#include <klugeextouprocess.hpp>
Inheritance diagram for KlugeExtOUProcess:
Collaboration diagram for KlugeExtOUProcess:
Public Member Functions | |
| KlugeExtOUProcess (Real rho, ext::shared_ptr< ExtOUWithJumpsProcess > kluge, ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > extOU) | |
| 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< ExtOUWithJumpsProcess > | getKlugeProcess () const |
| ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | getExtOUProcess () const |
| Real | rho () 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 | rho_ |
| const Real | sqrtMRho_ |
| const ext::shared_ptr< ExtOUWithJumpsProcess > | klugeProcess_ |
| const ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | ouProcess_ |
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 correlated Kluge - extended Ornstein-Uhlenbeck process governed by
\[ \begin{array}{rcl} P_t &=& \exp(p_t + X_t + Y_t) \\ dX_t &=& -\alpha X_tdt + \sigma_x dW_t^x \\ dY_t &=& -\beta Y_{t-}dt + J_tdN_t \\ \omega(J) &=& \eta e^{-\eta J} \\ G_t &=& \exp(g_t + U_t) \\ dU_t &=& -\kappa U_tdt + \sigma_udW_t^u \\ \rho &=& \mathrm{corr} (dW_t^x, dW_t^u) \end{array} \]
References: 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 56 of file klugeextouprocess.hpp.
Constructor & Destructor Documentation
◆ KlugeExtOUProcess()
| KlugeExtOUProcess | ( | Real | rho, |
| ext::shared_ptr< ExtOUWithJumpsProcess > | kluge, | ||
| ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > | extOU | ||
| ) |
Definition at line 28 of file klugeextouprocess.cpp.
Member Function Documentation
◆ size()
|
overridevirtual |
returns the number of dimensions of the stochastic process
Implements StochasticProcess.
Definition at line 38 of file klugeextouprocess.cpp.
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◆ factors()
|
overridevirtual |
returns the number of independent factors of the process
Reimplemented from StochasticProcess.
Definition at line 42 of file klugeextouprocess.cpp.
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◆ initialValues()
|
overridevirtual |
returns the initial values of the state variables
Implements StochasticProcess.
Definition at line 46 of file klugeextouprocess.cpp.
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◆ drift()
returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 55 of file klugeextouprocess.cpp.
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◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 64 of file klugeextouprocess.cpp.
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◆ 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 76 of file klugeextouprocess.cpp.
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◆ getKlugeProcess()
| ext::shared_ptr< ExtOUWithJumpsProcess > getKlugeProcess | ( | ) | const |
Definition at line 90 of file klugeextouprocess.cpp.
◆ getExtOUProcess()
| ext::shared_ptr< ExtendedOrnsteinUhlenbeckProcess > getExtOUProcess | ( | ) | const |
Definition at line 94 of file klugeextouprocess.cpp.
◆ rho()
| Real rho | ( | ) | const |
Definition at line 98 of file klugeextouprocess.cpp.
Member Data Documentation
◆ rho_
|
private |
Definition at line 76 of file klugeextouprocess.hpp.
◆ sqrtMRho_
|
private |
Definition at line 76 of file klugeextouprocess.hpp.
◆ klugeProcess_
|
private |
Definition at line 77 of file klugeextouprocess.hpp.
◆ ouProcess_
|
private |
Definition at line 78 of file klugeextouprocess.hpp.