Vol_Curve__Vol_Input

Available

The volatility bears no dependence on Key Vol::Peg Date or any other relevant parameter and may thus be entered as a single number.

It is implemented either through the QuantLib BlackConstantVol or ConstantSwaptionVolatility or ConstantCapFloorVolatility, depending on the referenced quantity.

The volatility depends only on Key Vol::Peg Date

It is specified by a Set object consisting of 2 columns that contain volatilities for various maturities.

The first column must bear the title #Maturity and contain the maturities, entered either as dates or steps.

The second column must bear the title #Vol and contain the respective volatilities.

It is implemented through the QuantLib

Regarding the maturities that do not appear in the Set a separately supplied user-defined interpolation scheme is also needed.

Note that since the initial variance is always zero, such an interpolation cannot be log based, since the logarithm of the initial zero value does not exist.

The volatility depends on both Key Vol::Peg Date and strike.

It is specified by a Table2D object containing volatilities for various (maturity,strike) combinations.

The first dimension must span the maturities and the second the strikes.

Note this type only makes sense if the entry Key Vol Spec::Vol Type defined within

It is implemented either through the QuantLib

In the BlackVarianceSurface case, a separately supplied user-defined two-dimensional interpolation scheme is also needed for those dates and tenors that do not appear in the Table2D

Otherwise linear interpolation and flat extrapolation is assumed.

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

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

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

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 diffusion parameters apply to all different combinations of

In other words, for each pair

This gives rise to a non-flat volatility surface

For a given discrete collection of pairs

Deriscope allows you to specify this grid of market vols as a Table2D object containing volatilities for various

One dimension must span the option expiries (entered as dates or steps) and the second the swap tenors (entered as steps).

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

The extrapolation type is controlled by a separate input.

The QuantLib implementation is the