Class OptionOnBondHullWhiteModelBoundary

java.lang.Object

net.finmath.finitedifference.interestrate.boundaries.OptionOnBondHullWhiteModelBoundary

All Implemented Interfaces:

FiniteDifferenceInterestRateBoundary

public class OptionOnBondHullWhiteModelBoundary
extends Object
implements FiniteDifferenceInterestRateBoundary

Exact boundary conditions for OptionOnBond under FDMHullWhiteModel.

For a one-factor Hull-White model, a European option on a deterministic- cashflow bond admits an exact valuation by Jamshidian decomposition. Let T be the exercise date and let the remaining cashflows of the underlying bond at and after T be

\sum_{i} C_i P(T,T_i;x).

Since the bond value is strictly decreasing in the one-factor state variable x, there exists a unique state x* solving

\sum_i C_i P(T,T_i;x^*) = K,

where K is the strike of the bond option. The bond option value is then given by the sum of zero-coupon bond options with strikes

K_i = P(T,T_i;x^*).

Hence both lower and upper finite-difference boundaries can be imposed by exact Dirichlet conditions.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
OptionOnBondHullWhiteModelBoundary(FDMHullWhiteModel model)	Creates the exact Hull-White boundary for OptionOnBond.

Method Summary

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

OptionOnBondHullWhiteModelBoundary

public OptionOnBondHullWhiteModelBoundary(FDMHullWhiteModel model)

Creates the exact Hull-White boundary for OptionOnBond.

Parameters:

model - The Hull-White model.

Method Details

getBoundaryConditionsAtLowerBoundary

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

Description copied from interface: FiniteDifferenceInterestRateBoundary

Returns the boundary conditions at the lower boundary.

Specified by:

getBoundaryConditionsAtLowerBoundary in interface FiniteDifferenceInterestRateBoundary

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(FiniteDifferenceInterestRateProduct product,
 double time,
 double... stateVariables)

Description copied from interface: FiniteDifferenceInterestRateBoundary

Returns the boundary conditions at the upper boundary.

Specified by:

getBoundaryConditionsAtUpperBoundary in interface FiniteDifferenceInterestRateBoundary

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.