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

Class MonteCarloMultiAssetBlackScholesModel

java.lang.Object
net.finmath.montecarlo.model.AbstractProcessModel
net.finmath.montecarlo.assetderivativevaluation.MonteCarloMultiAssetBlackScholesModel
All Implemented Interfaces:
Model, AssetModelMonteCarloSimulationModel, ProcessModel, MonteCarloSimulationModel
public class MonteCarloMultiAssetBlackScholesModel extends AbstractProcessModel implements AssetModelMonteCarloSimulationModel
This class implements a multi-asset Black Schole Model as Monte-Carlo simulation implementing AssetModelMonteCarloSimulationModel. The model is \[ dS_{i} = r S_{i} dt + \sigma_{i} S_{i} dW_{i}, \quad S_{i}(0) = S_{i,0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] \[ dW_{i} dW_{j} = \rho_{i,j} dt, \] 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 \[ dX_{i} = \mu_{i} dt + \lambda_{i,j} dW, \quad X_{i}(0) = \log(S_{i,0}), \] with \( S = f(X) \). See MonteCarloProcess for the notation.
Version:
1.1
Author:
Christian Fries, Roland Bachl
See Also:
The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.

  • Constructor Details

    • MonteCarloMultiAssetBlackScholesModel

      public MonteCarloMultiAssetBlackScholesModel​(RandomVariableFactory randomVariableFactory, BrownianMotion brownianMotion, double[] initialValues, double riskFreeRate, double[][] factorLoadings)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      randomVariableFactory - The RandomVariableFactory used to construct model parameters as random variables.
      brownianMotion - The Brownian motion to be used for the numerical scheme.
      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.

    • MonteCarloMultiAssetBlackScholesModel

      public MonteCarloMultiAssetBlackScholesModel​(BrownianMotion brownianMotion, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      brownianMotion - The Brownian motion to be used for the numerical scheme.
      initialValues - Spot values.
      riskFreeRate - The risk free rate.
      volatilities - The log volatilities.
      correlations - A correlation matrix.

    • MonteCarloMultiAssetBlackScholesModel

      public MonteCarloMultiAssetBlackScholesModel​(TimeDiscretization timeDiscretization, int numberOfPaths, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      timeDiscretization - The time discretization.
      numberOfPaths - The number of Monte-Carlo path to be used.
      initialValues - Spot values.
      riskFreeRate - The risk free rate.
      volatilities - The log volatilities.
      correlations - A correlation matrix.

    • MonteCarloMultiAssetBlackScholesModel

      public MonteCarloMultiAssetBlackScholesModel​(TimeDiscretization timeDiscretization, int numberOfPaths, int seed, double[] initialValues, double riskFreeRate, double[] volatilities, double[][] correlations)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      timeDiscretization - The time discretization.
      numberOfPaths - The number of Monte-Carlo path to be used.
      seed - The seed to be used.
      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.
      Specified by:
      getInitialState in interface ProcessModel
      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 \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).
      Specified by:
      getDrift in interface ProcessModel
      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.
      Specified by:
      getFactorLoading in interface ProcessModel
      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.
      Specified by:
      applyStateSpaceTransform in interface ProcessModel
      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.
      Specified by:
      applyStateSpaceTransformInverse in interface ProcessModel
      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.

    • getAssetValue

      public RandomVariable getAssetValue​(double time, int assetIndex) throws CalculationException
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Returns the random variable representing the asset's value at a given time for a given asset.
      Specified by:
      getAssetValue in interface AssetModelMonteCarloSimulationModel
      Parameters:
      time - Simulation time
      assetIndex - Index of the asset (0 for a single asset model)
      Returns:
      The asset process as seen on simulation time
      Throws:
      CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

    • getAssetValue

      public RandomVariable getAssetValue​(int timeIndex, int assetIndex) throws CalculationException
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Returns the random variable representing the asset's value at a given time for a given asset.
      Specified by:
      getAssetValue in interface AssetModelMonteCarloSimulationModel
      Parameters:
      timeIndex - Index of simulation time
      assetIndex - Index of the asset (0 for a single asset model)
      Returns:
      The asset process as seen on simulation time
      Throws:
      CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

    • getMonteCarloWeights

      public RandomVariable getMonteCarloWeights​(double time) throws CalculationException
      Description copied from interface: MonteCarloSimulationModel
      This method returns the weights of a weighted Monte Carlo method (the probability density).
      Specified by:
      getMonteCarloWeights in interface MonteCarloSimulationModel
      Parameters:
      time - Time at which the process should be observed
      Returns:
      A vector of positive weights which sums up to one
      Throws:
      CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

    • 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.
      Specified by:
      getNumeraire in interface ProcessModel
      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

    • getNumeraire

      public RandomVariable getNumeraire​(int timeIndex) throws CalculationException
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Returns the numeraire associated with the valuation measure used by this model.
      Specified by:
      getNumeraire in interface AssetModelMonteCarloSimulationModel
      Parameters:
      timeIndex - The time index (associated with this models time discretization).
      Returns:
      The numeraire associated with the valuation measure used by this model.
      Throws:
      CalculationException - Thrown if calculation of numeraire fails.

    • getNumeraire

      public RandomVariable getNumeraire​(double time) throws CalculationException
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Returns the numeraire associated with the valuation measure used by this model.
      Specified by:
      getNumeraire in interface AssetModelMonteCarloSimulationModel
      Parameters:
      time - The time for which the numeraire is requested.
      Returns:
      The numeraire associated with the valuation measure used by this model.
      Throws:
      CalculationException - Thrown if calculation of numeraire fails.

    • getRandomVariableForConstant

      public RandomVariable getRandomVariableForConstant​(double value)
      Description copied from interface: MonteCarloSimulationModel
      Returns a random variable which is initialized to a constant, but has exactly the same number of paths or discretization points as the ones used by this MonteCarloSimulationModel.
      Specified by:
      getRandomVariableForConstant in interface MonteCarloSimulationModel
      Specified by:
      getRandomVariableForConstant in interface ProcessModel
      Parameters:
      value - The constant value to be used for initialized the random variable.
      Returns:
      A new random variable.

    • getNumberOfComponents

      public int getNumberOfComponents()
      Description copied from interface: ProcessModel
      Returns the number of components
      Specified by:
      getNumberOfComponents in interface ProcessModel
      Returns:
      The number of components

    • getNumberOfAssets

      public int getNumberOfAssets()
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Returns the number of asset price processes.
      Specified by:
      getNumberOfAssets in interface AssetModelMonteCarloSimulationModel
      Returns:
      The number of asset price processes

    • 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.

    • getFactorLoadings

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

    • getVolatilities

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

    • getCorrelations

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

    • getNumberOfPaths

      public int getNumberOfPaths()
      Returns the number of paths.
      Specified by:
      getNumberOfPaths in interface MonteCarloSimulationModel
      Returns:
      The number of paths.
      See Also:
      MonteCarloProcess.getNumberOfPaths()

    • getCloneWithModifiedData

      public MonteCarloMultiAssetBlackScholesModel getCloneWithModifiedData​(Map<String,​Object> dataModified)
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Create a clone of this simulation modifying some of its properties (if any).
      Specified by:
      getCloneWithModifiedData in interface AssetModelMonteCarloSimulationModel
      Specified by:
      getCloneWithModifiedData in interface MonteCarloSimulationModel
      Specified by:
      getCloneWithModifiedData in interface ProcessModel
      Parameters:
      dataModified - The data which should be changed in the new model
      Returns:
      Returns a clone of this model, with some data modified (then it is no longer a clone :-)

    • getCloneWithModifiedSeed

      public AssetModelMonteCarloSimulationModel getCloneWithModifiedSeed​(int seed)
      Description copied from interface: AssetModelMonteCarloSimulationModel
      Create a clone of the object implementing AssetModelMonteCarloSimulationModel using a different Monte-Carlo seed.
      Specified by:
      getCloneWithModifiedSeed in interface AssetModelMonteCarloSimulationModel
      Parameters:
      seed - The seed of the underlying random number generator.
      Returns:
      Returns a clone of this model except for a modified Monte-Carlo seed.

    • getTimeDiscretization

      public TimeDiscretization getTimeDiscretization()
      Description copied from interface: MonteCarloSimulationModel
      Returns the timeDiscretizationFromArray.
      Specified by:
      getTimeDiscretization in interface MonteCarloSimulationModel
      Returns:
      Returns the timeDiscretizationFromArray.

    • getTime

      public double getTime​(int timeIndex)
      Description copied from interface: MonteCarloSimulationModel
      Returns the time for a given time index.
      Specified by:
      getTime in interface MonteCarloSimulationModel
      Parameters:
      timeIndex - Time index
      Returns:
      Returns the time for a given time index.

    • getTimeIndex

      public int getTimeIndex​(double time)
      Description copied from interface: MonteCarloSimulationModel
      Returns the time index for a given time.
      Specified by:
      getTimeIndex in interface MonteCarloSimulationModel
      Parameters:
      time - The time.
      Returns:
      Returns the time index for a given time.

    • getMonteCarloWeights

      public RandomVariable getMonteCarloWeights​(int timeIndex) throws CalculationException
      Description copied from interface: MonteCarloSimulationModel
      This method returns the weights of a weighted Monte Carlo method (the probability density).
      Specified by:
      getMonteCarloWeights in interface MonteCarloSimulationModel
      Parameters:
      timeIndex - Time index at which the process should be observed
      Returns:
      A vector of positive weights which sums up to one
      Throws:
      CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.

    • getNumberOfFactors

      public int getNumberOfFactors()
      Description copied from interface: ProcessModel
      Returns the number of factors m, i.e., the number of independent Brownian drivers.
      Specified by:
      getNumberOfFactors in interface ProcessModel
      Returns:
      The number of factors.