Module net.finmath.lib
Package net.finmath.fouriermethod.models

Class HestonModel

java.lang.Object
net.finmath.fouriermethod.models.HestonModel
All Implemented Interfaces:
CharacteristicFunctionModel, Model
public class HestonModel extends Object implements CharacteristicFunctionModel
Implements the characteristic function of a Heston model. The model is \[ dS(t) = r^{\text{c}}(t) S(t) dt + \sqrt{V(t)} S(t) dW_{1}(t), \quad S(0) = S_{0}, \] \[ dV(t) = \kappa ( \theta - V(t) ) dt + \xi \sqrt{V(t)} dW_{2}(t), \quad V(0) = \sigma^2, \] \[ dW_{1} dW_{2} = \rho dt \] \[ dN(t) = r^{\text{d}}(t) N(t) dt, \quad N(0) = N_{0}, \] where \( W \) is a Brownian motion. The model allows to specify two independent rate for forwarding (\( r^{\text{c}} \)) and discounting (\( r^{\text{d}} \)). It thus allow for a simple modelling of a funding / collateral curve (via (\( r^{\text{d}} \)) and/or the specification of a dividend yield. The free parameters of this model are:
\( S_{0} \)
spot - initial value of S
\( r^{\text{c}} \)
the risk free rate (may be provided as a curve or a constant)
\( \sigma \)
the initial volatility level
\( r^{\text{d}} \)
the discount rate (may be provided as a curve or a constant)
\( \xi \)
the volatility of volatility
\( \theta \)
the mean reversion level of the stochastic volatility
\( \kappa \)
the mean reversion speed of the stochastic volatility
\( \rho \)
the correlation of the Brownian drivers
Version:
1.0
Author:
Christian Fries, Andy Graf, Lorenzo Toricelli

  • Constructor Details

    • HestonModel

      public HestonModel​(LocalDate referenceDate, double initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, double volatility, double theta, double kappa, double xi, double rho)
      Create a Heston model (characteristic function)
      Parameters:
      referenceDate - The date representing the time t = 0. All other double times are following FloatingpointDate.
      initialValue - \( S_{0} \) - spot - initial value of S
      discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate
      discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate
      volatility - \( \sigma \) the initial volatility level
      theta - \( \theta \) - the mean reversion level of the stochastic volatility
      kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility
      xi - \( \xi \) - the volatility of volatility
      rho - \( \rho \) - the correlation of the Brownian drivers

    • HestonModel

      public HestonModel​(double initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, double volatility, double theta, double kappa, double xi, double rho)
      Create a Heston model (characteristic function)
      Parameters:
      initialValue - \( S_{0} \) - spot - initial value of S
      discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate
      discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate
      volatility - \( \sigma \) the initial volatility level
      theta - \( \theta \) - the mean reversion level of the stochastic volatility
      kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility
      xi - \( \xi \) - the volatility of volatility
      rho - \( \rho \) - the correlation of the Brownian drivers

    • HestonModel

      public HestonModel​(double initialValue, double riskFreeRate, double volatility, double discountRate, double theta, double kappa, double xi, double rho)
      Create a Heston model (characteristic function)
      Parameters:
      initialValue - \( S_{0} \) - spot - initial value of S
      riskFreeRate - \( r^{\text{c}} \) - the risk free rate
      volatility - \( \sigma \) the initial volatility level
      discountRate - \( r^{\text{d}} \) - the discount rate
      theta - \( \theta \) - the mean reversion level of the stochastic volatility
      kappa - \( \kappa \) - the mean reversion speed of the stochastic volatility
      xi - \( \xi \) - the volatility of volatility
      rho - \( \rho \) - the correlation of the Brownian drivers

    • HestonModel

      public HestonModel​(double initialValue, double riskFreeRate, double volatility, double theta, double kappa, double xi, double rho)

  • Method Details

    • apply

      public CharacteristicFunction apply​(double time)
      Description copied from interface: CharacteristicFunctionModel
      Returns the characteristic function of X(t), where X is this stochastic process.
      Specified by:
      apply in interface CharacteristicFunctionModel
      Parameters:
      time - The time at which the stochastic process is observed.
      Returns:
      The characteristic function of X(t).

    • getReferenceDate

      public LocalDate getReferenceDate()
      Returns:
      the referenceDate

    • getInitialValue

      public double getInitialValue()
      Returns:
      the initialValue

    • getDiscountCurveForForwardRate

      public DiscountCurve getDiscountCurveForForwardRate()
      Returns:
      the discountCurveForForwardRate

    • getRiskFreeRate

      public double getRiskFreeRate()
      Returns:
      the riskFreeRate

    • getDiscountCurveForDiscountRate

      public DiscountCurve getDiscountCurveForDiscountRate()
      Returns:
      the discountCurveForDiscountRate

    • getDiscountRate

      public double getDiscountRate()
      Returns:
      the discountRate

    • getVolatility

      public double getVolatility()
      Returns:
      the volatility

    • getTheta

      public double getTheta()
      Returns:
      the theta

    • getKappa

      public double getKappa()
      Returns:
      the kappa

    • getXi

      public double getXi()
      Returns:
      the xi

    • getRho

      public double getRho()
      Returns:
      the rho

    • toString

      public String toString()
      Overrides:
      toString in class Object