A Market Model for Inflation

Abstract

The various macro econometrics model for inflation are helpless when it comes to the pricing of inflation derivatives. The only article targeting inflation option pricing, the Jarrow Yildirim model, relies on non observable data. This makes the estimation of the model parameters a non trivial problem. In addition, their framework do not examine any relationship between the most liquid inflation derivatives instruments: the year to year and zero coupon swap. To fill this gap, we see how to derive a model on inflation, based on traded and liquid market instrument. Applying the same strategy as the one for a market model on interest rates, we derive no-arbitrage relationship between zero coupon and year to year swaps. We explain how to compute the convexity adjustment and what relationship the volatility surface should satisfy. Within this framework, it becomes much easier to estimate model parameters and to price inflation derivatives in a consistent way.

Keywords: Inflation index, forward, zero-coupon, year-on-year, volatility cube, convexity adjustment

JEL Classification: G13, G12