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
where:
 * 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 $$N{\psi_i}[\frac{I(T_i)}{I(T_{i-1})} - 1]$$
 * 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 $$T_M$$)