Class WorstOfOptionMultiAssetBlackScholesModelBoundary

java.lang.Object
net.finmath.finitedifference.assetderivativevaluation.boundaries.WorstOfOptionMultiAssetBlackScholesModelBoundary
All Implemented Interfaces:
FiniteDifferenceBoundary
public class WorstOfOptionMultiAssetBlackScholesModelBoundary extends Object implements FiniteDifferenceBoundary
Boundary conditions for WorstOfOption under FDMMultiAssetBlackScholesModel.

The product payoff is

\left( \omega \left( \min(S_1(T), S_2(T)) - K \right) \right)^{+},

where \omega \in \{+1,-1\} is the call/put sign.

The multidimensional boundary convention of the framework is used:

  • index 0 of the returned array corresponds to the first state variable,
  • index 1 corresponds to the second state variable.

On the lower faces S_1 = 0 and S_2 = 0, the worst-of underlying is locked at zero for all future times, since zero is absorbing in the Black-Scholes model. Hence the option value on the lower faces is the discounted deterministic payoff

e^{-r \tau} \left( \omega (0 - K) \right)^{+}.

Accordingly, this boundary class requires both asset grids to start at zero.

On the upper faces, asymptotically one asset is so large that the worst-of underlying behaves like the remaining asset. Therefore:

  • on S_1 = S_{1,max}, the boundary is approximated by the corresponding one-dimensional vanilla option on S_2,
  • on S_2 = S_{2,max}, the boundary is approximated by the corresponding one-dimensional vanilla option on S_1.
Author:
Alessandro Gnoatto

  • Constructor Details

    • WorstOfOptionMultiAssetBlackScholesModelBoundary

      public WorstOfOptionMultiAssetBlackScholesModelBoundary(FDMMultiAssetBlackScholesModel model)
      Creates the boundary class.
      Parameters:
      model - The underlying finite-difference model.

  • Method Details