# 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).

## 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 $T_{M}$ )