Class BestOfOptionMultiAssetBlackScholesModelBoundary

java.lang.Object

net.finmath.finitedifference.assetderivativevaluation.boundaries.BestOfOptionMultiAssetBlackScholesModelBoundary

All Implemented Interfaces:

FiniteDifferenceBoundary

public class BestOfOptionMultiAssetBlackScholesModelBoundary
extends Object
implements FiniteDifferenceBoundary

Boundary conditions for BestOfOption under FDMMultiAssetBlackScholesModel.

The payoff is

\left( \omega \left( \max(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 best-of payoff reduces exactly to a one-dimensional vanilla option on the remaining asset. Accordingly, this boundary class requires both asset grids to start at zero.

On the upper faces, asymptotically correct Dirichlet values are used:

• on S_1 = S_{1,\max}, the call is approximated by S_1 e^{-q_1 \tau} - K e^{-r \tau} and the put by 0,
• on S_2 = S_{2,\max}, the call is approximated by S_2 e^{-q_2 \tau} - K e^{-r \tau} and the put by 0.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
BestOfOptionMultiAssetBlackScholesModelBoundary(FDMMultiAssetBlackScholesModel model)	Performs the operation.

Method Summary

Modifier and Type	Method	Description
BoundaryCondition[]	getBoundaryConditionsAtLowerBoundary(FiniteDifferenceEquityProduct product, double time, double... stateVariables)	Returns the boundary conditions at the lower boundary.
BoundaryCondition[]	getBoundaryConditionsAtUpperBoundary(FiniteDifferenceEquityProduct product, double time, double... stateVariables)	Returns the boundary conditions at the upper boundary.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

BestOfOptionMultiAssetBlackScholesModelBoundary

public BestOfOptionMultiAssetBlackScholesModelBoundary(FDMMultiAssetBlackScholesModel model)

Performs the operation.

Parameters:

model - The value.

Method Details

getBoundaryConditionsAtLowerBoundary

public BoundaryCondition[] getBoundaryConditionsAtLowerBoundary(FiniteDifferenceEquityProduct product,
 double time,
 double... stateVariables)

Description copied from interface: FiniteDifferenceBoundary

Returns the boundary conditions at the lower boundary.

The returned array is indexed by state-variable dimension.

Specified by:

getBoundaryConditionsAtLowerBoundary in interface FiniteDifferenceBoundary

Parameters:

product - The product being valued.

time - The running time.

stateVariables - The state variables specifying the boundary location.

Returns:

The lower-boundary conditions by dimension.

getBoundaryConditionsAtUpperBoundary

public BoundaryCondition[] getBoundaryConditionsAtUpperBoundary(FiniteDifferenceEquityProduct product,
 double time,
 double... stateVariables)

Description copied from interface: FiniteDifferenceBoundary

Returns the boundary conditions at the upper boundary.

The returned array is indexed by state-variable dimension.

Specified by:

getBoundaryConditionsAtUpperBoundary in interface FiniteDifferenceBoundary

Parameters:

product - The product being valued.

time - The running time.

stateVariables - The state variables specifying the boundary location.

Returns:

The upper-boundary conditions by dimension.