QuantLib: a free/open-source library for quantitative finance
fully annotated source code - version 1.34
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Square-root stochastic-volatility Bates process. More...
#include <batesprocess.hpp>
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 () | |
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_ |
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.
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 |
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) |
Definition at line 26 of file batesprocess.cpp.
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overridevirtual |
returns the number of independent factors of the process
Reimplemented from StochasticProcess.
Definition at line 65 of file batesprocess.cpp.
returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Implements StochasticProcess.
Definition at line 40 of file batesprocess.cpp.
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.
Real lambda | ( | ) | const |
Definition at line 69 of file batesprocess.cpp.
Real nu | ( | ) | const |
Definition at line 73 of file batesprocess.cpp.
Real delta | ( | ) | const |
Definition at line 77 of file batesprocess.cpp.
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private |
Definition at line 68 of file batesprocess.hpp.
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private |
Definition at line 68 of file batesprocess.hpp.
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private |
Definition at line 68 of file batesprocess.hpp.
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private |
Definition at line 68 of file batesprocess.hpp.
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private |
Definition at line 69 of file batesprocess.hpp.