QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.20
Public Member Functions | List of all members
BatesProcess Class Reference

Square-root stochastic-volatility Bates process. More...

#include <ql/processes/batesprocess.hpp>

+ Inheritance diagram for BatesProcess:

Public Member Functions

 BatesProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Real lambda, Real nu, Real delta, HestonProcess::Discretization d=HestonProcess::FullTruncation)
 
Size factors () const
 returns the number of independent factors of the process
 
Disposable< Arraydrift (Time t, const Array &x) const
 returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
 
Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
 
Real lambda () const
 
Real nu () const
 
Real delta () const
 
- Public Member Functions inherited from HestonProcess
 HestonProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Discretization d=QuadraticExponentialMartingale)
 
Size size () const
 returns the number of dimensions of the stochastic process
 
Size factors () const
 returns the number of independent factors of the process
 
Disposable< ArrayinitialValues () const
 returns the initial values of the state variables
 
Disposable< Arraydrift (Time t, const Array &x) const
 returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
 
Disposable< Matrixdiffusion (Time t, const Array &x) const
 returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
 
Disposable< Arrayapply (const Array &x0, const Array &dx) const
 
Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
 
Real v0 () const
 
Real rho () const
 
Real kappa () const
 
Real theta () const
 
Real sigma () const
 
const Handle< Quote > & s0 () const
 
const Handle< YieldTermStructure > & dividendYield () const
 
const Handle< YieldTermStructure > & riskFreeRate () const
 
Time time (const Date &) const
 
Real pdf (Real x, Real v, Time t, Real eps=1e-3) const
 
- Public Member Functions inherited from StochasticProcess
virtual Disposable< Arrayexpectation (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< MatrixstdDeviation (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< Matrixcovariance (Time t0, const Array &x0, Time dt) const
 
void update ()
 
- Public Member Functions inherited from Observer
 Observer (const Observer &)
 
Observeroperator= (const Observer &)
 
std::pair< iterator, bool > registerWith (const ext::shared_ptr< Observable > &)
 
void registerWithObservables (const ext::shared_ptr< Observer > &)
 
Size unregisterWith (const ext::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 
virtual void deepUpdate ()
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observableoperator= (const Observable &)
 
void notifyObservers ()
 

Additional Inherited Members

- Public Types inherited from HestonProcess
enum  Discretization {
  PartialTruncation, FullTruncation, Reflection, NonCentralChiSquareVariance,
  QuadraticExponential, QuadraticExponentialMartingale, BroadieKayaExactSchemeLobatto, BroadieKayaExactSchemeLaguerre,
  BroadieKayaExactSchemeTrapezoidal
}
 
- Public Types inherited from Observer
typedef boost::unordered_set< ext::shared_ptr< Observable > > set_type
 
typedef set_type::iterator iterator
 
- Protected Member Functions inherited from StochasticProcess
 StochasticProcess ()
 
 StochasticProcess (const ext::shared_ptr< discretization > &)
 
- Protected Attributes inherited from StochasticProcess
ext::shared_ptr< discretizationdiscretization_
 

Detailed Description

Square-root stochastic-volatility Bates process.

This class describes the square root stochastic volatility process incl jumps governed by

\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \end{array} \]

Examples
EquityOption.cpp.

Member Function Documentation

◆ evolve()

Disposable<Array> evolve ( Time  t0,
const Array x0,
Time  dt,
const Array dw 
) const
virtual

returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns

\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]

where \( E \) is the expectation and \( S \) the standard deviation.

Reimplemented from StochasticProcess.