batesengine.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2005 Klaus Spanderen
 Copyright (C) 2007 StatPro Italia srl
 
 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/
 
 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <quantlib-dev@lists.sf.net>. The license is also available online at
 <http://quantlib.org/license.shtml>.
 
 This program is distributed in the hope that it will be useful, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 FOR A PARTICULAR PURPOSE.  See the license for more details.
*/
 
/*! \file batesengine.hpp
    \brief analytic Bates model engine
*/
 
#ifndef quantlib_bates_engine_hpp
#define quantlib_bates_engine_hpp
 
#include <ql/qldefines.hpp>
#include <ql/models/equity/batesmodel.hpp>
#include <ql/pricingengines/vanilla/analytichestonengine.hpp>
 
namespace QuantLib {
 
    //! Bates model engines based on Fourier transform
    /*! this classes price european options under the following processes
 
        1. Jump-Diffusion with Stochastic Volatility
 
        \f[
        \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}
        \f]
 
        N is a Poisson process with the intensity \f$ \lambda
        \f$. When a jump occurs the magnitude J has the probability
        density function \f$ \omega(J) \f$.
 
        1.1 Log-Normal Jump Diffusion: BatesEngine
 
        Logarithm of the jump size J is normally distributed
        \f[
        \omega(J) = \frac{1}{\sqrt{2\pi \delta^2}}
                    \exp\left[-\frac{(J-\nu)^2}{2\delta^2}\right]
        \f]
 
        1.2  Double-Exponential Jump Diffusion: BatesDoubleExpEngine
 
        The jump size has an asymmetric double exponential distribution
        \f[
        \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}
        \f]
 
        2. Stochastic Volatility with Jump Diffusion
           and Deterministic Jump Intensity
 
        \f[
        \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}
        \f]
 
        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>)
 
        \ingroup vanillaengines
 
        \test 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.
    */
    class BatesEngine : public AnalyticHestonEngine {
      public:
        explicit BatesEngine(const ext::shared_ptr<BatesModel>& model,
                             Size integrationOrder = 144);
        BatesEngine(const ext::shared_ptr<BatesModel>& model,
                    Real relTolerance, Size maxEvaluations);
 
      protected:
        std::complex<Real> addOnTerm(Real phi, Time t, Size j) const override;
    };
 
 
    class BatesDetJumpEngine : public BatesEngine {
      public:
        explicit BatesDetJumpEngine(const ext::shared_ptr<BatesDetJumpModel>& model,
                                    Size integrationOrder = 144);
        BatesDetJumpEngine(const ext::shared_ptr<BatesDetJumpModel>& model,
                           Real relTolerance, Size maxEvaluations);
 
      protected:
        std::complex<Real> addOnTerm(Real phi, Time t, Size j) const override;
    };
 
 
    class BatesDoubleExpEngine : public AnalyticHestonEngine {
      public:
        explicit BatesDoubleExpEngine(
            const ext::shared_ptr<BatesDoubleExpModel>& model,
            Size integrationOrder = 144);
        BatesDoubleExpEngine(
            const ext::shared_ptr<BatesDoubleExpModel>& model,
            Real relTolerance, Size maxEvaluations);
 
      protected:
        std::complex<Real> addOnTerm(Real phi, Time t, Size j) const override;
    };
 
 
    class BatesDoubleExpDetJumpEngine : public BatesDoubleExpEngine {
      public:
        explicit BatesDoubleExpDetJumpEngine(
            const ext::shared_ptr<BatesDoubleExpDetJumpModel>& model,
            Size integrationOrder = 144);
        BatesDoubleExpDetJumpEngine(
            const ext::shared_ptr<BatesDoubleExpDetJumpModel>& model,
            Real relTolerance, Size maxEvaluations);
 
      protected:
        std::complex<Real> addOnTerm(Real phi, Time t, Size j) const override;
    };
 
}
 
#endif