CMS Cliquet

A CMS cliquet option has two legs: One leg of this deal is based on (regular) floating rates. The other leg links to CMS swap rates. Due to the “set-in-arrear” feature in the structured leg, convexity and timing adjustments have to be considered.

Due to the embedded option and convexity adjustments in the structure leg, we need swap rate volatilities and forward rate volatilities. The former can be interpolated from the implied swaption volatility surface. The latter should be interpolated from the so-called implied forward volatility surface.

However, this surface is currently not available in the market. Therefore, the swap rate volatility surface is also applied to forward rate volatilities. The convexity adjustment does not explicitly depend on the correlation coefficient between the swap rate and the forward rate.

Consider a fixed income contract consisting of a regular floating leg and a structured floating leg.

The payoff of the regular leg determined at the ith reset date ti and paid at the ith payment date ti+1 is given by

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