BatesEngine Class Reference

Bates model engines based on Fourier transform. More...

#include <ql/pricingengines/vanilla/batesengine.hpp>

Inheritance diagram for BatesEngine:

Public Member Functions
	BatesEngine (const boost::shared_ptr< BatesModel > &model, Size integrationOrder=144)

	BatesEngine (const boost::shared_ptr< BatesModel > &model, Real relTolerance, Size maxEvaluations)

Public Member Functions inherited from AnalyticHestonEngine
	AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, Real relTolerance, Size maxEvaluations)

	AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, Size integrationOrder=144)

	AnalyticHestonEngine (const boost::shared_ptr< HestonModel > &model, ComplexLogFormula cpxLog, const Integration &itg)

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 boost::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 Observer
	Observer (const Observer &)

Observer &	operator= (const Observer &)

std::pair< std::set < boost::shared_ptr < Observable > >::iterator, bool >	registerWith (const boost::shared_ptr< Observable > &)

Size	unregisterWith (const boost::shared_ptr< Observable > &)

void	unregisterWithAll ()

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 }

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, const ComplexLogFormula cpxLog, const AnalyticHestonEngine *const enginePtr, Real &value, Size &evaluations)

Protected Attributes inherited from GenericModelEngine< HestonModel, VanillaOption::arguments, VanillaOption::results >
Handle< HestonModel >	model_

Detailed Description

Bates model engines based on Fourier transform.

this classes price european options under the following processes

   1. 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 \form#29@_fakenl. When a jump occurs the magnitude J has the probability
  density function \form#323.

  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

$\begin{array}{rcl} \omega(J)&=& p\frac{1}{\eta_u}e^{-\frac{1}{\eta_u}J} 1_{J>0} + q\frac{1}{\eta_d}e^{\frac{1}{\eta_d}J} 1_{J<0} \\ p + q &=& 1 \end{array}$

  2. 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>)

Tests:: the correctness of the returned value is tested by reproducing results available in web/literature, testing against QuantLib's jump diffusion engine and comparison with Black pricing.

Examples:: EquityOption.cpp.

A free/open-source library for quantitative finance

Version 1.2.1

Getting started

Reference manual

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description