net.finmath.montecarlo.assetderivativevaluation.models

Class BlackScholesModelWithCurves

java.lang.Object

net.finmath.montecarlo.model.AbstractProcessModel

net.finmath.montecarlo.assetderivativevaluation.models.BlackScholesModelWithCurves

All Implemented Interfaces:

ProcessModel

public class BlackScholesModelWithCurves
extends AbstractProcessModel

This class implements a Black Scholes Model, that is, it provides the drift and volatility specification and performs the calculation of the numeraire (consistent with the dynamics, i.e. the drift). The model is \[ dS = r S dt + \sigma S dW, \quad S(0) = S_{0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] The class provides the model of S to an MonteCarloProcess via the specification of \( f = exp \), \( \mu = r - \frac{1}{2} \sigma^2 \), \( \lambda_{1,1} = \sigma \), i.e., of the SDE \[ dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(S_{0}), \] with \( S = f(X) \). See MonteCarloProcess for the notation.

Version:

1.0

Author:

Christian Fries

See Also:

The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.

Constructor Summary

Constructors

Constructor and Description
BlackScholesModelWithCurves(Double initialValue, DiscountCurve discountCurveForForwardRate, Double volatility, DiscountCurve discountCurveForDiscountRate, AbstractRandomVariableFactory randomVariableFactory) Create a Black-Scholes specification implementing AbstractProcessModel.
BlackScholesModelWithCurves(RandomVariable initialValue, DiscountCurve discountCurveForForwardRate, RandomVariable volatility, DiscountCurve discountCurveForDiscountRate, AbstractRandomVariableFactory randomVariableFactory) Create a Black-Scholes specification implementing AbstractProcessModel.

Method Summary

Modifier and Type	Method and Description
RandomVariable	applyStateSpaceTransform(int componentIndex, RandomVariable randomVariable) Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
RandomVariable	applyStateSpaceTransformInverse(int componentIndex, RandomVariable randomVariable)
BlackScholesModelWithCurves	getCloneWithModifiedData(Map<String,Object> dataModified) Returns a clone of this model where the specified properties have been modified.
RandomVariable[]	getDrift(int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor) This method has to be implemented to return the drift, i.e.
RandomVariable[]	getFactorLoading(int timeIndex, int component, RandomVariable[] realizationAtTimeIndex) This method has to be implemented to return the factor loadings, i.e.
RandomVariable[]	getInitialState() Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.
RandomVariable[]	getInitialValue() Return the initial value of this model.
int	getNumberOfComponents() Returns the number of components
RandomVariable	getNumeraire(double time) Return the numeraire at a given time index.
RandomVariable	getRandomVariableForConstant(double value) Return a random variable initialized with a constant using the models random variable factory.
RandomVariable	getVolatility() Returns the volatility parameter of this model.
String	toString()

Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel

getMonteCarloWeights, getNumberOfFactors, getProcess, getProcessValue, getReferenceDate, getTime, getTimeDiscretization, getTimeIndex, setProcess

Methods inherited from class java.lang.Object

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

Constructor Detail

BlackScholesModelWithCurves

public BlackScholesModelWithCurves(RandomVariable initialValue,
                                   DiscountCurve discountCurveForForwardRate,
                                   RandomVariable volatility,
                                   DiscountCurve discountCurveForDiscountRate,
                                   AbstractRandomVariableFactory randomVariableFactory)

Create a Black-Scholes specification implementing AbstractProcessModel.

Parameters:

initialValue - Spot value.

discountCurveForForwardRate - The curve used for calcuation of the forward.

volatility - The log volatility.

discountCurveForDiscountRate - The curve used for calcualtion of the disocunt factor / numeraire.

randomVariableFactory - The random variable factory used to create random variables from constants.

BlackScholesModelWithCurves

public BlackScholesModelWithCurves(Double initialValue,
                                   DiscountCurve discountCurveForForwardRate,
                                   Double volatility,
                                   DiscountCurve discountCurveForDiscountRate,
                                   AbstractRandomVariableFactory randomVariableFactory)

Create a Black-Scholes specification implementing AbstractProcessModel.

Parameters:

initialValue - Spot value.

discountCurveForForwardRate - The curve used for calcuation of the forward.

volatility - The log volatility.

discountCurveForDiscountRate - The curve used for calcualtion of the disocunt factor / numeraire.

randomVariableFactory - The random variable factory used to create random variables from constants.

Method Detail

getInitialState

public RandomVariable[] getInitialState()

Description copied from interface: ProcessModel

Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.

Returns:

The initial value of the state variable of the process Y(t=0).

getDrift

public RandomVariable[] getDrift(int timeIndex,
                                 RandomVariable[] realizationAtTimeIndex,
                                 RandomVariable[] realizationPredictor)

Description copied from interface: ProcessModel

This method has to be implemented to return the drift, i.e. the coefficient vector
μ = (μ₁, ..., μ_n) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process. Since the model is provided only on a time discretization, the method may also (should try to) return the drift as \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).

Parameters:

timeIndex - The time index (related to the model times discretization).

realizationAtTimeIndex - The given realization at timeIndex

realizationPredictor - The given realization at timeIndex+1 or null if no predictor is available.

Returns:

The drift or average drift from timeIndex to timeIndex+1, i.e. \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \) (or a suitable approximation).

getFactorLoading

public RandomVariable[] getFactorLoading(int timeIndex,
                                         int component,
                                         RandomVariable[] realizationAtTimeIndex)

Description copied from interface: ProcessModel

This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λ_j = (λ_1,j, ..., λ_m,j) such that X = f(Y) and
dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m
in an m-factor model. Here j denotes index of the component of the resulting process.

Parameters:

timeIndex - The time index (related to the model times discretization).

component - The index j of the driven component.

realizationAtTimeIndex - The realization of X at the time corresponding to timeIndex (in order to implement local and stochastic volatlity models).

Returns:

The factor loading for given factor and component.

applyStateSpaceTransform

public RandomVariable applyStateSpaceTransform(int componentIndex,
                                               RandomVariable randomVariable)

Description copied from interface: ProcessModel

Applies the state space transform f_i to the given state random variable such that Y_i → f_i(Y_i) =: X_i.

Parameters:

componentIndex - The component index i.

randomVariable - The state random variable Y_i.

Returns:

New random variable holding the result of the state space transformation.

applyStateSpaceTransformInverse

public RandomVariable applyStateSpaceTransformInverse(int componentIndex,
                                                      RandomVariable randomVariable)

getNumeraire

public RandomVariable getNumeraire(double time)

Description copied from interface: ProcessModel

Return the numeraire at a given time index. Note: The random variable returned is a defensive copy and may be modified.

Parameters:

time - The time t for which the numeraire N(t) should be returned.

Returns:

The numeraire at the specified time as RandomVariableFromDoubleArray

getNumberOfComponents

public int getNumberOfComponents()

Description copied from interface: ProcessModel

Returns the number of components

Returns:

The number of components

getRandomVariableForConstant

public RandomVariable getRandomVariableForConstant(double value)

Description copied from interface: ProcessModel

Return a random variable initialized with a constant using the models random variable factory.

Parameters:

value - The constant value.

Returns:

A new random variable initialized with a constant value.

getCloneWithModifiedData

public BlackScholesModelWithCurves getCloneWithModifiedData(Map<String,Object> dataModified)

Description copied from interface: ProcessModel

Returns a clone of this model where the specified properties have been modified. Note that there is no guarantee that a model reacts on a specification of a properties in the parameter map dataModified. If data is provided which is ignored by the model no exception may be thrown.

Parameters:

dataModified - Key-value-map of parameters to modify.

Returns:

A clone of this model (or this model if no parameter was modified).

toString

public String toString()

Overrides:

toString in class Object

getInitialValue

public RandomVariable[] getInitialValue()

Return the initial value of this model.

Overrides:

getInitialValue in class AbstractProcessModel

Returns:

the initial value of this model.

getVolatility

public RandomVariable getVolatility()

Returns the volatility parameter of this model.

Returns:

Returns the volatility.