Square-root stochastic-volatility Heston process. More...
#include <hestonprocess.hpp>
Inheritance diagram for HestonProcess:
Collaboration diagram for HestonProcess:
Public Types | |
| enum | Discretization { PartialTruncation , FullTruncation , Reflection , NonCentralChiSquareVariance , QuadraticExponential , QuadraticExponentialMartingale , BroadieKayaExactSchemeLobatto , BroadieKayaExactSchemeLaguerre , BroadieKayaExactSchemeTrapezoidal } |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
Public Member Functions | |
| 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 () | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| virtual | ~Observable ()=default |
| void | notifyObservers () |
Private Member Functions | |
| Real | varianceDistribution (Real v, Real dw, Time dt) const |
Private Attributes | |
| Handle< YieldTermStructure > | riskFreeRate_ |
| Handle< YieldTermStructure > | dividendYield_ |
| Handle< Quote > | s0_ |
| Real | v0_ |
| Real | kappa_ |
| Real | theta_ |
| Real | sigma_ |
| Real | rho_ |
| Discretization | discretization_ |
Additional Inherited Members | |
| 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 Heston process.
This class describes the square root stochastic volatility process governed by
\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]
Definition at line 46 of file hestonprocess.hpp.
Member Enumeration Documentation
◆ Discretization
| enum Discretization |
Definition at line 48 of file hestonprocess.hpp.
Constructor & Destructor Documentation
◆ HestonProcess()
| HestonProcess | ( | Handle< YieldTermStructure > | riskFreeRate, |
| Handle< YieldTermStructure > | dividendYield, | ||
| Handle< Quote > | s0, | ||
| Real | v0, | ||
| Real | kappa, | ||
| Real | theta, | ||
| Real | sigma, | ||
| Real | rho, | ||
| Discretization | d = QuadraticExponentialMartingale |
||
| ) |
Member Function Documentation
◆ size()
|
overridevirtual |
returns the number of dimensions of the stochastic process
Implements StochasticProcess.
Definition at line 56 of file hestonprocess.cpp.
◆ factors()
|
overridevirtual |
returns the number of independent factors of the process
Reimplemented from StochasticProcess.
Definition at line 60 of file hestonprocess.cpp.
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◆ initialValues()
|
overridevirtual |
returns the initial values of the state variables
Implements StochasticProcess.
Definition at line 66 of file hestonprocess.cpp.
◆ drift()
returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 70 of file hestonprocess.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 83 of file hestonprocess.cpp.
◆ apply()
applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \).
Reimplemented from StochasticProcess.
Definition at line 104 of file hestonprocess.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 396 of file hestonprocess.cpp.
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◆ v0()
| Real v0 | ( | ) | const |
Definition at line 77 of file hestonprocess.hpp.
◆ rho()
| Real rho | ( | ) | const |
Definition at line 78 of file hestonprocess.hpp.
◆ kappa()
| Real kappa | ( | ) | const |
Definition at line 79 of file hestonprocess.hpp.
◆ theta()
| Real theta | ( | ) | const |
Definition at line 80 of file hestonprocess.hpp.
◆ sigma()
| Real sigma | ( | ) | const |
Definition at line 81 of file hestonprocess.hpp.
◆ s0()
◆ dividendYield()
| const Handle< YieldTermStructure > & dividendYield | ( | ) | const |
Definition at line 556 of file hestonprocess.cpp.
◆ riskFreeRate()
| const Handle< YieldTermStructure > & riskFreeRate | ( | ) | const |
Definition at line 560 of file hestonprocess.cpp.
◆ time()
returns the time value corresponding to the given date in the reference system of the stochastic process.
- Note
- As a number of processes might not need this functionality, a default implementation is given which raises an exception.
Reimplemented from StochasticProcess.
Definition at line 564 of file hestonprocess.cpp.
◆ pdf()
◆ varianceDistribution()
Member Data Documentation
◆ riskFreeRate_
|
private |
Definition at line 96 of file hestonprocess.hpp.
◆ dividendYield_
|
private |
Definition at line 96 of file hestonprocess.hpp.
◆ s0_
Definition at line 97 of file hestonprocess.hpp.
◆ v0_
|
private |
Definition at line 98 of file hestonprocess.hpp.
◆ kappa_
|
private |
Definition at line 98 of file hestonprocess.hpp.
◆ theta_
|
private |
Definition at line 98 of file hestonprocess.hpp.
◆ sigma_
|
private |
Definition at line 98 of file hestonprocess.hpp.
◆ rho_
|
private |
Definition at line 98 of file hestonprocess.hpp.
◆ discretization_
|
private |
Definition at line 99 of file hestonprocess.hpp.