Vol_Curve__Vol_Input__Swaption_Cube

This type is exclusively used to describe the volatility of forward interest rate swap rates.

Web blog example here

It thus only makes sense if the entry Key Vol Spec::Ref Quotable defined within

The fundamental assumption is that for a fixed expiry

Note that we do not assume that the same SABR parameters apply to all different combinations of

In other words, for each pair

All this gives rise to a non-flat Black volatility structure in the following sense:

For any pair

In general, there must exist a Black vol

This defines the vol

The exact same argument applies with regard to the Vol Spec::Vol Type::Normal vol

We could perhaps specify the SABR vol structure through an array of quartets

A far simpler method adopted by Deriscope is to specify instead the 3-dimensional grid of market vols as defined above.

Such an input grid is referred as "vol cube" and may consist by the

In addition, certain SABR model switches, such as initial guesses of SABR parameters, may be specified in an optional input object of type SABR Model

The 3-dimensional grid is specified by a HyperTable object containing volatilities for various combinations of strike spread, expiry and swap tenor.

Typically the first cube dimension spans the strike spreads (differences from the atm rate level), the second the option expiries and the third the swap tenors.

The strike spread coordinate must include the number 0 and the corresponding 2-dimensioal sub-table must contain the at-the-money swaption vols.

The 2-dimensioal sub-tables associated with the non-zero strike spread coordinates should not contain the absolute vol levels but rather the vol spreads, defined as the differences between the vol levels for the respective strike and the atm vol levels.

Bilinear interpolation is assumed for any missing entries in the supplied tables.

The QuantLib implementation is the