finMath lib documentation
net.finmath.montecarlo.assetderivativevaluation.models

Class InhomogenousBachelierModel

• All Implemented Interfaces:
ProcessModel

public class InhomogenousBachelierModel
extends AbstractProcessModel
This class implements a (variant of the) Bachelier 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 $dS = r S dt + \sigma dW, \quad S(0) = S_{0},$ $dN = r N dt, \quad N(0) = N_{0},$ The class provides the model of S to an MonteCarloProcess via the specification of $$f = \text{identity}$$, $$\mu = \frac{exp(r \Delta t_{i}) - 1}{\Delta t_{i}} S(t_{i})$$, $$\lambda_{1,1} = \sigma \frac{exp(-2 r t_{i}) - exp(-2 r t_{i+1})}{2 r \Delta t_{i}}$$, i.e., of the SDE $dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(S_{0}),$ with $$S = X$$. See MonteCarloProcess for the notation. The model's implied Bachelier volatility for a given maturity T is volatility * Math.sqrt((Math.exp(2 * riskFreeRate * optionMaturity) - 1)/(2*riskFreeRate*optionMaturity))
Version:
1.0
Author:
Christian Fries
The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.
• Constructor Summary

Constructors
Constructor and Description
InhomogenousBachelierModel(double initialValue, double riskFreeRate, double volatility)
Create a Monte-Carlo simulation using given time discretization.
• Method Summary

All Methods
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)
InhomogenousBachelierModel 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.
double getImpliedBachelierVolatility(double maturity)
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.
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.
double getRiskFreeRate()
Returns the risk free rate parameter of this model.
double getVolatility()
Returns the volatility parameter of this model.
String toString()
• Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel

getInitialValue, 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

• InhomogenousBachelierModel

public InhomogenousBachelierModel(double initialValue,
double riskFreeRate,
double volatility)
Create a Monte-Carlo simulation using given time discretization.
Parameters:
initialValue - Spot value.
riskFreeRate - The risk free rate.
volatility - The volatility.
• 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, ..., μn) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
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).

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
λj = (λ1,j, ..., λm,j) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
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:
• applyStateSpaceTransform

public RandomVariable applyStateSpaceTransform(int componentIndex,
RandomVariable randomVariable)
Description copied from interface: ProcessModel
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
Parameters:
componentIndex - The component index i.
randomVariable - The state random variable Yi.
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 InhomogenousBachelierModel 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
• getRiskFreeRate

public double getRiskFreeRate()
Returns the risk free rate parameter of this model.
Returns:
Returns the riskFreeRate.
• getVolatility

public double getVolatility()
Returns the volatility parameter of this model.
Returns:
Returns the volatility.
• getImpliedBachelierVolatility

public double getImpliedBachelierVolatility(double maturity)