A free/open-source library for quantitative finance
GJRGARCHProcess Class Reference
Stochastic-volatility GJR-GARCH(1,1) process. More...
#include <ql/processes/gjrgarchprocess.hpp>
Inheritance diagram for GJRGARCHProcess:
Public Types | |
| enum | Discretization { PartialTruncation, FullTruncation, Reflection } |
Public Member Functions | |
| GJRGARCHProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > ÷ndYield, const Handle< Quote > &s0, Real v0, Real omega, Real alpha, Real beta, Real gamma, Real lambda, Real daysPerYear=252.0, Discretization d=FullTruncation) | |
| Size | size () const |
| returns the number of dimensions of the stochastic 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.,  | |
| Disposable< Matrix > | diffusion (Time t, const Array &x) const |
returns the diffusion part of the equation, i.e.  | |
| 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 | lambda () const |
| Real | omega () const |
| Real | alpha () const |
| Real | beta () const |
| Real | gamma () const |
| Real | daysPerYear () const |
| const Handle< Quote > & | s0 () const |
|
const Handle < YieldTermStructure > & | dividendYield () const |
|
const Handle < YieldTermStructure > & | riskFreeRate () const |
| Time | time (const Date &) const |
 Public Member Functions inherited from StochasticProcess | |
| virtual Size | factors () const |
| returns the number of independent factors of the process | |
| 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< std::set < boost::shared_ptr < Observable > >::iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) |
| Size | unregisterWith (const boost::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
| 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_ |
Detailed Description
Stochastic-volatility GJR-GARCH(1,1) process.
This class describes the stochastic volatility process governed by
![\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& (\omega + (\beta + \alpha * q_{2} + \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12} + \gamma \sigma_{13}) v dW_1 + \sqrt{\alpha^{2} (\sigma^{2}_{2} - \sigma^{2}_{12}) + \gamma^{2} (\sigma^{2}_{3} - \sigma^{2}_{13}) + 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \ \ N = normalCDF(\lambda) \\ n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \\ q_{2} &=& 1 + \lambda^{2} \\ q_{3} &=& \lambda n + N + \lambda^2 N \\ \sigma^{2}_{2} = 2 + 4 \lambda^{4} \\ \sigma^{2}_{3} = \lambda^{3} n + 5 \lambda n + 3N + \lambda^{4} N + 6 \lambda^{2} N -\\lambda^{2} n^{2} - N^{2} - \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN - 2 \lambda^{2} N^{2} \ \ \sigma_{12} = -2 \lambda \\ \sigma_{13} = -2 n - 2 \lambda N \\ \sigma_{23} = 2N + \sigma_{12} \sigma_{13} \\ \end{array} \]](form_356.png)
Member Function Documentation
|
virtual |
applies a change to the asset value. By default, it returns 
.
Reimplemented from StochasticProcess.
returns the asset value after a time interval 
according to the given discretization. By default, it returns
![\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]](form_368.png)
where 
is the expectation and 
the standard deviation.
Reimplemented from StochasticProcess.
returns the time value corresponding to the given date in the reference system of the stochastic process.
- Note
- As a number of processes might not need this functionality, a default implementation is given which raises an exception.
Reimplemented from StochasticProcess.