Partial payoff swap pays periodically, the payoff from a particular European style put option on the spread between respective ten and two-year CMS rates. Moreover, this payoff is algebraically equivalent to the sum of the spread above and the payoff from a related European style put option.

A method is presented to calculating a particular multiplicative factor, which appears in a formula for a CMS rate convexity adjustment. A CMS rate convexity adjustment provides a correction term to the forward CMS rate to match the mean value of the CMS rate under the forward probability measure.

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 note that the option price depends critically on the HW volatility level. We develop a technique to calibrate the HW volatility for GIC pricing. The idea is to associate a European swaption specification to the particular GIC specification. The HW volatility can then be determined by matching the HW model price for the swaption to the swaption's market price. We note that this technique may be highly sensitive to the selection of the associated swaption; moreover, this selection must reflect the hedging strategy for the GIC embedded option.