Stochastic-volatility GJR-GARCH(1,1) process. More...
#include <ql/processes/gjrgarchprocess.hpp>
Public Types | |
enum | Discretization { PartialTruncation, FullTruncation, Reflection } |
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typedef boost::unordered_set< ext::shared_ptr< Observable > > | set_type |
typedef set_type::iterator | iterator |
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., \( \mu(t, \mathrm{x}_t) \) | |
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 | 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 |
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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 () |
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Observer (const Observer &) | |
Observer & | operator= (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 () |
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Observable (const Observable &) | |
Observable & | operator= (const Observable &) |
void | notifyObservers () |
Additional Inherited Members | |
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StochasticProcess () | |
StochasticProcess (const ext::shared_ptr< discretization > &) | |
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ext::shared_ptr< discretization > | discretization_ |
Stochastic-volatility GJR-GARCH(1,1) process.
This class describes the stochastic volatility process governed by
\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& (\omega + (\beta + \alpha * q_{2} + \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12} + \gamma \sigma_{13}) v dW_1 + \sqrt{\alpha^{2} (\sigma^{2}_{2} - \sigma^{2}_{12}) + \gamma^{2} (\sigma^{2}_{3} - \sigma^{2}_{13}) + 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \ \ N = normalCDF(\lambda) \\ n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \\ q_{2} &=& 1 + \lambda^{2} \\ q_{3} &=& \lambda n + N + \lambda^2 N \\ \sigma^{2}_{2} = 2 + 4 \lambda^{4} \\ \sigma^{2}_{3} = \lambda^{3} n + 5 \lambda n + 3N + \lambda^{4} N + 6 \lambda^{2} N -\\lambda^{2} n^{2} - N^{2} - \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN - 2 \lambda^{2} N^{2} \ \ \sigma_{12} = -2 \lambda \\ \sigma_{13} = -2 n - 2 \lambda N \\ \sigma_{23} = 2N + \sigma_{12} \sigma_{13} \\ \end{array} \]
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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.