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

Class DisplacedLognomalModel

java.lang.Object
net.finmath.montecarlo.model.AbstractProcessModel
net.finmath.montecarlo.assetderivativevaluation.models.DisplacedLognomalModel
All Implemented Interfaces:
ProcessModel
public class DisplacedLognomalModel extends AbstractProcessModel
This class implements a displaced lognormal 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 \[ \mathrm{d}S = r S \mathrm{d}t + \sigma (d \cdot N + S) \mathrm{d}W, \quad S(0) = S_{0}, \] \[ \mathrm{d}N = r N \mathrm{d}t, \quad N(0) = N_{0}, \] Note that \[ \mathrm{d}(S/N) = \sigma (d+S/N) \mathrm{d}W \] that is \[ \mathrm{d}X = - 1/2 \sigma^2 \mathrm{d}t + \sigma \mathrm{d}W \] with exp(X) = d + S/N, i.e. S = N ( exp(X)-d ). The class provides the model of S to an MonteCarloProcess via the specification of \( S = f(X) = N (exp(X)-d) \), \( \mu = -\frac{1}{2} \sigma^{2} \), \( \lambda_{1,1} = \sigma \), i.e., of the SDE \[ dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(d+S_{0}), \] with \( N(0) = 1 \). See MonteCarloProcess for the notation. The model can be interpreted as a linear interpolation of the Black-Scholes model BlackScholesModel and the homogeneous Bachelier model BachelierModel.
Version:
1.1
Author:
Christian Fries
See Also:
The interface for numerical schemes., The interface for models provinding parameters to numerical schemes.

  • Constructor Details

    • DisplacedLognomalModel

      public DisplacedLognomalModel​(RandomVariableFactory randomVariableFactory, RandomVariable initialValue, RandomVariable riskFreeRate, RandomVariable displacement, RandomVariable volatility)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      randomVariableFactory - The RandomVariableFactory used to generate random variables from constants.
      initialValue - Spot value.
      riskFreeRate - The risk free rate.
      displacement - The displacement parameter d.
      volatility - The volatility.

    • DisplacedLognomalModel

      public DisplacedLognomalModel​(RandomVariableFactory randomVariableFactory, double initialValue, double riskFreeRate, double displacement, double volatility)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      randomVariableFactory - The RandomVariableFactory used to generate random variables from constants.
      initialValue - Spot value.
      riskFreeRate - The risk free rate.
      displacement - The displacement parameter d.
      volatility - The volatility.

    • DisplacedLognomalModel

      public DisplacedLognomalModel​(double initialValue, double riskFreeRate, double displacement, double volatility)
      Create a Monte-Carlo simulation using given time discretization.
      Parameters:
      initialValue - Spot value.
      riskFreeRate - The risk free rate.
      displacement - The displacement parameter d.
      volatility - The volatility.

  • 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

    • 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 DisplacedLognomalModel 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

    • getRandomVariableFactory

      public RandomVariableFactory getRandomVariableFactory()

    • getInitialValue

      public RandomVariable getInitialValue()

    • getRiskFreeRate

      public RandomVariable getRiskFreeRate()
      Returns the risk free rate parameter of this model.
      Returns:
      Returns the riskFreeRate.

    • getDisplacement

      public RandomVariable getDisplacement()

    • getVolatility

      public RandomVariable getVolatility()
      Returns the volatility parameter of this model.
      Returns:
      Returns the volatility.