Square-root stochastic-volatility Heston process. More...
#include <ql/processes/hestonprocess.hpp>
Inheritance diagram for HestonProcess:Public Types | |
| enum | Discretization { PartialTruncation, FullTruncation, Reflection, NonCentralChiSquareVariance, QuadraticExponential, QuadraticExponentialMartingale, BroadieKayaExactSchemeLobatto, BroadieKayaExactSchemeLaguerre, BroadieKayaExactSchemeTrapezoidal } |
Public Types inherited from Observer | |
| typedef std::set< boost::shared_ptr< Observable > > | set_type |
| typedef set_type::iterator | iterator |
Public Member Functions | |
| HestonProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > ÷ndYield, 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< Array > | initialValues () const |
| returns the initial values of the state variables | |
| Disposable< Array > | drift (Time t, const Array &x) const |
| returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) | |
| Disposable< Matrix > | diffusion (Time t, const Array &x) const |
| returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) | |
| Disposable< Array > | apply (const Array &x0, const Array &dx) const |
| Disposable< Array > | evolve (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< Array > | expectation (Time t0, const Array &x0, Time dt) const |
| virtual Disposable< Matrix > | stdDeviation (Time t0, const Array &x0, Time dt) const |
| virtual Disposable< Matrix > | covariance (Time t0, const Array &x0, Time dt) const |
| void | update () |
Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| std::pair< iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) |
| void | registerWithObservables (const boost::shared_ptr< Observer > &) |
| Size | unregisterWith (const boost::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
| virtual void | deepUpdate () |
Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| void | notifyObservers () |
Additional Inherited Members | |
Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess (const boost::shared_ptr< discretization > &) | |
Protected Attributes inherited from StochasticProcess | |
| boost::shared_ptr< discretization > | discretization_ |
Square-root stochastic-volatility Heston process.
This class describes the square root stochastic volatility process governed by
\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]
|
virtual |
applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \).
Reimplemented from StochasticProcess.
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.
returns the time value corresponding to the given date in the reference system of the stochastic process.
Reimplemented from StochasticProcess.