Inflation Swap and Cap

A model is presented for pricing swaps, caps, and floors on inflation index returns. To capture general term structures of interest rates and index volatilities, the model requires time-averaged forward rate, and volatility inputs.

we consider swap-type payments of the following form

• At maturity time • At each reset time

We assume that the level of the inflation index satisfies a domestic risk-neutral SDE of the form

Given SDE (1) for index levels, we may model the level of the inflation index

We note that, in marginal distribution, Equations 2 and 3 are equivalent

Given the assumptions described in Sections 3.1 and 3.2 above, we have the results

CMS Convexity Adjustment

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