  We formulate a forward inflation index model with multi-factor volatility
structure featuring a parametric form that allows calibration to correlations
between indices of different tenors observed in the market. Assuming the
nominal interest rate follows a single factor Gaussian short rate model, we
present analytical prices for zero-coupon and year-on-year swaps, caps, and
floors. The same method applies to any interest rate model for which one can
compute the zero-coupon bond prices and measure shifts. We extend the
multi-factor model with leverage functions to capture the entire market
volatility skew with a single process. The time-consuming calibration step of
this model can be avoided in the simplified model that we further propose. We
demonstrate the leveraged and the simplified models with market data.
