Variance gamma process. More...
#include <variancegammaprocess.hpp>
Inheritance diagram for VarianceGammaProcess:
Collaboration diagram for VarianceGammaProcess:
Public Member Functions | |
| VarianceGammaProcess (Handle< Quote > s0, Handle< YieldTermStructure > dividendYield, Handle< YieldTermStructure > riskFreeRate, Real sigma, Real nu, Real theta) | |
| Real | x0 () const override |
| returns the initial value of the state variable More... | |
| Real | drift (Time t, Real x) const override |
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) More... | |
| Real | diffusion (Time t, Real x) const override |
| returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) More... | |
| Real | sigma () const |
| Real | nu () const |
| Real | theta () const |
| const Handle< Quote > & | s0 () const |
| const Handle< YieldTermStructure > & | dividendYield () const |
| const Handle< YieldTermStructure > & | riskFreeRate () const |
| Public Member Functions inherited from StochasticProcess1D | |
| virtual Real | expectation (Time t0, Real x0, Time dt) const |
| virtual Real | stdDeviation (Time t0, Real x0, Time dt) const |
| virtual Real | variance (Time t0, Real x0, Time dt) const |
| virtual Real | evolve (Time t0, Real x0, Time dt, Real dw) const |
| virtual Real | apply (Real x0, Real dx) const |
| Public Member Functions inherited from StochasticProcess | |
| ~StochasticProcess () override=default | |
| virtual Size | factors () const |
| returns the number of independent factors of the process More... | |
| virtual Time | time (const Date &) const |
| void | update () override |
| Public Member Functions inherited from Observer | |
| Observer ()=default | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| virtual | ~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 | update ()=0 |
| virtual void | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable () | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| virtual | ~Observable ()=default |
| void | notifyObservers () |
Private Attributes | |
| Handle< Quote > | s0_ |
| Handle< YieldTermStructure > | dividendYield_ |
| Handle< YieldTermStructure > | riskFreeRate_ |
| Real | sigma_ |
| Real | nu_ |
| Real | theta_ |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| Protected Member Functions inherited from StochasticProcess1D | |
| StochasticProcess1D ()=default | |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess ()=default | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| Protected Attributes inherited from StochasticProcess1D | |
| ext::shared_ptr< discretization > | discretization_ |
| Protected Attributes inherited from StochasticProcess | |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
Variance gamma process.
This class describes the stochastic volatility process. With a Brownian motion given by
\[ db = \theta dt + \sigma dW_t \]
then a Variance Gamma process X is defined by evaluating this Brownian motion at sample times driven by a Gamma process. If T is the value of a Gamma process with mean 1 and variance rate \( \nu \) then the Variance Gamma process is given by
\[ X(t) = B(T) \]
Definition at line 50 of file variancegammaprocess.hpp.
Constructor & Destructor Documentation
◆ VarianceGammaProcess()
| VarianceGammaProcess | ( | Handle< Quote > | s0, |
| Handle< YieldTermStructure > | dividendYield, | ||
| Handle< YieldTermStructure > | riskFreeRate, | ||
| Real | sigma, | ||
| Real | nu, | ||
| Real | theta | ||
| ) |
Member Function Documentation
◆ x0()
|
overridevirtual |
returns the initial value of the state variable
Implements StochasticProcess1D.
Definition at line 42 of file variancegammaprocess.cpp.
◆ drift()
returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Implements StochasticProcess1D.
Definition at line 47 of file variancegammaprocess.cpp.
◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Implements StochasticProcess1D.
Definition at line 52 of file variancegammaprocess.cpp.
◆ sigma()
| Real sigma | ( | ) | const |
Definition at line 63 of file variancegammaprocess.hpp.
◆ nu()
| Real nu | ( | ) | const |
Definition at line 64 of file variancegammaprocess.hpp.
◆ theta()
| Real theta | ( | ) | const |
Definition at line 65 of file variancegammaprocess.hpp.
◆ s0()
Definition at line 57 of file variancegammaprocess.cpp.
◆ dividendYield()
| const Handle< YieldTermStructure > & dividendYield | ( | ) | const |
Definition at line 61 of file variancegammaprocess.cpp.
◆ riskFreeRate()
| const Handle< YieldTermStructure > & riskFreeRate | ( | ) | const |
Definition at line 65 of file variancegammaprocess.cpp.
Member Data Documentation
◆ s0_
Definition at line 72 of file variancegammaprocess.hpp.
◆ dividendYield_
|
private |
Definition at line 73 of file variancegammaprocess.hpp.
◆ riskFreeRate_
|
private |
Definition at line 73 of file variancegammaprocess.hpp.
◆ sigma_
|
private |
Definition at line 74 of file variancegammaprocess.hpp.
◆ nu_
|
private |
Definition at line 74 of file variancegammaprocess.hpp.
◆ theta_
|
private |
Definition at line 74 of file variancegammaprocess.hpp.