Square-root stochastic-volatility Bates process. More...
#include <batesprocess.hpp>
Inheritance diagram for BatesProcess:
Collaboration diagram for BatesProcess:
Public Member Functions | |
| BatesProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > ÷ndYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Real lambda, Real nu, Real delta, HestonProcess::Discretization d=HestonProcess::FullTruncation) | |
| Size | factors () const override |
| returns the number of independent factors of the process 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... | |
| Array | evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override |
| Real | lambda () const |
| Real | nu () const |
| Real | delta () const |
| Public Member Functions inherited from HestonProcess | |
| HestonProcess (Handle< YieldTermStructure > riskFreeRate, Handle< YieldTermStructure > dividendYield, Handle< Quote > s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Discretization d=QuadraticExponentialMartingale) | |
| 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 | apply (const Array &x0, const Array &dx) const override |
| Array | evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override |
| Real | v0 () const |
| Real | rho () const |
| Real | kappa () const |
| Real | theta () const |
| Real | sigma () const |
| const Handle< Quote > & | s0 () const |
| const Handle< YieldTermStructure > & | dividendYield () const |
| const Handle< YieldTermStructure > & | riskFreeRate () const |
| Time | time (const Date &) const override |
| Real | pdf (Real x, Real v, Time t, Real eps=1e-3) 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 |
| 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 ()=default | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| virtual | ~Observable ()=default |
| void | notifyObservers () |
Private Attributes | |
| const Real | lambda_ |
| const Real | delta_ |
| const Real | nu_ |
| const Real | m_ |
| const CumulativeNormalDistribution | cumNormalDist_ |
Additional Inherited Members | |
| Public Types inherited from HestonProcess | |
| enum | Discretization { PartialTruncation , FullTruncation , Reflection , NonCentralChiSquareVariance , QuadraticExponential , QuadraticExponentialMartingale , BroadieKayaExactSchemeLobatto , BroadieKayaExactSchemeLaguerre , BroadieKayaExactSchemeTrapezoidal } |
| 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
Square-root stochastic-volatility Bates process.
This class describes the square root stochastic volatility process incl jumps governed by
\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \\ \omega(J) &=& \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \end{array} \]
Definition at line 49 of file batesprocess.hpp.
Constructor & Destructor Documentation
◆ BatesProcess()
| BatesProcess | ( | const Handle< YieldTermStructure > & | riskFreeRate, |
| const Handle< YieldTermStructure > & | dividendYield, | ||
| const Handle< Quote > & | s0, | ||
| Real | v0, | ||
| Real | kappa, | ||
| Real | theta, | ||
| Real | sigma, | ||
| Real | rho, | ||
| Real | lambda, | ||
| Real | nu, | ||
| Real | delta, | ||
| HestonProcess::Discretization | d = HestonProcess::FullTruncation |
||
| ) |
Definition at line 26 of file batesprocess.cpp.
Member Function Documentation
◆ factors()
|
overridevirtual |
returns the number of independent factors of the process
Reimplemented from StochasticProcess.
Definition at line 65 of file batesprocess.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 40 of file batesprocess.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 46 of file batesprocess.cpp.
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◆ lambda()
| Real lambda | ( | ) | const |
Definition at line 69 of file batesprocess.cpp.
◆ nu()
| Real nu | ( | ) | const |
Definition at line 73 of file batesprocess.cpp.
◆ delta()
| Real delta | ( | ) | const |
Definition at line 77 of file batesprocess.cpp.
Member Data Documentation
◆ lambda_
|
private |
Definition at line 68 of file batesprocess.hpp.
◆ delta_
|
private |
Definition at line 68 of file batesprocess.hpp.
◆ nu_
|
private |
Definition at line 68 of file batesprocess.hpp.
◆ m_
|
private |
Definition at line 68 of file batesprocess.hpp.
◆ cumNormalDist_
|
private |
Definition at line 69 of file batesprocess.hpp.