Module net.finmath.lib
Class MultiAssetBlackScholesModel
- java.lang.Object
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- net.finmath.montecarlo.model.AbstractProcessModel
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- net.finmath.montecarlo.assetderivativevaluation.models.MultiAssetBlackScholesModel
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- All Implemented Interfaces:
ProcessModel
public class MultiAssetBlackScholesModel extends AbstractProcessModel
This class implements a multi-asset Black Scholes model providing anAbstractProcessModel
. The class can be used with an EulerSchemeFromProcessModel to create a Monte-Carlo simulation. The model can be specified by general factor loadings, that is, in the form \[ dS_{i} = r S_{i} dt + S_{i} \sum_{j=0}^{m-1} f{i,j} dW_{j}, \quad S_{i}(0) = S_{i,0}, \] \[ dN = r N dt, \quad N(0) = N_{0}. \] Alternatively, the model can be specifies by providing volatilities and correlations from which the factor loadings \( f_{i,j} \) are derived such that \[ \sum_{k=0}^{m-1} f{i,k} f{j,k} = \sigma_{i} \sigma_{j} \rho_{i,j} \] such that the effective model is \[ dS_{i} = r S_{i} dt + \sigma_{i} S_{i} dW_{i}, \quad S_{i}(0) = S_{i,0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] \[ dW_{i} dW_{j} = \rho_{i,j} dt, \] Note that in case the model is used with an EulerSchemeFromProcessModel, the BrownianMotion used can have a correlation, which alters the simulation (which is admissible). The specification above hold, provided that the BrownianMotion used has independent components. The class provides the model of \( S_{i} \) to an
via the specification of \( f = exp \), \( \mu_{i} = r - \frac{1}{2} \sigma_{i}^2 \), \( \lambda_{i,j} = \sigma_{i} g_{i,j} \), i.e., of the SDE \[ dX_{i} = \mu_{i} dt + \sum_{j=0}^{m-1} \lambda_{i,j} dW_{j}, \quad X_{i}(0) = \log(S_{i,0}), \] with \( S = f(X) \). SeeMonteCarloProcess
MonteCarloProcess
for the notation.- Version:
- 1.1
- Author:
- Christian Fries
- See Also:
The interface for numerical schemes.
,The interface for models provinding parameters to numerical schemes.
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Constructor Summary
Constructors Constructor Description MultiAssetBlackScholesModel(double[] initialValues, double riskFreeRate, double[][] factorLoadings)
Create a multi-asset Black-Scholes model.MultiAssetBlackScholesModel(double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
Create a multi-asset Black-Scholes model.MultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory, double[] initialValues, double riskFreeRate, double[][] factorLoadings)
Create a multi-asset Black-Scholes model.MultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
Create a multi-asset Black-Scholes model.
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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 fi to the given state random variable such that Yi → fi(Yi) =: Xi.RandomVariable
applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.MultiAssetBlackScholesModel
getCloneWithModifiedData(Map<String,Object> dataModified)
Returns a clone of this model where the specified properties have been modified.double[][]
getCorrelationMatrix()
Returns the volatility parameters of this model.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.double[][]
getFactorLoadingMatrix()
Returns the factorLoadings parameters of this model.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.int
getNumberOfComponents()
Returns the number of componentsint
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.double
getRiskFreeRate()
Returns the risk free rate parameter of this model.double[]
getVolatilityVector()
Returns the volatility parameters of this model.String
toString()
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Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel
getInitialValue, getReferenceDate
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Constructor Detail
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MultiAssetBlackScholesModel
public MultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory, double[] initialValues, double riskFreeRate, double[][] factorLoadings)
Create a multi-asset Black-Scholes model.- Parameters:
randomVariableFactory
- The RandomVariableFactory used to construct model parameters as random variables.initialValues
- Spot values.riskFreeRate
- The risk free rate.factorLoadings
- The matrix of factor loadings, where factorLoadings[underlyingIndex][factorIndex] is the coefficient of the Brownian driver factorIndex used for the underlying underlyingIndex.
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MultiAssetBlackScholesModel
public MultiAssetBlackScholesModel(RandomVariableFactory randomVariableFactory, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
Create a multi-asset Black-Scholes model.- Parameters:
randomVariableFactory
- The RandomVariableFactory used to construct model parameters as random variables.initialValues
- Spot values.riskFreeRate
- The risk free rate.volatilities
- The log volatilities.correlations
- A correlation matrix.
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MultiAssetBlackScholesModel
public MultiAssetBlackScholesModel(double[] initialValues, double riskFreeRate, double[][] factorLoadings)
Create a multi-asset Black-Scholes model.- Parameters:
initialValues
- Spot values.riskFreeRate
- The risk free rate.factorLoadings
- The matrix of factor loadings, where factorLoadings[underlyingIndex][factorIndex] is the coefficient of the Brownian driver factorIndex used for the underlying underlyingIndex.
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MultiAssetBlackScholesModel
public MultiAssetBlackScholesModel(double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
Create a multi-asset Black-Scholes model.- Parameters:
initialValues
- Spot values.riskFreeRate
- The risk free rate.volatilities
- The log volatilities.correlations
- A correlation matrix.
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Method Detail
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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).
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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, ..., 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:
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 timeIndexrealizationPredictor
- The given realization attimeIndex+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).
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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
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:
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.
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applyStateSpaceTransform
public RandomVariable applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, 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:
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 Yi.- Returns:
- New random variable holding the result of the state space transformation.
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applyStateSpaceTransformInverse
public RandomVariable applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Description copied from interface:ProcessModel
Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.- 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 Xi.- Returns:
- New random variable holding the result of the state space transformation.
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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
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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.
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getNumberOfComponents
public int getNumberOfComponents()
Description copied from interface:ProcessModel
Returns the number of components- Returns:
- The number of components
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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.
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getCloneWithModifiedData
public MultiAssetBlackScholesModel 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 mapdataModified
. 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).
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getRiskFreeRate
public double getRiskFreeRate()
Returns the risk free rate parameter of this model.- Returns:
- Returns the riskFreeRate.
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getFactorLoadingMatrix
public double[][] getFactorLoadingMatrix()
Returns the factorLoadings parameters of this model.- Returns:
- Returns the factorLoadings.
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getVolatilityVector
public double[] getVolatilityVector()
Returns the volatility parameters of this model.- Returns:
- Returns the volatilities.
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getCorrelationMatrix
public double[][] getCorrelationMatrix()
Returns the volatility parameters of this model.- Returns:
- Returns the volatilities.
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