inflation swaptions with a formula similar to the Black's formula, thus
justify the current market practice. We demonstrate how to further extend the
market model to cope with volatility smiles. Moreover, we establish a
consistency condition on the volatility of real zero-coupon bonds using
arbitrage arguments, and with that re-derive the model of Jarrow and Yildirim
(2003) with real forward rates based on "foreign currency analogy", and thus
interconnect the two modeling paradigms.
