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The Year-on-Year Inflation Swap is a financial contract where, at the end of each accrual period, one party - the inflation receiver - pays a fixed rate coupon Fxd and receives a floating payment Flt linked to a specific inflation index from the other party - the inflation payer.
Fxd = NrΔt
where N is the swap notional, Δt is the length of the accrual period expressed in number of years and
Flt = N[m*YoY(Tend)+s]Δt
where YoY(t) = I(t-lag)/I(t-1Year-lag) - 1 represents the inflation rate at time t realized over the course of the preceding year with Tend being the end of the respective accrual period and lag being a contractually specified time lag.
The multiplier (also called gearing) m and spread s are constants with typical values 1 and 0 respectively.
Note Δt may not be the same in the above formulas if the fixed and floating legs have different daycount conventions.
Furthermore, for dates on which no directly applicable published inflation data exist, the referenced inflation index also depends on interpolation assumptions.