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conundrumpricer.hpp

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/*
 Copyright (C) 2006 Giorgio Facchinetti
 Copyright (C) 2006 Mario Pucci

 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 conundrumpricer.hpp
    \brief CMS-coupon pricer
*/

#ifndef quantlib_conundrum_pricer_hpp
#define quantlib_conundrum_pricer_hpp

#include <ql/cashflows/couponpricer.hpp>
#include <ql/instruments/payoffs.hpp>

namespace QuantLib {

    class CmsCoupon;
    class YieldTermStructure;
    class Quote;

00035     class VanillaOptionPricer {
      public:
        virtual ~VanillaOptionPricer() {}
        virtual Real operator()(Real strike,
                                Option::Type optionType,
                                Real deflator) const = 0;
    };

00043     class BlackVanillaOptionPricer : public VanillaOptionPricer {
      public:
        BlackVanillaOptionPricer(
                Rate forwardValue,
                Date expiryDate,
                const Period& swapTenor,
                const boost::shared_ptr<SwaptionVolatilityStructure>&
                                                         volatilityStructure);

        Real operator()(Real strike,
                        Option::Type optionType,
                        Real deflator) const;
      private:
        Rate forwardValue_;
        Date expiryDate_;
        Period swapTenor_;
        boost::shared_ptr<SwaptionVolatilityStructure> volatilityStructure_;
        boost::shared_ptr<SmileSection> smile_;
    };

00063     class GFunction {
      public:
        virtual ~GFunction() {}
        virtual Real operator()(Real x) = 0;
        virtual Real firstDerivative(Real x) = 0;
        virtual Real secondDerivative(Real x) = 0;
    };

00071     class GFunctionFactory {
      public:
        enum YieldCurveModel { Standard,
                               ExactYield,
                               ParallelShifts,
                               NonParallelShifts
        };
        static boost::shared_ptr<GFunction>
        newGFunctionStandard(Size q,
                             Real delta,
                             Size swapLength);
        static boost::shared_ptr<GFunction>
        newGFunctionExactYield(const CmsCoupon& coupon);
        static boost::shared_ptr<GFunction>
        newGFunctionWithShifts(const CmsCoupon& coupon,
                               const Handle<Quote>& meanReversion);
      private:
        GFunctionFactory();

00090         class GFunctionStandard : public GFunction {
          public:
            GFunctionStandard(Size q,
                              Real delta,
                              Size swapLength)
            : q_(q), delta_(delta), swapLength_(swapLength) {}
            Real operator()(Real x);
            Real firstDerivative(Real x);
            Real secondDerivative(Real x);
          protected:
            /* number of period per year */
            const int q_;
            /* fraction of a period between the swap start date and
               the pay date  */
            Real delta_;
            /* length of swap*/
            Size swapLength_;
        };

00109         class GFunctionExactYield : public GFunction {
          public:
            GFunctionExactYield(const CmsCoupon& coupon);
            Real operator()(Real x) ;
            Real firstDerivative(Real x);
            Real secondDerivative(Real x);
          protected:
            /* fraction of a period between the swap start date and
               the pay date  */
            Real delta_;
            /* accruals fraction*/
            std::vector<Time> accruals_;
        };

00123         class GFunctionWithShifts : public GFunction {

            Time swapStartTime_;

            Time shapedPaymentTime_;
            std::vector<Time> shapedSwapPaymentTimes_;

            std::vector<Time> accruals_;
            std::vector<Real> swapPaymentDiscounts_;
            Real discountAtStart_, discountRatio_;

            Real swapRateValue_;
            Handle<Quote> meanReversion_;

            Real calibratedShift_, tmpRs_;
            const Real accuracy_;

            //* function describing the non-parallel shape of the curve shift*/
            Real shapeOfShift(Real s) const;
            //* calibration of shift*/
            Real calibrationOfShift(Real Rs);
            Real functionZ(Real x);
            Real derRs_derX(Real x);
            Real derZ_derX(Real x);
            Real der2Rs_derX2(Real x);
            Real der2Z_derX2(Real x);

            class ObjectiveFunction;
            friend class ObjectiveFunction;
00152             class ObjectiveFunction : public std::unary_function<Real, Real> {
                const GFunctionWithShifts& o_;
                Real Rs_;
                mutable Real derivative_;
                public:
              virtual ~ObjectiveFunction() {}
                ObjectiveFunction(const GFunctionWithShifts& o,
                                  const Real Rs)
                : o_(o), Rs_(Rs) {}
                virtual Real operator()(const Real& x) const;
                Real derivative (const Real& x) const;
                void setSwapRateValue(Real x);
                const GFunctionWithShifts& gFunctionWithShifts() const {
                    return o_; }
            };

            boost::shared_ptr<ObjectiveFunction> objectiveFunction_;
          public:
            GFunctionWithShifts(const CmsCoupon& coupon,
                                const Handle<Quote>& meanReversion);
            Real operator()(Real x) ;
            Real firstDerivative(Real x);
            Real secondDerivative(Real x);
        };

    };

    inline std::ostream& operator<<(std::ostream& out,
                                    GFunctionFactory::YieldCurveModel type) {
        switch (type) {
          case GFunctionFactory::Standard:
            return out << "Standard";
          case GFunctionFactory::ExactYield:
            return out << "ExactYield";
          case GFunctionFactory::ParallelShifts:
            return out << "ParallelShifts";
          case GFunctionFactory::NonParallelShifts:
            return out << "NonParallelShifts";
          default:
            QL_FAIL("unknown option type");
        }
    }

    //! CMS-coupon pricer
    /*! Base class for the pricing of a CMS coupon via static replication
        as in Hagan's "Conundrums..." article
    */
00199     class HaganPricer: public CmsCouponPricer {
      public:
        /* */
        virtual Real swapletPrice() const = 0;
        virtual Rate swapletRate() const;
        virtual Real capletPrice(Rate effectiveCap) const;
        virtual Rate capletRate(Rate effectiveCap) const;
        virtual Real floorletPrice(Rate effectiveFloor) const;
        virtual Rate floorletRate(Rate effectiveFloor) const;
        /* */
        Real meanReversion() const;
        void setMeanReversion(const Handle<Quote>& meanReversion) {
            unregisterWith(meanReversion_);
            meanReversion_ = meanReversion;
            registerWith(meanReversion_);
            update();
        };
      protected:
        HaganPricer(
                const Handle<SwaptionVolatilityStructure>& swaptionVol,
                GFunctionFactory::YieldCurveModel modelOfYieldCurve,
                const Handle<Quote>& meanReversion);
        void initialize(const FloatingRateCoupon& coupon);

        virtual Real optionletPrice(Option::Type optionType,
                                    Real strike) const = 0;

        boost::shared_ptr<YieldTermStructure> rateCurve_;
        GFunctionFactory::YieldCurveModel modelOfYieldCurve_;
        boost::shared_ptr<GFunction> gFunction_;
        const CmsCoupon* coupon_;
        Date paymentDate_, fixingDate_;
        Rate swapRateValue_;
        DiscountFactor discount_;
        Real annuity_;
        Real gearing_;
        Spread spread_;
        Real spreadLegValue_;
        Rate cutoffForCaplet_, cutoffForFloorlet_;
        Handle<Quote> meanReversion_;
        Period swapTenor_;
        boost::shared_ptr<VanillaOptionPricer> vanillaOptionPricer_;
    };


    //! CMS-coupon pricer
    /*! Prices a cms coupon via static replication as in Hagan's
        "Conundrums..." article via numerical integration based on
        prices of vanilla swaptions
    */
00249     class NumericHaganPricer : public HaganPricer {
      public:
        NumericHaganPricer(
            const Handle<SwaptionVolatilityStructure>& swaptionVol,
            GFunctionFactory::YieldCurveModel modelOfYieldCurve,
            const Handle<Quote>& meanReversion,
            Rate lowerLimit = 0.0,
            Rate upperLimit = 1.0,
            Real precision = 1.0e-6);

       Real upperLimit() { return upperLimit_; }
       Real stdDeviations() { return stdDeviationsForUpperLimit_; }

      //private:
00263         class Function : public std::unary_function<Real, Real> {
          public:
            virtual ~Function() {}
            virtual Real operator()(Real x) const = 0;
        };

00269         class ConundrumIntegrand : public Function {
            friend class NumericHaganPricer;
          public:
            ConundrumIntegrand(
                       const boost::shared_ptr<VanillaOptionPricer>& o,
                       const boost::shared_ptr<YieldTermStructure>& rateCurve,
                       const boost::shared_ptr<GFunction>& gFunction,
                       Date fixingDate,
                       Date paymentDate,
                       Real annuity,
                       Real forwardValue,
                       Real strike,
                       Option::Type optionType);
            Real operator()(Real x) const;
          protected:
            Real functionF(const Real x) const;
            Real firstDerivativeOfF(const Real x) const;
            Real secondDerivativeOfF(const Real x) const;

            Real strike() const;
            Real annuity() const;
            Date fixingDate() const;
            void setStrike(Real strike);

            const boost::shared_ptr<VanillaOptionPricer> vanillaOptionPricer_;
            const Real forwardValue_, annuity_;
            const Date fixingDate_, paymentDate_;
            Real strike_;
            const Option::Type optionType_;
            boost::shared_ptr<GFunction> gFunction_;
        };

        Real integrate(Real a,
                       Real b,
                       const ConundrumIntegrand& Integrand) const;
        virtual Real optionletPrice(Option::Type optionType,
                                    Rate strike) const;
        virtual Real swapletPrice() const;
        Real resetUpperLimit(Real stdDeviationsForUpperLimit) const;
        Real refineIntegration(Real integralValue, const ConundrumIntegrand& integrand) const;

        mutable Real upperLimit_, stdDeviationsForUpperLimit_;
        const Real lowerLimit_, requiredStdDeviations_, precision_, refiningIntegrationTolerance_;
    };

    //! CMS-coupon pricer
00315     class AnalyticHaganPricer : public HaganPricer {
      public:
        AnalyticHaganPricer(
            const Handle<SwaptionVolatilityStructure>& swaptionVol,
            GFunctionFactory::YieldCurveModel modelOfYieldCurve,
            const Handle<Quote>& meanReversion);
      protected:
        Real optionletPrice(Option::Type optionType,
                            Real strike) const;
        Real swapletPrice() const;
    };

}


#endif

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