Module net.finmath.lib
Package net.finmath.montecarlo.assetderivativevaluation.models

Class MultiAssetBlackScholesModel

java.lang.Object
net.finmath.montecarlo.model.AbstractProcessModel
net.finmath.montecarlo.assetderivativevaluation.models.MultiAssetBlackScholesModel
All Implemented Interfaces:
ProcessModel
public class MultiAssetBlackScholesModel extends AbstractProcessModel
This class implements a multi-asset Black Scholes model providing an AbstractProcessModel. 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 MonteCarloProcess 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 \( S = f(X) \). See MonteCarloProcess for the notation.
Version:
1.1
Author:
Christian Fries
See Also:

  • Constructor Details

    • 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.

    • 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.

    • 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.

    • 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.

  • Method Details

    • 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, ..., 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 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
      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.

    • 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.

    • 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.

    • 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

    • 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.

    • 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.

    • 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 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.

    • getFactorLoadingMatrix

      public double[][] getFactorLoadingMatrix()
      Returns the factorLoadings parameters of this model.
      Returns:
      Returns the factorLoadings.

    • getVolatilityVector

      public double[] getVolatilityVector()
      Returns the volatility parameters of this model.
      Returns:
      Returns the volatilities.

    • getCorrelationMatrix

      public double[][] getCorrelationMatrix()
      Returns the volatility parameters of this model.
      Returns:
      Returns the volatilities.