Year-on-Year Inflation Swap

ORE defines the product as follows:

A YoYIIS is a swap contract where one leg has annual inflation linked coupon payments that are exchanged for fixed payments on the other leg.

Source: ORE User Guide, Products catalogue, yyswap.tex. YoYIIS is ORE's shorthand for the year-on-year inflation swap.

Two parties swap the yearly change of an inflation index against a fixed rate. One side pays the index rise of each coming year. The other side pays a fixed rate for the whole life. The exposure resets every year, so each coupon covers only its own twelve months.

ORE states the input form as follows:

A Year on Year inflation swap can be set up with trade type Swap, with one leg of type YY.

Source: ORE User Guide, Products catalogue, yyswap.tex.

The YY leg carries a YYLegData block. It names the inflation index and the observation conventions. The structure mirrors the CPI Swap, which uses the InflationSwap trade type and a CPI leg. A year-on-year coupon at time Ti equals the notional times the index change I(Ti)/I(Ti-1) minus one, times the day count fraction. The fixings Ti-1 and Ti are one year apart. YoY coupons can be capped or floored.

• The discount curve of the payment currency. It moves every payment.
• The inflation index curve. It projects each annual index change.
• The fixed rate. It sets the level of the non-inflation leg.
• The cap or floor, when present. It adds an inflation-volatility sensitivity.

A long-inflation leg gains value when the projected index rises. The exposure resets each year, so the index curve matters mainly at its one-year points.

Each printed fixing settles one annual coupon. The remaining coupons cover the years still ahead. Unlike a CPI swap, no index ratio accumulates over the whole life. The exposure rolls forward year by year, and the trade keeps a similar annual structure until maturity.

A customer who wants inflation protection for a defined horizon picks YoY exposure when annual index changes matter more than the cumulative level. The product suits caps and floors on single-year inflation. In ORE Studio a customer books YoY swaps to value them and run sensitivities on the ORE engine.

ORE's catalogue shows the structure with the Swap trade type. The fixed-rate leg is abbreviated.

<SwapData>
  <LegData>
    <LegType>Floating</LegType>
    <Payer>true</Payer>
    ...
  </LegData>
  <LegData>
    <LegType>YY</LegType>
    <Payer>false</Payer>
    ...
    <YYLegData>
      ...
    </YYLegData>
  </LegData>
</SwapData>

Source: ORE User Guide, Products catalogue, yyswap.tex, listing Year on Year Swap Data (using Swap trade type).