## CMS

**is a direct subtype of IRS with functions CMS Functions, keys CMS keys and example object CMS#1 that represents an interest rate swap (**

*CMS***onstant**

*C***aturity**

*M***wap), whereby a swap rate with a fixed tenor is exchanged against an ibor rate in regular time intervals until the swap's maturity.**

*S*It may be regarded as a special case of IRS with the index of one leg being of type Swap Rate and the index of the other leg being of type Ibor Rate

In formal terms:

Each floating payment associated with the swap rate equals:

*NrΔt*where

**is the realized value of the swap rate index Swap Rate at the begining of each cms cash flow period.**

*r*Further on,

**is the entry in**

*N***and**

*Notional***is the length of the respective accrual period.**

*Δt*Each floating payment associated with the ibor rate equals:

*N(i+s)Δt*where

**is the realized value of the ibor rate index Ibor Rate at the begining of each ibor cash flow period.**

*i*Further on,

**is the entry in**

*s*

*Ibor Spread*The cash flow currency is assumed to be that of the respective index.

The pricing methodology is specified in Model[IRS]