Generalized Black-Scholes stochastic process. More...
#include <blackscholesprocess.hpp>
Inheritance diagram for GeneralizedBlackScholesProcess:
Collaboration diagram for GeneralizedBlackScholesProcess:
Public Member Functions | |
| GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false) | |
| GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, Handle< LocalVolTermStructure > localVolTS) | |
StochasticProcess1D interface | |
| Real | x0 () const override |
| returns the initial value of the state variable More... | |
| Real | drift (Time t, Real x) const override |
| Real | diffusion (Time t, Real x) const override |
| Real | apply (Real x0, Real dx) const override |
| Real | expectation (Time t0, Real x0, Time dt) const override |
| Real | stdDeviation (Time t0, Real x0, Time dt) const override |
| Real | variance (Time t0, Real x0, Time dt) const override |
| Real | evolve (Time t0, Real x0, Time dt, Real dw) const override |
| Time | time (const Date &) const override |
Observer interface | |
| void | update () override |
| Public Member Functions inherited from StochasticProcess1D | |
| Public Member Functions inherited from StochasticProcess | |
| ~StochasticProcess () override=default | |
| virtual Size | factors () const |
| returns the number of independent factors of the process More... | |
| 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 () |
Inspectors | |
| Handle< Quote > | x0_ |
| Handle< YieldTermStructure > | riskFreeRate_ |
| Handle< YieldTermStructure > | dividendYield_ |
| Handle< BlackVolTermStructure > | blackVolatility_ |
| Handle< LocalVolTermStructure > | externalLocalVolTS_ |
| bool | forceDiscretization_ |
| bool | hasExternalLocalVol_ |
| RelinkableHandle< LocalVolTermStructure > | localVolatility_ |
| bool | updated_ |
| bool | isStrikeIndependent_ |
| const Handle< Quote > & | stateVariable () const |
| const Handle< YieldTermStructure > & | dividendYield () const |
| const Handle< YieldTermStructure > & | riskFreeRate () const |
| const Handle< BlackVolTermStructure > & | blackVolatility () const |
| const Handle< LocalVolTermStructure > & | localVolatility () const |
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
Generalized Black-Scholes stochastic process.
This class describes the stochastic process \( S \) governed by
\[ d\ln S(t) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]
- Warning:
- while the interface is expressed in terms of \( S \), the internal calculations work on \( ln S \).
Definition at line 54 of file blackscholesprocess.hpp.
Constructor & Destructor Documentation
◆ GeneralizedBlackScholesProcess() [1/2]
| GeneralizedBlackScholesProcess | ( | Handle< Quote > | x0, |
| Handle< YieldTermStructure > | dividendTS, | ||
| Handle< YieldTermStructure > | riskFreeTS, | ||
| Handle< BlackVolTermStructure > | blackVolTS, | ||
| const ext::shared_ptr< discretization > & | d = ext::shared_ptr<discretization>(new EulerDiscretization), |
||
| bool | forceDiscretization = false |
||
| ) |
◆ GeneralizedBlackScholesProcess() [2/2]
| GeneralizedBlackScholesProcess | ( | Handle< Quote > | x0, |
| Handle< YieldTermStructure > | dividendTS, | ||
| Handle< YieldTermStructure > | riskFreeTS, | ||
| Handle< BlackVolTermStructure > | blackVolTS, | ||
| Handle< LocalVolTermStructure > | localVolTS | ||
| ) |
Member Function Documentation
◆ x0()
|
overridevirtual |
returns the initial value of the state variable
Implements StochasticProcess1D.
Definition at line 70 of file blackscholesprocess.cpp.
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◆ drift()
Implements StochasticProcess1D.
Definition at line 74 of file blackscholesprocess.cpp.
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◆ diffusion()
Implements StochasticProcess1D.
Definition at line 84 of file blackscholesprocess.cpp.
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◆ apply()
applies a change to the asset value. By default, it returns \( x + \Delta x \).
Reimplemented from StochasticProcess1D.
Definition at line 88 of file blackscholesprocess.cpp.
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◆ expectation()
- Warning:
- in general raises a "not implemented" exception. It should be rewritten to return the expectation E(S) of the process, not exp(E(log S)).
Reimplemented from StochasticProcess1D.
Definition at line 92 of file blackscholesprocess.cpp.
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◆ stdDeviation()
returns the standard deviation \( S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented from StochasticProcess1D.
Definition at line 108 of file blackscholesprocess.cpp.
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◆ variance()
returns the variance \( V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Reimplemented from StochasticProcess1D.
Definition at line 119 of file blackscholesprocess.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
\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]
where \( E \) is the expectation and \( S \) the standard deviation.
Reimplemented from StochasticProcess1D.
Definition at line 131 of file blackscholesprocess.cpp.
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◆ 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 149 of file blackscholesprocess.cpp.
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◆ update()
|
overridevirtual |
This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.
Implements Observer.
Definition at line 154 of file blackscholesprocess.cpp.
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◆ stateVariable()
Definition at line 160 of file blackscholesprocess.cpp.
◆ dividendYield()
| const Handle< YieldTermStructure > & dividendYield | ( | ) | const |
◆ riskFreeRate()
| const Handle< YieldTermStructure > & riskFreeRate | ( | ) | const |
◆ blackVolatility()
| const Handle< BlackVolTermStructure > & blackVolatility | ( | ) | const |
◆ localVolatility()
| const Handle< LocalVolTermStructure > & localVolatility | ( | ) | const |
Definition at line 180 of file blackscholesprocess.cpp.
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Member Data Documentation
◆ x0_
Definition at line 101 of file blackscholesprocess.hpp.
◆ riskFreeRate_
|
private |
Definition at line 102 of file blackscholesprocess.hpp.
◆ dividendYield_
|
private |
Definition at line 102 of file blackscholesprocess.hpp.
◆ blackVolatility_
|
private |
Definition at line 103 of file blackscholesprocess.hpp.
◆ externalLocalVolTS_
|
private |
Definition at line 104 of file blackscholesprocess.hpp.
◆ forceDiscretization_
|
private |
Definition at line 105 of file blackscholesprocess.hpp.
◆ hasExternalLocalVol_
|
private |
Definition at line 106 of file blackscholesprocess.hpp.
◆ localVolatility_
|
mutableprivate |
Definition at line 107 of file blackscholesprocess.hpp.
◆ updated_
|
mutableprivate |
Definition at line 108 of file blackscholesprocess.hpp.
◆ isStrikeIndependent_
|
private |
Definition at line 108 of file blackscholesprocess.hpp.