A free/open-source library for quantitative finance
Reference manual - version 1.20
|
|
A free/open-source library for quantitative finance
Reference manual - version 1.20
|
Bates model engines based on Fourier transform. More...
#include <ql/pricingengines/vanilla/batesengine.hpp>
Inheritance diagram for BatesEngine:Public Member Functions | |
| BatesEngine (const ext::shared_ptr< BatesModel > &model, Size integrationOrder=144) | |
| BatesEngine (const ext::shared_ptr< BatesModel > &model, Real relTolerance, Size maxEvaluations) | |
| Public Member Functions inherited from AnalyticHestonEngine | |
| AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, Real relTolerance, Size maxEvaluations) | |
| AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, Size integrationOrder=144) | |
| AnalyticHestonEngine (const ext::shared_ptr< HestonModel > &model, ComplexLogFormula cpxLog, const Integration &itg, Real andersenPiterbargEpsilon=1e-8) | |
| std::complex< Real > | chF (const std::complex< Real > &z, Time t) const |
| std::complex< Real > | lnChF (const std::complex< Real > &z, Time t) const |
| void | calculate () const |
| Size | numberOfEvaluations () const |
| Public Member Functions inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results > | |
| GenericModelEngine (const Handle< HestonModel > &model=Handle< HestonModel >()) | |
| GenericModelEngine (const ext::shared_ptr< HestonModel > &model) | |
| Public Member Functions inherited from GenericEngine< VanillaOption::arguments, VanillaOption::results > | |
| PricingEngine::arguments * | getArguments () const |
| const PricingEngine::results * | getResults () const |
| void | reset () |
| void | update () |
| Public Member Functions inherited from PricingEngine | |
| virtual arguments * | getArguments () const =0 |
| virtual const results * | getResults () const =0 |
| Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| void | notifyObservers () |
| Public Member Functions inherited from Observer | |
| 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 () |
Protected Member Functions | |
| std::complex< Real > | addOnTerm (Real phi, Time t, Size j) const |
Additional Inherited Members | |
| Public Types inherited from AnalyticHestonEngine | |
| enum | ComplexLogFormula { Gatheral, BranchCorrection, AndersenPiterbarg, AndersenPiterbargOptCV, AsymptoticChF, OptimalCV } |
| Public Types inherited from Observer | |
| typedef boost::unordered_set< ext::shared_ptr< Observable > > | set_type |
| typedef set_type::iterator | iterator |
| Static Public Member Functions inherited from AnalyticHestonEngine | |
| static void | doCalculation (Real riskFreeDiscount, Real dividendDiscount, Real spotPrice, Real strikePrice, Real term, Real kappa, Real theta, Real sigma, Real v0, Real rho, const TypePayoff &type, const Integration &integration, ComplexLogFormula cpxLog, const AnalyticHestonEngine *enginePtr, Real &value, Size &evaluations) |
| static ComplexLogFormula | optimalControlVariate (Time t, Real v0, Real kappa, Real theta, Real sigma, Real rho) |
| Protected Attributes inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results > | |
| Handle< HestonModel > | model_ |
| Protected Attributes inherited from GenericEngine< VanillaOption::arguments, VanillaOption::results > | |
| VanillaOption::arguments | arguments_ |
| VanillaOption::results | results_ |
Bates model engines based on Fourier transform.
this classes price european options under the following processes
Jump-Diffusion with Stochastic Volatility
\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]
N is a Poisson process with the intensity \( \lambda \). When a jump occurs the magnitude J has the probability density function \( \omega(J) \).
1.1 Log-Normal Jump Diffusion: BatesEngine
Logarithm of the jump size J is normally distributed
\[ \omega(J) = \frac{1}{\sqrt{2\pi \delta^2}} \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right] \]
1.2 Double-Exponential Jump Diffusion: BatesDoubleExpEngine
The jump size has an asymmetric double exponential distribution
\[ \begin{array}{rcl} \omega(J)&=& p\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J} 1_{J>0} + q\frac{1}{\eta_d}e^{\frac{1}{\eta_d}J} 1_{J<0} \\ p + q &=& 1 \end{array} \]
Stochastic Volatility with Jump Diffusion and Deterministic Jump Intensity
\[ \begin{array}{rcl} dS(t, S) &=& (r-d-\lambda m) S dt +\sqrt{v} S dW_1 + (e^J - 1) S dN \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ d\lambda(t) &=& \kappa_\lambda(\theta_\lambda-\lambda) dt \\ dW_1 dW_2 &=& \rho dt \end{array} \]
2.1 Log-Normal Jump Diffusion with Deterministic Jump Intensity BatesDetJumpEngine
2.2 Double-Exponential Jump Diffusion with Deterministic Jump Intensity BatesDoubleExpDetJumpEngine
References:
D. Bates, Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options, Review of Financial Sudies 9, 69-107.
A. Sepp, Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform (http://math.ut.ee/~spartak/papers/stochjumpvols.pdf)
