Class is implements Heston process. More...

#include <hestonProcess.hpp>

Inheritance diagram for julian::HestonProcess:

Public Member Functions
	HestonProcess (double drift, double mean_rev, double curr_var, double lt_var, double vov, double corr)
	constructor More...

virtual Path	getPath (double, const TimeGrid &, SmartPointer< UniformRNG > &rng) const
	Generates path. More...

virtual Path	getPath (double, const TimeGrid &, const std::vector< double > &rnds) const
	Generates path. More...

virtual HestonProcess *	clone () const
	Virtual copy constructor. More...

Public Member Functions inherited from julian::StochasticProcess
	StochasticProcess ()
	Constructor. More...

virtual	~StochasticProcess ()
	Destructor. More...

Private Attributes
double	drift_
	Drift of the X process. More...

double	mean_rev_
	Mean reversion speed of Y process. More...

double	curr_var_
	Initial value of Y process of Y process. More...

double	lt_var_
	Long term value of Y process. More...

double	vov_
	Volatility of Y process. More...

double	corr_
	Correlation between X process and Y process. More...

Detailed Description

Class is implements Heston process.

Heston process is a stochastic process governed by following SDE:

$dX_{t} = \mu X_{t} dt + \sqrt{Y_{t}} X_{t} dW^{X}_{t}$

$dY_{t} = \alpha (\theta - Y_{t}) dt + \sqrt{Y_{t}} \sigma dW^{Y}_{t}$

$\langle dW^{X}_{t}, dW^{Y}_{t}\rangle = \rho$

where:

$\mu$ is drift
$\alpha$ is mean reversion speed
$\theta$ is long-term volatility
$\sigma$ is volatility of volatility
$\rho$ is correlation
$dW^{X},dW^{Y}$ are Wiener Processes

As we see the process $X$ is Geometric Brownian Motion with stochastic volatility governed by CIR process. More information see [37]

Constructor & Destructor Documentation

julian::HestonProcess::HestonProcess	(	double	drift,
		double	mean_rev,
		double	curr_var,
		double	lt_var,
		double	vov,
		double	corr
	)

inline

constructor

Parameters

drift	Drift of the X process
mean_rev	Mean reversion speed of Y process
curr_var	Initial value of Y process of Y process
lt_var	Long term value of Y process
vov	Volatility of Y process
corr	Correlation between X process and Y process

Member Function Documentation

HestonProcess * julian::HestonProcess::clone ( ) const

virtual

Virtual copy constructor.

Implements julian::StochasticProcess.

Path julian::HestonProcess::getPath	(	double	x0,
		const TimeGrid &	tg,
		SmartPointer< UniformRNG > &	rng
	)		const

virtual

Generates path.

Parameters

x0	initial_value Value of the process for t = 0;
tg	points in time for which the value of process is generated
rng	random number generator that will be used to generate stochastic process

Returns: path representing time series

Implements julian::StochasticProcess.

Path julian::HestonProcess::getPath	(	double	x0,
		const TimeGrid &	tg,
		const std::vector< double > &	rnds
	)		const

virtual

Generates path.

Parameters

x0	Value of the process for t = 0;
tg	points in time for which the value of process is generated
rnds	random number that will be used to generate the path

Returns: path representing time series

Implements julian::StochasticProcess.

Member Data Documentation

double julian::HestonProcess::corr_

private

Correlation between X process and Y process.

double julian::HestonProcess::curr_var_

private

Initial value of Y process of Y process.

double julian::HestonProcess::drift_

private

Drift of the X process.

double julian::HestonProcess::lt_var_

private

Long term value of Y process.

double julian::HestonProcess::mean_rev_

private

Mean reversion speed of Y process.

double julian::HestonProcess::vov_

private

Volatility of Y process.

The documentation for this class was generated from the following files:

C:/Unix/home/OEM/jULIAN/src/mathematics/stochasticProcesses/hestonProcess.hpp
C:/Unix/home/OEM/jULIAN/src/mathematics/stochasticProcesses/hestonProcess.cpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation