## Bipolar

Subtype of Buckets TreatmentThe various buckets (i.e. single numerical values, such as deposit rates or vols) inherent in each referenced market element are not separately simulated.

They are first grouped into groups so that each group contains buckets of the same market element that are capable of being processed together.

For example, if the referenced market element represents a vol surface, all vols in the contained two-dimensional table constitute one such group.

If the referenced market element represents a yield curve, then all rates constitute one group, regardless of their instrument type.

Futures prices, bond prices and BMA ibor fractions are not considered rates and therefore form their separate groups.

An exception to that is when the yield curve object has VaR Type = By Rate or VaR Type = By Rate, in which case the futures or bond prices can be treated as rates and thus combined with deposits, forwards and swaps.

Then only two single risk factors

**and**

*x_min***are simulated that correspond to the two extreme coordinates that span the buckets of the respective group.**

*x_max*For example, in the yield curve case the two extreme coordinates are the shortest and longest maturity among the instruments of the respective group, in that order.

In the vol surface case the two extreme coordinates apply on each of the two involved dimensions separately.

In the vol cube case the two extreme coordinates apply on each of the three involved dimensions separately.

Given the values

**and**

*x_min***on the two extreme coordinates, appropriate risk factor values are produced by linear interpolation for all intermediate coordinates.**

*x_max*After the risk factor values

**have been thus calculated for all buckets indexed by**

*x_i***within the respective group, the buckets themselves can be calculated from**

*i***according to the mapping defined in Modelled Factor**

*x_i*