Generalized Black-Scholes stochastic process. More...
#include <ql/processes/blackscholesprocess.hpp>
Public Member Functions | |
GeneralizedBlackScholesProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > ÷ndTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false) | |
GeneralizedBlackScholesProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > ÷ndTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const Handle< LocalVolTermStructure > &localVolTS) | |
StochasticProcess1D interface | |
Real | x0 () const |
returns the initial value of the state variable | |
Real | drift (Time t, Real x) const |
Real | diffusion (Time t, Real x) const |
Real | apply (Real x0, Real dx) const |
Real | expectation (Time t0, Real x0, Time dt) const |
Real | stdDeviation (Time t0, Real x0, Time dt) const |
Real | variance (Time t0, Real x0, Time dt) const |
Real | evolve (Time t0, Real x0, Time dt, Real dw) const |
Time | time (const Date &) const |
Observer interface | |
void | update () |
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virtual Size | factors () const |
returns the number of independent factors of the process | |
void | update () |
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Observer (const Observer &) | |
Observer & | operator= (const 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 | deepUpdate () |
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Observable (const Observable &) | |
Observable & | operator= (const Observable &) |
void | notifyObservers () |
Inspectors | |
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 | |
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typedef boost::unordered_set< ext::shared_ptr< Observable > > | set_type |
typedef set_type::iterator | iterator |
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StochasticProcess1D () | |
StochasticProcess1D (const ext::shared_ptr< discretization > &) | |
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StochasticProcess () | |
StochasticProcess (const ext::shared_ptr< discretization > &) | |
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ext::shared_ptr< discretization > | discretization_ |
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ext::shared_ptr< discretization > | discretization_ |
Generalized Black-Scholes stochastic process.
This class describes the stochastic process \( S \) governed by
\[ d\ln S(t) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]
Implements StochasticProcess1D.
Implements StochasticProcess1D.
applies a change to the asset value. By default, it returns \( x + \Delta x \).
Reimplemented from StochasticProcess1D.
Reimplemented from StochasticProcess1D.
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.
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.
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.
returns the time value corresponding to the given date in the reference system of the stochastic process.
Reimplemented from StochasticProcess.
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virtual |
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.