#include <extouwithjumpsprocess.hpp>
Inheritance diagram for ExtOUWithJumpsProcess:
Collaboration diagram for ExtOUWithJumpsProcess:
Public Member Functions | |
| ExtOUWithJumpsProcess (ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > process, Real Y0, Real beta, Real jumpIntensity, Real eta) | |
| Size | size () const override |
| returns the number of dimensions of the stochastic process More... | |
| Size | factors () const override |
| returns the number of independent factors of the process More... | |
| Array | initialValues () const override |
| returns the initial values of the state variables More... | |
| Array | drift (Time t, const Array &x) const override |
| returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) More... | |
| Matrix | diffusion (Time t, const Array &x) const override |
| returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) More... | |
| Array | evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override |
| ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | getExtendedOrnsteinUhlenbeckProcess () const |
| Real | beta () const |
| Real | eta () const |
| Real | jumpIntensity () const |
| Public Member Functions inherited from StochasticProcess | |
| ~StochasticProcess () override=default | |
| virtual Array | expectation (Time t0, const Array &x0, Time dt) const |
| virtual Matrix | stdDeviation (Time t0, const Array &x0, Time dt) const |
| virtual Matrix | covariance (Time t0, const Array &x0, Time dt) const |
| virtual Array | apply (const Array &x0, const Array &dx) const |
| 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 | |
| const Real | Y0_ |
| const Real | beta_ |
| const Real | jumpIntensity_ |
| const Real | eta_ |
| const ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | ouProcess_ |
| const CumulativeNormalDistribution | cumNormalDist_ |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess ()=default | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| Protected Attributes inherited from StochasticProcess | |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
This class describes a Ornstein Uhlenbeck model plus exp jump, an extension of the Lucia and Schwartz model
\[ \begin{array}{rcl} S &=& exp(X_t + Y_t) \\ dX_t &=& \alpha(\mu(t)-X_t)dt + \sigma dW_t \\ dY_t &=& -\beta Y_{t-}dt + J_tdN_t \\ \omega(J)&=& \eta_u e^{-\eta_u J} \end{array} \]
References: T. Kluge, 2008. Pricing Swing Options and other Electricity Derivatives, http://eprints.maths.ox.ac.uk/246/1/kluge.pdf
B. Hambly, S. Howison, T. Kluge, Modelling spikes and pricing swing options in electricity markets, http://people.maths.ox.ac.uk/hambly/PDF/Papers/elec.pdf
Definition at line 59 of file extouwithjumpsprocess.hpp.
Constructor & Destructor Documentation
◆ ExtOUWithJumpsProcess()
| ExtOUWithJumpsProcess | ( | ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | process, |
| Real | Y0, | ||
| Real | beta, | ||
| Real | jumpIntensity, | ||
| Real | eta | ||
| ) |
Definition at line 30 of file extouwithjumpsprocess.cpp.
Member Function Documentation
◆ size()
|
overridevirtual |
returns the number of dimensions of the stochastic process
Implements StochasticProcess.
Definition at line 41 of file extouwithjumpsprocess.cpp.
◆ factors()
|
overridevirtual |
returns the number of independent factors of the process
Reimplemented from StochasticProcess.
Definition at line 44 of file extouwithjumpsprocess.cpp.
◆ initialValues()
|
overridevirtual |
returns the initial values of the state variables
Implements StochasticProcess.
Definition at line 61 of file extouwithjumpsprocess.cpp.
◆ drift()
returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 68 of file extouwithjumpsprocess.cpp.
◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 75 of file extouwithjumpsprocess.cpp.
◆ evolve()
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.
Definition at line 82 of file extouwithjumpsprocess.cpp.
◆ getExtendedOrnsteinUhlenbeckProcess()
| ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > getExtendedOrnsteinUhlenbeckProcess | ( | ) | const |
Definition at line 48 of file extouwithjumpsprocess.cpp.
◆ beta()
| Real beta | ( | ) | const |
Definition at line 51 of file extouwithjumpsprocess.cpp.
◆ eta()
| Real eta | ( | ) | const |
Definition at line 57 of file extouwithjumpsprocess.cpp.
◆ jumpIntensity()
| Real jumpIntensity | ( | ) | const |
Definition at line 54 of file extouwithjumpsprocess.cpp.
Member Data Documentation
◆ Y0_
|
private |
Definition at line 82 of file extouwithjumpsprocess.hpp.
◆ beta_
|
private |
Definition at line 82 of file extouwithjumpsprocess.hpp.
◆ jumpIntensity_
|
private |
Definition at line 82 of file extouwithjumpsprocess.hpp.
◆ eta_
|
private |
Definition at line 82 of file extouwithjumpsprocess.hpp.
◆ ouProcess_
|
private |
Definition at line 83 of file extouwithjumpsprocess.hpp.
◆ cumNormalDist_
|
private |
Definition at line 85 of file extouwithjumpsprocess.hpp.