Class DigitalOptionBlackScholesModelBoundary

java.lang.Object

net.finmath.finitedifference.assetderivativevaluation.boundaries.DigitalOptionBlackScholesModelBoundary

All Implemented Interfaces:

FiniteDifferenceBoundary

public class DigitalOptionBlackScholesModelBoundary
extends Object
implements FiniteDifferenceBoundary

Boundary conditions for DigitalOption under the FDMBlackScholesModel.

The boundary asymptotics depend on the exercise style:

• European exercise: discounted continuation asymptotics.
• Bermudan / American exercise: early-exercise asymptotics.

Conventions:

• For a cash-or-nothing call, the lower boundary is zero.
• For a cash-or-nothing put, the upper boundary is zero.
• For an asset-or-nothing call, the lower boundary is zero.
• For an asset-or-nothing put, the upper boundary is zero.

At the in-the-money far boundary, the value is:

• European cash digital: discounted cash payoff.
• European asset digital: dividend-adjusted stock value.
• Bermudan/American cash digital: immediate cash payoff.
• Bermudan/American asset digital: immediate stock value.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
DigitalOptionBlackScholesModelBoundary(FDMBlackScholesModel model)	Creates the boundary condition associated with a given FDMBlackScholesModel.

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

DigitalOptionBlackScholesModelBoundary

public DigitalOptionBlackScholesModelBoundary(FDMBlackScholesModel model)

Creates the boundary condition associated with a given FDMBlackScholesModel.

Parameters:

model - The Black-Scholes model used to determine risk-free and dividend discount factors.

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.