Deriscope ## The Excel Derivatives Periscope

##### Coverage

BMA_Swap

*BMA Swap* is a child type of Swap 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.

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 *I* of the BMA index on each Wednesday during a bma leg accrual period leads to an average rate *R* defined as F/Δt, where *F* is the total accrued interest, i.e. the sum over *i* of *I(i)Δ(i)* and *Δt* is the number of calendar days of the respective accrual period.

Here *I(i)* is the fixing of *I* at the *i*th Wednesday and *Δ(i)* is the the number of calendar days between two successive *valuation dates*.

Here by *valuation date* is meant the business day following the Wednesday, at which Wednesday the BMA index is fixed.

It must be emphasized that the weights *Δ(i)* are not equal to the difference between the successive *fixing dates*.

QuantLib ensures that the sum of *Δ(i)* equals *Δt*.

The resulting rate *R* is used to calculate the respective cash flow amount *C* as *C = NRΔt*, where *N* is the applicable notional.

The pricing methodology is specified in Model[BMA Swap]