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# Year-on-Year Inflation-Indexed Swap

The Year-on-Year Inflation-Indexed Swap (YYIIS) is a standard derivative product over Inflation rate. The underlying 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).

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## Detailed flows

• Each year, at time ${\displaystyle T_{i}}$
• Party B pays Party A the fixed amount ${\displaystyle N{\phi _{i}}K}$
• Party A pays Party B the floating amount ${\displaystyle N{\psi _{i}}[{\frac {I(T_{i})}{I(T_{i-1})}}-1]}$

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)
• ${\displaystyle \phi _{i}}$ is the fixed-leg year fractions for the interval [Ti−1, Ti]
• ${\displaystyle \psi _{i}}$ is the floating-leg year fractions for the interval [Ti−1, Ti]
• ${\displaystyle T_{0}}$ is the start date
• ${\displaystyle T_{i}}$ is the time of the flow i
• ${\displaystyle T_{M}}$ is the maturity date (end of the swap)
• ${\displaystyle I(T_{0})}$ is the inflation at start date (time ${\displaystyle T_{0}}$)
• ${\displaystyle I(T_{i})}$ is the inflation at time of the flow i (time ${\displaystyle T_{i}}$)
• ${\displaystyle I(T_{M})}$ is the inflation at maturity date (time ${\displaystyle T_{M}}$)