Last Change: 2018-09-07, 16:50
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StochasticProcess1D − 1-dimensional stochastic process
#include <ql/stochasticprocess.hpp>
Inherits StochasticProcess.
Inherited by CoxIngersollRoss::HelperProcess, ExtendedOrnsteinUhlenbeckProcess, ForwardMeasureProcess1D, GemanRoncoroniProcess, GeneralizedBlackScholesProcess, GeneralizedOrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, HullWhiteProcess, Merton76Process, MfStateProcess, OrnsteinUhlenbeckProcess, SquareRootProcess, and VarianceGammaProcess.
Classes
class discretization
discretization of a 1-D stochastic process
Public Member Functions
1-D stochastic process interface
virtual Real x0 () const =0
returns the initial value of the state variable
virtual Real drift (Time t, Real x) const =0
returns the drift part of the equation, i.e. $ (t, x_t) $
virtual Real diffusion (Time t, Real x) const =0
returns the diffusion part of the equation, i.e. $ ma(t, x_t) $
virtual Real expectation (Time t0, Real x0, Time dt) const
virtual Real stdDeviation (Time t0, Real x0, Time dt) const
virtual Real variance (Time t0, Real x0, Time dt) const
virtual Real evolve (Time t0, Real x0, Time dt, Real dw) const
virtual Real apply (Real x0, Real dx) const
Protected Member Functions
StochasticProcess1D (const boost::shared_ptr< discretization > &)
Protected Attributes
boost::shared_ptr< discretization > discretization_
Additional Inherited Members
1-dimensional stochastic process
This class describes a stochastic process governed by dx_t = (t, x_t)dt + ma(t, x_t)dW_t. ]
virtual Real expectation (Time t0, Real x0, Time dt) const [virtual]
returns the expectation $ E(x_{t_0 + process after a time interval $ given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in GeneralizedBlackScholesProcess, HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
virtual Real stdDeviation (Time t0, Real x0, Time dt) const [virtual]
returns the standard deviation $ S(x_{t_0 + process after a time interval $ given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in GeneralizedBlackScholesProcess, HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
virtual Real variance (Time t0, Real x0, Time dt) const [virtual]
returns the variance $ V(x_{t_0 + process after a time interval $ given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented in GeneralizedBlackScholesProcess, HullWhiteForwardProcess, OrnsteinUhlenbeckProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, GsrProcess, HullWhiteProcess, and MfStateProcess.
virtual Real evolve (Time t0, Real x0, Time dt, Real dw) const [virtual]
returns the asset value after a time interval $ given discretization. By default, it returns E(x_0,t_0, expectation and $ S $ the standard deviation.
Reimplemented in GeneralizedBlackScholesProcess, GemanRoncoroniProcess, and ExtendedBlackScholesMertonProcess.
virtual Real apply (Real x0, Real dx) const [virtual]
applies a change to the asset value. By default, it returns $ x + .PP Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.
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