java.lang.Object
- net.finmath.montecarlo.model.AbstractProcessModel
- - net.finmath.montecarlo.assetderivativevaluation.models.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 \[ dS = r S \mathrm{d}t + \sigma \mathrm{d}W, \quad S(0) = S_{0}, \] \[ dN = r N \mathrm{d}t, \quad N(0) = N_{0}, \]
Note, the model corresponds to the following dynamic for the numeraire relative stock value \( F(t) = S(t)/N(t) \): \[ \mathrm{d}F = exp(-r t) \sigma \mathrm{d}W, \quad F(0) = F_{0} = S_{0}/N_{0}, \]
Note that the variance of \( \int_{t}^{t+\Delta t} \mathrm{d}F \) is \[ \int_{t}^{t+\Delta t} ( exp(-r s) \sigma )^{2} \mathrm{d}s = \frac{\exp(-2 r t)}{2 r} \left( 1 - \exp(-2 r \Delta t) \right) \] 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

See Also:

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

Constructor Summary

Constructors
Constructor	Description
`InhomogenousBachelierModel(double initialValue, double riskFreeRate, double volatility)`	Create a Monte-Carlo simulation using given time discretization.
`InhomogenousBachelierModel(RandomVariableFactory randomVariableFactory, RandomVariable initialValue, RandomVariable riskFreeRate, RandomVariable volatility)`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`RandomVariable`	`applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)`	Applies the state space transform f_i to the given state random variable such that Y_i → f_i(Y_i) =: X_i.
`RandomVariable`	`applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)`	Applies the inverse state space transform f^-1_i to the given random variable such that X_i → f^-1_i(X_i) =: Y_i.
`InhomogenousBachelierModel`	`getCloneWithModifiedData(Map<String,Object> dataModified)`	Returns a clone of this model where the specified properties have been modified.
`RandomVariable[]`	`getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)`	This method has to be implemented to return the drift, i.e.
`RandomVariable[]`	`getFactorLoading(MonteCarloProcess process, int timeIndex, int component, RandomVariable[] realizationAtTimeIndex)`	This method has to be implemented to return the factor loadings, i.e.
`RandomVariable`	`getImpliedBachelierVolatility(double maturity)`
`RandomVariable[]`	`getInitialState(MonteCarloProcess process)`	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()`	Returns the initial value parameter of this model.
`int`	`getNumberOfComponents()`	Returns the number of components
`int`	`getNumberOfFactors()`	Returns the number of factors m, i.e., the number of independent Brownian drivers.
`RandomVariable`	`getNumeraire(MonteCarloProcess process, 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`	`getRiskFreeRate()`	Returns the risk free rate parameter of this model.
`RandomVariable`	`getVolatility()`	Returns the volatility parameter of this model.
`String`	`toString()`

Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel
getInitialValue, getReferenceDate

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - InhomogenousBachelierModel
```
public InhomogenousBachelierModel(RandomVariableFactory randomVariableFactory,
                                  RandomVariable initialValue,
                                  RandomVariable riskFreeRate,
                                  RandomVariable volatility)
```
  - 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(MonteCarloProcess process)
```
    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.
    
    Parameters:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    Returns:
    
    The initial value of the state variable of the process Y(t=0).
  - getDrift
```
public RandomVariable[] getDrift(MonteCarloProcess process,
                                 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:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    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(MonteCarloProcess process,
                                         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:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    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(MonteCarloProcess process,
                                               int timeIndex,
                                               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:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    timeIndex - The time index (related to the model times discretization).
    
    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(MonteCarloProcess process,
                                                      int timeIndex,
                                                      int componentIndex,
                                                      RandomVariable randomVariable)
```
    Description copied from interface: ProcessModel
    
    Applies the inverse state space transform f^-1_i to the given random variable such that X_i → f^-1_i(X_i) =: Y_i.
    
    Parameters:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    timeIndex - The time index (related to the model times discretization).
    
    componentIndex - The component index i.
    
    randomVariable - The state random variable X_i.
    
    Returns:
    
    New random variable holding the result of the state space transformation.
  - getNumeraire
```
public RandomVariable getNumeraire(MonteCarloProcess process,
                                   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:
    
    process - The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.
    
    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: ProcessModel
    
    Returns the number of components
    
    Returns:
    
    The number of components
  - getNumberOfFactors
```
public int getNumberOfFactors()
```
    Description copied from interface: ProcessModel
    
    Returns the number of factors m, i.e., the number of independent Brownian drivers.
    
    Returns:
    
    The number of factors.
  - 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
  - getInitialValue
```
public RandomVariable getInitialValue()
```
    Returns the initial value parameter of this model.
    
    Returns:
    
    Returns the initialValue
  - getRiskFreeRate
```
public RandomVariable getRiskFreeRate()
```
    Returns the risk free rate parameter of this model.
    
    Returns:
    
    Returns the riskFreeRate.
  - getVolatility
```
public RandomVariable getVolatility()
```
    Returns the volatility parameter of this model.
    
    Returns:
    
    Returns the volatility.
  - getImpliedBachelierVolatility
```
public RandomVariable getImpliedBachelierVolatility(double maturity)
```

Class InhomogenousBachelierModel

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

InhomogenousBachelierModel

InhomogenousBachelierModel

Method Detail

getInitialState

getDrift

getFactorLoading

applyStateSpaceTransform

applyStateSpaceTransformInverse

getNumeraire

getNumberOfComponents

getNumberOfFactors

getRandomVariableForConstant

getCloneWithModifiedData

toString

getInitialValue

getRiskFreeRate

getVolatility

getImpliedBachelierVolatility