Logo Search packages:      
Sourcecode: quantlib version File versions

analyticbarrierengine.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2003 Neil Firth
 Copyright (C) 2002, 2003 Ferdinando Ametrano
 Copyright (C) 2002, 2003 Sadruddin Rejeb
 Copyright (C) 2000, 2001, 2002, 2003 RiskMap 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/reference/license.html>.

 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.
*/

#include <ql/PricingEngines/Barrier/analyticbarrierengine.hpp>
#include <ql/Processes/blackscholesprocess.hpp>

namespace QuantLib {

    void AnalyticBarrierEngine::calculate() const {

        boost::shared_ptr<PlainVanillaPayoff> payoff =
            boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non-plain payoff given");
        QL_REQUIRE(payoff->strike()>0.0,
                   "strike must be positive");

        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");

        Real strike = payoff->strike();

        Barrier::Type barrierType = arguments_.barrierType;

        switch (payoff->optionType()) {
          case Option::Call:
            switch (barrierType) {
              case Barrier::DownIn:
                if (strike >= barrier())
                    results_.value = C(1,1) + E(1);
                else
                    results_.value = A(1) - B(1) + D(1,1) + E(1);
                break;
              case Barrier::UpIn:
                if (strike >= barrier())
                    results_.value = A(1) + E(-1);
                else
                    results_.value = B(1) - C(-1,1) + D(-1,1) + E(-1);
                break;
              case Barrier::DownOut:
                if (strike >= barrier())
                    results_.value = A(1) - C(1,1) + F(1);
                else
                    results_.value = B(1) - D(1,1) + F(1);
                break;
              case Barrier::UpOut:
                if (strike >= barrier())
                    results_.value = F(-1);
                else
                    results_.value = A(1) - B(1) + C(-1,1) - D(-1,1) + F(-1);
                break;
            }
            break;
          case Option::Put:
            switch (barrierType) {
              case Barrier::DownIn:
                if (strike >= barrier())
                    results_.value = B(-1) - C(1,-1) + D(1,-1) + E(1);
                else
                    results_.value = A(-1) + E(1);
                break;
              case Barrier::UpIn:
                if (strike >= barrier())
                    results_.value = A(-1) - B(-1) + D(-1,-1) + E(-1);
                else
                    results_.value = C(-1,-1) + E(-1);
                break;
              case Barrier::DownOut:
                if (strike >= barrier())
                    results_.value = A(-1) - B(-1) + C(1,-1) - D(1,-1) + F(1);
                else
                    results_.value = F(1);
                break;
              case Barrier::UpOut:
                if (strike >= barrier())
                    results_.value = B(-1) - D(-1,-1) + F(-1);
                else
                    results_.value = A(-1) - C(-1,-1) + F(-1);
                break;
            }
            break;
          default:
            QL_FAIL("unknown type");
        }
    }


    Real AnalyticBarrierEngine::underlying() const {
        return arguments_.stochasticProcess->initialValues()[0];
    }

    Real AnalyticBarrierEngine::strike() const {
        boost::shared_ptr<PlainVanillaPayoff> payoff =
            boost::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non-plain payoff given");
        return payoff->strike();
    }

    Time AnalyticBarrierEngine::residualTime() const {
        return arguments_.stochasticProcess->time(
                                             arguments_.exercise->lastDate());
    }

    Volatility AnalyticBarrierEngine::volatility() const {
        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");
        return process->blackVolatility()->blackVol(residualTime(), strike());
    }

    Real AnalyticBarrierEngine::stdDeviation() const {
        return volatility() * std::sqrt(residualTime());
    }

    Real AnalyticBarrierEngine::barrier() const {
        return arguments_.barrier;
    }

    Real AnalyticBarrierEngine::rebate() const {
        return arguments_.rebate;
    }

    Rate AnalyticBarrierEngine::riskFreeRate() const {
        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");
        return process->riskFreeRate()->zeroRate(residualTime(), Continuous,
                                                 NoFrequency);
    }

    DiscountFactor AnalyticBarrierEngine::riskFreeDiscount() const {
        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");
        return process->riskFreeRate()->discount(residualTime());
    }

    Rate AnalyticBarrierEngine::dividendYield() const {
        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");
        return process->dividendYield()->zeroRate(residualTime(),
                                                  Continuous, NoFrequency);
    }

    DiscountFactor AnalyticBarrierEngine::dividendDiscount() const {
        boost::shared_ptr<GeneralizedBlackScholesProcess> process =
            boost::dynamic_pointer_cast<GeneralizedBlackScholesProcess>(
                                                arguments_.stochasticProcess);
        QL_REQUIRE(process, "Black-Scholes process required");
        return process->dividendYield()->discount(residualTime());
    }

    Rate AnalyticBarrierEngine::mu() const {
        Volatility vol = volatility();
        return (riskFreeRate() - dividendYield())/(vol * vol) - 0.5;
    }

    Real AnalyticBarrierEngine::muSigma() const {
        return (1 + mu()) * stdDeviation();
    }

    Real AnalyticBarrierEngine::A(Real phi) const {
        Real x1 =
            std::log(underlying()/strike())/stdDeviation() + muSigma();
        Real N1 = f_(phi*x1);
        Real N2 = f_(phi*(x1-stdDeviation()));
        return phi*(underlying() * dividendDiscount() * N1
                    - strike() * riskFreeDiscount() * N2);
    }

    Real AnalyticBarrierEngine::B(Real phi) const {
        Real x2 =
            std::log(underlying()/barrier())/stdDeviation() + muSigma();
        Real N1 = f_(phi*x2);
        Real N2 = f_(phi*(x2-stdDeviation()));
        return phi*(underlying() * dividendDiscount() * N1
                    - strike() * riskFreeDiscount() * N2);
    }

    Real AnalyticBarrierEngine::C(Real eta, Real phi) const {
        Real HS = barrier()/underlying();
        Real powHS0 = std::pow(HS, 2 * mu());
        Real powHS1 = powHS0 * HS * HS;
        Real y1 = std::log(barrier()*HS/strike())/stdDeviation() + muSigma();
        Real N1 = f_(eta*y1);
        Real N2 = f_(eta*(y1-stdDeviation()));
        return phi*(underlying() * dividendDiscount() * powHS1 * N1
                    - strike() * riskFreeDiscount() * powHS0 * N2);
    }

    Real AnalyticBarrierEngine::D(Real eta, Real phi) const {
        Real HS = barrier()/underlying();
        Real powHS0 = std::pow(HS, 2 * mu());
        Real powHS1 = powHS0 * HS * HS;
        Real y2 = std::log(barrier()/underlying())/stdDeviation() + muSigma();
        Real N1 = f_(eta*y2);
        Real N2 = f_(eta*(y2-stdDeviation()));
        return phi*(underlying() * dividendDiscount() * powHS1 * N1
                    - strike() * riskFreeDiscount() * powHS0 * N2);
    }

    Real AnalyticBarrierEngine::E(Real eta) const {
        if (rebate() > 0) {
            Real powHS0 = std::pow(barrier()/underlying(), 2 * mu());
            Real x2 =
                std::log(underlying()/barrier())/stdDeviation() + muSigma();
            Real y2 =
                std::log(barrier()/underlying())/stdDeviation() + muSigma();
            Real N1 = f_(eta*(x2 - stdDeviation()));
            Real N2 = f_(eta*(y2 - stdDeviation()));
            return rebate() * riskFreeDiscount() * (N1 - powHS0 * N2);
        } else {
            return 0.0;
        }
    }

    Real AnalyticBarrierEngine::F(Real eta) const {
        if (rebate() > 0) {
            Rate m = mu();
            Volatility vol = volatility();
            Real lambda = std::sqrt(m*m + 2.0*riskFreeRate()/(vol * vol));
            Real HS = barrier()/underlying();
            Real powHSplus = std::pow(HS, m + lambda);
            Real powHSminus = std::pow(HS, m - lambda);

            Real sigmaSqrtT = stdDeviation();
            Real z = std::log(barrier()/underlying())/sigmaSqrtT
                + lambda * sigmaSqrtT;

            Real N1 = f_(eta * z);
            Real N2 = f_(eta * (z - 2.0 * lambda * sigmaSqrtT));
            return rebate() * (powHSplus * N1 + powHSminus * N2);
        } else {
            return 0.0;
        }
    }

}


Generated by  Doxygen 1.6.0   Back to index