Class DigitalBarrierOption

java.lang.Object

net.finmath.finitedifference.assetderivativevaluation.products.DigitalBarrierOption

All Implemented Interfaces:

FiniteDifferenceEquityEventProduct, FiniteDifferenceEquityProduct, FiniteDifferenceInternalStateConstraint, FiniteDifferenceOneDimensionalKnockInProduct, FiniteDifferenceProduct<FiniteDifferenceEquityModel>, Product

public class DigitalBarrierOption
extends Object
implements FiniteDifferenceEquityEventProduct, FiniteDifferenceInternalStateConstraint, FiniteDifferenceOneDimensionalKnockInProduct

Finite-difference valuation of a single-barrier digital option on one asset.

Supported payoff families:

• cash-or-nothing call / put,
• asset-or-nothing call / put,
• down-in / up-in / down-out / up-out.

Current implementation policy:

• continuously monitored knock-out options are priced directly by the finite-difference solver,
• continuously monitored 1D knock-in options are priced directly through a coupled two-state PDE on an auxiliary spatial grid where the barrier is placed on an interior node,
• continuously monitored 2D knock-in options use the activated-branch / pre-hit formulation,
• for one-dimensional models, terminal payoff initialization is cell- averaged in order to reduce strike-discontinuity grid bias,
• discretely monitored 1D and 2D knock-out options are handled through event-time zeroing on breached nodes,
• discretely monitored 1D and 2D knock-in options are handled through event-time replacement by the activated vanilla digital continuation surface,
• for discretely monitored knock-ins with Bermudan/American exercise, only the activated state carries exercise rights; the pre-hit state is solved as a European continuation problem,
• 2D discrete monitoring is supported for Heston / SABR models.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
DigitalBarrierOption(double maturity, double strike, double barrierValue, double callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff)	Performs the operation.
DigitalBarrierOption(double maturity, double strike, double barrierValue, double callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise)	Performs the operation.
DigitalBarrierOption(double maturity, double strike, double barrierValue, double callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise, MonitoringType monitoringType, double[] monitoringTimes)	Performs the operation.
DigitalBarrierOption(double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff)	Performs the operation.
DigitalBarrierOption(double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise)	Performs the operation.
DigitalBarrierOption(double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise, MonitoringType monitoringType, double[] monitoringTimes)	Performs the operation.
DigitalBarrierOption(String underlyingName, double maturity, double strike, double barrierValue, double callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff)	Performs the operation.
DigitalBarrierOption(String underlyingName, double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff)	Performs the operation.
DigitalBarrierOption(String underlyingName, double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise)	Performs the operation.
DigitalBarrierOption(String underlyingName, double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, Exercise exercise, MonitoringType monitoringType, double[] monitoringTimes)	Performs the operation.
DigitalBarrierOption(String underlyingName, double maturity, double strike, double barrierValue, CallOrPut callOrPutSign, BarrierType barrierType, DigitalPayoffType digitalPayoffType, double cashPayoff, MonitoringType monitoringType, double[] monitoringTimes)	Performs the operation.

Method Summary

Modifier and Type	Method	Description
double[]	applyEventCondition(double time, double[] valuesAfterEvent, FiniteDifferenceEquityModel model)	Performs the operation.
BarrierType	getBarrierType()	Returns the barrier type.
double	getBarrierValue()	Returns the barrier level.
CallOrPut	getCallOrPut()	Returns the value.
double	getCashPayoff()	Returns the value.
double	getConstrainedValue(double time, double... stateVariables)	Returns the value to impose at a constrained node.
DigitalPayoffType	getDigitalPayoffType()	Returns the value.
double[]	getEventTimes()	Returns the value.
Exercise	getExercise()	Returns the value.
double	getInactiveValueAtMaturity()	Returns the value prescribed in the inactive regime at maturity.
double	getMaturity()	Returns the maturity.
double[]	getMonitoringTimes()	Returns the value.
MonitoringType	getMonitoringType()	Returns the value.
double	getStrike()	Returns the value.
String	getUnderlyingName()	Returns the value.
double[]	getValue(double evaluationTime, FiniteDifferenceEquityModel model)	Returns the value.
double[][]	getValues(FiniteDifferenceEquityModel model)	Returns the value.
boolean	isConstraintActive(double time, double... stateVariables)	Returns true if the internal constraint is active at the given node and time.

Methods inherited from class Object

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

Methods inherited from interface FiniteDifferenceEquityProduct

getModelClass

Methods inherited from interface FiniteDifferenceProduct

getValue

Methods inherited from interface Product

getValues

Constructor Details

DigitalBarrierOption

public DigitalBarrierOption(String underlyingName,
 double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise)

Performs the operation.

Parameters:

underlyingName - The value.

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

DigitalBarrierOption

public DigitalBarrierOption(String underlyingName,
 double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise,
 MonitoringType monitoringType,
 double[] monitoringTimes)

Performs the operation.

Parameters:

underlyingName - The value.

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

monitoringType - The value.

monitoringTimes - The value.

DigitalBarrierOption

public DigitalBarrierOption(String underlyingName,
 double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff)

Performs the operation.

Parameters:

underlyingName - The value.

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

DigitalBarrierOption

public DigitalBarrierOption(String underlyingName,
 double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 MonitoringType monitoringType,
 double[] monitoringTimes)

Performs the operation.

Parameters:

underlyingName - The value.

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

monitoringType - The value.

monitoringTimes - The value.

DigitalBarrierOption

public DigitalBarrierOption(String underlyingName,
 double maturity,
 double strike,
 double barrierValue,
 double callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff)

Performs the operation.

Parameters:

underlyingName - The value.

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 CallOrPut callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise,
 MonitoringType monitoringType,
 double[] monitoringTimes)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

monitoringType - The value.

monitoringTimes - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 double callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 double callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

DigitalBarrierOption

public DigitalBarrierOption(double maturity,
 double strike,
 double barrierValue,
 double callOrPutSign,
 BarrierType barrierType,
 DigitalPayoffType digitalPayoffType,
 double cashPayoff,
 Exercise exercise,
 MonitoringType monitoringType,
 double[] monitoringTimes)

Performs the operation.

Parameters:

maturity - The value.

strike - The value.

barrierValue - The value.

callOrPutSign - The value.

barrierType - The value.

digitalPayoffType - The value.

cashPayoff - The value.

exercise - The value.

monitoringType - The value.

monitoringTimes - The value.

Method Details

getValue

public double[] getValue(double evaluationTime,
 FiniteDifferenceEquityModel model)

Description copied from interface: FiniteDifferenceProduct

Returns the value.

Specified by:

getValue in interface FiniteDifferenceProduct<FiniteDifferenceEquityModel>

Parameters:

evaluationTime - The value.

model - The value.

Returns:

The value.

getValues

public double[][] getValues(FiniteDifferenceEquityModel model)

Description copied from interface: FiniteDifferenceProduct

Returns the value.

Specified by:

getValues in interface FiniteDifferenceProduct<FiniteDifferenceEquityModel>

Parameters:

model - The value.

Returns:

The value.

getEventTimes

public double[] getEventTimes()

Description copied from interface: FiniteDifferenceEquityEventProduct

Returns the value.

Specified by:

getEventTimes in interface FiniteDifferenceEquityEventProduct

Returns:

The value.

applyEventCondition

public double[] applyEventCondition(double time,
 double[] valuesAfterEvent,
 FiniteDifferenceEquityModel model)

Description copied from interface: FiniteDifferenceEquityEventProduct

Performs the operation.

Specified by:

applyEventCondition in interface FiniteDifferenceEquityEventProduct

Parameters:

time - The value.

valuesAfterEvent - The value.

model - The value.

Returns:

The value.

isConstraintActive

public boolean isConstraintActive(double time,
 double... stateVariables)

Description copied from interface: FiniteDifferenceInternalStateConstraint

Returns true if the internal constraint is active at the given node and time.

Specified by:

isConstraintActive in interface FiniteDifferenceInternalStateConstraint

Parameters:

time - Running time.

stateVariables - State variables at the grid node.

Returns:

True if the node is constrained.

getConstrainedValue

public double getConstrainedValue(double time,
 double... stateVariables)

Description copied from interface: FiniteDifferenceInternalStateConstraint

Returns the value to impose at a constrained node.

This method is called only if FiniteDifferenceInternalStateConstraint.isConstraintActive(double, double...) returns true.

Specified by:

getConstrainedValue in interface FiniteDifferenceInternalStateConstraint

Parameters:

time - Running time.

stateVariables - State variables at the grid node.

Returns:

The constrained value.

getUnderlyingName

public String getUnderlyingName()

Returns the value.

Returns:

The value.

getMaturity

public double getMaturity()

Description copied from interface: FiniteDifferenceOneDimensionalKnockInProduct

Returns the maturity.

Specified by:

getMaturity in interface FiniteDifferenceOneDimensionalKnockInProduct

Returns:

The maturity.

getStrike

public double getStrike()

Returns the value.

Returns:

The value.

getBarrierValue

public double getBarrierValue()

Description copied from interface: FiniteDifferenceOneDimensionalKnockInProduct

Returns the barrier level.

Specified by:

getBarrierValue in interface FiniteDifferenceOneDimensionalKnockInProduct

Returns:

The barrier level.

getCallOrPut

public CallOrPut getCallOrPut()

Returns the value.

Returns:

The value.

getBarrierType

public BarrierType getBarrierType()

Description copied from interface: FiniteDifferenceOneDimensionalKnockInProduct

Returns the barrier type.

Specified by:

getBarrierType in interface FiniteDifferenceOneDimensionalKnockInProduct

Returns:

The barrier type.

getDigitalPayoffType

public DigitalPayoffType getDigitalPayoffType()

Returns the value.

Returns:

The value.

getCashPayoff

public double getCashPayoff()

Returns the value.

Returns:

The value.

getExercise

public Exercise getExercise()

Returns the value.

Returns:

The value.

getMonitoringType

public MonitoringType getMonitoringType()

Returns the value.

Returns:

The value.

getMonitoringTimes

public double[] getMonitoringTimes()

Returns the value.

Returns:

The value.

getInactiveValueAtMaturity

public double getInactiveValueAtMaturity()

Description copied from interface: FiniteDifferenceOneDimensionalKnockInProduct

Returns the value prescribed in the inactive regime at maturity.

This is the terminal value in the no-hit region. For vanilla barrier options this is typically the rebate. For digital barrier options it is typically 0.0.

Specified by:

getInactiveValueAtMaturity in interface FiniteDifferenceOneDimensionalKnockInProduct

Returns:

The inactive value at maturity.