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The Inflation Adjusted Rate Swap is a financial contract where, at the end of each accrual period, one party - the inflation receiver - pays a non-inflation linked coupon, for example libor + spread and receives a payment Inf, based on a rate that is linked to a specific inflation index, from the other party - the inflation payer.
Inf = NQ(t)rΔt
where N is the swap notional, r is a constant rate, Δt is the length of the accrual period expressed in number of years and
Q(t) = I(t-lag)/I0 represents the inflation index I at time t-lag in units of the so called base value I0, where lag is a contractually specified time lag.