Pricing Inflation Indexed Derivatives : A Reinterpretation of the Jarrow-Yildirim model

The Jarrow and Yildirim model for pricing inflation indexed derivatives is still the main reference technique adopted in the inflation market. Despite its popularity it has several shortcomings, the most immediate of which is the difficulty of calibration to market prices of options. The model relies heavily on the nominal and real economies, whilst the market trades options on the inflation rate or index. We offer a reinterpretation of the Jarrow and Yildirim approach based upon the notion of breakeven inflation. The main advantage is that the pricing of the most popular inflation derivatives (i.e. zero coupon and year-on-year swaps and zero coupon and year-on-year caps and floors) amounts to calibrating just three parameters: breakeven volatility, the volatility of the CPI price index and the correlation between them. The resulting Black-Scholes implied volatilities are very straight-forward to implement and the geometric interpretation of the model makes it intuitive to calibrate