# Zero-Coupon Inflation-Indexed Swap

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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).

In finance, inflation derivative refers to an over-the-counter and exchange-traded derivative that is used to transfer inflation risk from one counterparty to another. See Exotic derivatives.

A consumer price index (CPI) measures changes in the price level of market basket of consumer goods and services purchased by households.

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.

A swap is a derivative in which two counterparties exchange cash flows of one party's financial instrument for those of the other party's financial instrument. The benefits in question depend on the type of financial instruments involved. For example, in the case of a swap involving two bonds, the benefits in question can be the periodic interest (coupon) payments associated with such bonds. Specifically, two counterparties agree to exchange one stream of cash flows against another stream. These streams are called the legs of the swap. The swap agreement defines the dates when the cash flows are to be paid and the way they are accrued and calculated. Usually at the time when the contract is initiated, at least one of these series of cash flows is determined by an uncertain variable such as a floating interest rate, foreign exchange rate, equity price, or commodity price.

In finance, maturity or maturity date refers to the final payment date of a loan or other financial instrument, at which point the principal is due to be paid.

## 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 ${\displaystyle T_{M}}$)

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