# Zero-Coupon Inflation-Indexed Swap

The Zero-Coupon Inflation Swap (ZCIS) is a standard derivative product which payoff depends on the Inflation rate realized over a given period of time. The underlying asset is a single Consumer price index (CPI).

It is called Zero-Coupon because there is only one cash flow at the maturity of the swap, without any intermediate coupon.

It is called Swap because at maturity date, one counterparty pays a fixed amount to the other in exchange for a floating amount (in this case linked to inflation). The final cash flow will therefore consist of the difference between the fixed amount and the value of the floating amount at expiry of the swap.

## Detailed Flows

• At time ${\displaystyle T_{M}}$ = M years
• Party B pays Party A the fixed amount ${\displaystyle N[(1+K)^{M}-1]}$
• Party A pays Party B the floating amount ${\displaystyle N[{\frac {I(T_{M})}{I(T_{0})}}-1]}$

where:

• K is the contract fixed rate
• N the contract nominal value
• M the number of years
• ${\displaystyle T_{0}}$ is the start date
• ${\displaystyle T_{M}}$ is the maturity date (end of the swap)
• ${\displaystyle I(T_{0})}$ is the inflation at start date (time ${\displaystyle T_{0}}$)
• ${\displaystyle I(T_{M})}$ is the inflation at maturity date (time ${\displaystyle T_{M}}$)