finMath lib documentation
net.finmath.montecarlo.assetderivativevaluation

## Class InhomogenousBachelierModel

• All Implemented Interfaces:
AbstractModelInterface

public class InhomogenousBachelierModel
extends AbstractModel
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 AbstractProcessInterface 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 AbstractProcessInterface 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))
Author:
Christian Fries
The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.
• ### 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 RandomVariableInterface[] getInitialState()
Description copied from interface: AbstractModelInterface
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 RandomVariableInterface[] getDrift(int timeIndex,
RandomVariableInterface[] realizationAtTimeIndex,
RandomVariableInterface[] realizationPredictor)
Description copied from interface: AbstractModelInterface
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).

int component,
RandomVariableInterface[] realizationAtTimeIndex)
Description copied from interface: AbstractModelInterface
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 RandomVariableInterface applyStateSpaceTransform(int componentIndex,
RandomVariableInterface randomVariable)
Description copied from interface: AbstractModelInterface
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.
• #### getNumeraire

public RandomVariableInterface getNumeraire(double time)
Description copied from interface: AbstractModelInterface
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 RandomVariable
• #### getNumberOfComponents

public int getNumberOfComponents()
Description copied from interface: AbstractModelInterface
Returns the number of components
Returns:
The number of components
• #### getRandomVariableForConstant

public RandomVariableInterface getRandomVariableForConstant(double value)
Description copied from interface: AbstractModelInterface
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: AbstractModelInterface
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).
• #### 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)