Class SwaptionHullWhiteModelBoundary

java.lang.Object
net.finmath.finitedifference.interestrate.boundaries.SwaptionHullWhiteModelBoundary
All Implemented Interfaces:
FiniteDifferenceInterestRateBoundary
public class SwaptionHullWhiteModelBoundary extends Object implements FiniteDifferenceInterestRateBoundary
Boundary conditions for Swaption under FDMHullWhiteModel.

This implementation provides asymptotic Dirichlet boundary values compatible with European, Bermudan, and American swaption exercise.

The guiding asymptotics are:

  • on the deep out-of-the-money side, the swaption value tends to zero,
  • on the deep in-the-money side, the swaption value approaches the intrinsic value envelope over the remaining admissible exercise opportunities.

Concretely:

  • for a RECEIVER swaption, the lower boundary is treated as the deep in-the-money side and the upper boundary as the deep out-of-the-money side,
  • for a PAYER swaption, the upper boundary is treated as the deep in-the-money side and the lower boundary as the deep out-of-the-money side.

On the deep in-the-money side, the boundary value is chosen as

\max_{j \in \mathcal{E}(t)} \bigl( V_{\mathrm{swap},j}(t,x), 0 \bigr),

where \mathcal{E}(t) denotes the set of remaining admissible exercise opportunities and V_swap,j(t,x) is the value of the corresponding underlying swap.

This is a pragmatic boundary choice for the unified PDE swaption class. A European-only Jamshidian-exact boundary can be added later as a refinement.

Author:
Alessandro Gnoatto