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# Year-on-Year Inflation-Indexed Swap

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 Title: Year-on-Year Inflation-Indexed Swap Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Year-on-Year Inflation-Indexed Swap

The Year-on-Year Inﬂation-Indexed Swap (YYIIS) ia a standard derivative product over Inflation rate. The underlying asset is a single Consumer price index (CPI).

It is called Swap because each year there is a swap of a ﬁxed amount against a ﬂoating amount. But in reality only a one way payment is made (ﬁxed amount - ﬂoating amount).

## Detailed flows

• Each year, at time T_i
• Party B pays Party A the ﬁxed amount N{\phi_i}K
• Party A pays Party B the ﬂoating amount N{\psi_i}[\frac{I(T_i)}{I(T_{i-1})} - 1]

where:

• K is the contract ﬁxed rate
• N the contract nominal value
• M the number of years corresponding to the deal maturity
• i the number of years (0 < i <= M)
• \phi_i is the ﬁxed-leg year fractions for the interval [Ti−1, Ti]
• \psi_i is the ﬂoating-leg year fractions for the interval [Ti−1, Ti]
• T_0 is the start date
• T_i is the time of the flow i
• T_M is the maturity date (end of the swap)
• I(T_0) is the inflation at start date (time T_0)
• I(T_i) is the inflation at time of the flow i (time T_i)
• I(T_M) is the inflation at maturity date (time T_M)