## BMA Swap

**is a direct subtype of Swap with functions BMA Swap Functions, keys BMA Swap keys and example object BMASwap that represents an interest rate swap, whereby a BMA Rate is exchanged for a fraction of Ibor Rate in regular time intervals until the swap's maturity.**

*BMA Swap*Each cash flow of the bma leg is based on a time-weighted arithmetic average of the weekly fixings of the BMA index during each coupon accrual period.

On the ibor leg, the fraction of Ibor Rate may be incremented by a fixed spread before it is used in the calculation of the respective cash flow amount.

The time-weighted arithmetic average is calculated as follows:

The realized value

**of the BMA index on each Wednesday during a bma leg accrual period leads to an average rate**

*I***defined as F/Δt, where**

*R***is the total accrued interest, i.e. the sum over**

*F***of**

*i***and**

*I(i)Δ(i)***is the number of calendar days of the respective accrual period.**

*Δt*Here

**is the fixing of**

*I(i)***at the**

*I***th Wednesday and**

*i***is the the number of calendar days between two successive**

*Δ(i)***.**

*valuation dates*Here by

**is meant the business day following the Wednesday, at which Wednesday the BMA index is fixed.**

*valuation date*It must be emphasized that the weights

**are not equal to the difference between the successive**

*Δ(i)***.**

*fixing dates*QuantLib ensures that the sum of

**equals**

*Δ(i)***.**

*Δt*The resulting rate

**is used to calculate the respective cash flow amount**

*R***as**

*C***, where**

*C = NRΔt***is the applicable notional.**

*N*The pricing methodology is specified in Model[BMA Swap]