## Swaption Surface

Subtype of Vol InputThis 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 Ref Quotable defined within

**relates to a Swap Rate.**

*Vol Spec*The fundamental assumption is that for a fixed expiry

**and underlying swap maturity**

*T1***, the forward rate**

*T2***is diffused in a Black, Normal or Shifted Lognormal fashion.**

*F(T1,T2)*Note that we do not assume that the same diffusion parameters apply to all different combinations of

**and**

*T1***.**

*T2*In other words, for each pair

**, we allow the respective forward rate**

*T1, T2***to diffuse with a different vol parameter**

*F(T1,T2)***that depends on**

*σ***.**

*T1, T2*This gives rise to a non-flat volatility surface

**.**

*σ(T1,T2)*For a given discrete collection of pairs

**, the surface becomes a 2-dimensional grid.**

*T1, T2*Deriscope allows you to specify this grid of market vols as a Table2D object containing volatilities for various

**combinations.**

*T1, T2*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

**.**

*SwaptionVolatilityMatrix*