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

/*
 Copyright (C) 2003, 2007 Ferdinando Ametrano
 Copyright (C) 2003, 2007 StatPro Italia srl
 Copyright (C) 2009 Klaus Spanderen
 
 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
 <https://www.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.
*/

#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/instruments/europeanoption.hpp>
#include <ql/math/randomnumbers/rngtraits.hpp>
#include <ql/math/interpolations/bicubicsplineinterpolation.hpp>
#include <ql/math/interpolations/bilinearinterpolation.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/analyticdividendeuropeanengine.hpp>
#include <ql/pricingengines/vanilla/binomialengine.hpp>
#include <ql/pricingengines/vanilla/fdblackscholesvanillaengine.hpp>
#include <ql/experimental/variancegamma/fftvanillaengine.hpp>
#include <ql/pricingengines/vanilla/mceuropeanengine.hpp>
#include <ql/pricingengines/vanilla/integralengine.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/termstructures/yield/forwardcurve.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/volatility/equityfx/blackvariancesurface.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <map>

using namespace QuantLib;
using namespace boost::unit_test_framework;

BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)

BOOST_AUTO_TEST_SUITE(EuropeanOptionTests)

#undef REPORT_FAILURE
#define REPORT_FAILURE(greekName, payoff, exercise, s, q, r, today, \
                       v, expected, calculated, error, tolerance) \
    BOOST_ERROR(exerciseTypeToString(exercise) << " " \
               << payoff->optionType() << " option with " \
               << payoffTypeToString(payoff) << " payoff:\n" \
               << "    spot value:       " << s << "\n" \
               << "    strike:           " << payoff->strike() << "\n" \
               << "    dividend yield:   " << io::rate(q) << "\n" \
               << "    risk-free rate:   " << io::rate(r) << "\n" \
               << "    reference date:   " << today << "\n" \
               << "    maturity:         " << exercise->lastDate() << "\n" \
               << "    volatility:       " << io::volatility(v) << "\n\n" \
               << "    expected " << greekName << ":   " << expected << "\n" \
               << "    calculated " << greekName << ": " << calculated << "\n"\
               << "    error:            " << error << "\n" \
               << "    tolerance:        " << tolerance);

// utilities

struct EuropeanOptionData {
    Option::Type type;
    Real strike;
    Real s;        // spot
    Rate q;        // dividend
    Rate r;        // risk-free rate
    Time t;        // time to maturity
    Volatility v;  // volatility
    Real result;   // expected result
    Real tol;      // tolerance
};

enum EngineType { Analytic,
                  JR, CRR, EQP, TGEO, TIAN, LR, JOSHI,
                  FiniteDifferences,
                  Integral,
                  PseudoMonteCarlo, QuasiMonteCarlo,
                  FFT };

ext::shared_ptr<GeneralizedBlackScholesProcess>
makeProcess(const ext::shared_ptr<Quote>& u,
            const ext::shared_ptr<YieldTermStructure>& q,
            const ext::shared_ptr<YieldTermStructure>& r,
            const ext::shared_ptr<BlackVolTermStructure>& vol) {
    return ext::make_shared<BlackScholesMertonProcess>(
           Handle<Quote>(u),
           Handle<YieldTermStructure>(q),
           Handle<YieldTermStructure>(r),
           Handle<BlackVolTermStructure>(vol));
}

ext::shared_ptr<VanillaOption>
makeOption(const ext::shared_ptr<StrikedTypePayoff>& payoff,
           const ext::shared_ptr<Exercise>& exercise,
           const ext::shared_ptr<Quote>& u,
           const ext::shared_ptr<YieldTermStructure>& q,
           const ext::shared_ptr<YieldTermStructure>& r,
           const ext::shared_ptr<BlackVolTermStructure>& vol,
           EngineType engineType,
           Size binomialSteps,
           Size samples) {

    ext::shared_ptr<GeneralizedBlackScholesProcess> stochProcess =
        makeProcess(u,q,r,vol);

    ext::shared_ptr<PricingEngine> engine;
    switch (engineType) {
      case Analytic:
        engine = ext::shared_ptr<PricingEngine>(
                                    new AnalyticEuropeanEngine(stochProcess));
        break;
      case JR:
        engine = ext::shared_ptr<PricingEngine>(
                        new BinomialVanillaEngine<JarrowRudd>(stochProcess,
                                                              binomialSteps));
        break;
      case CRR:
        engine = ext::shared_ptr<PricingEngine>(
                 new BinomialVanillaEngine<CoxRossRubinstein>(stochProcess,
                                                              binomialSteps));
        break;
      case EQP:
        engine = ext::shared_ptr<PricingEngine>(
                 new BinomialVanillaEngine<AdditiveEQPBinomialTree>(
                                                              stochProcess,
                                                              binomialSteps));
        break;
      case TGEO:
        engine = ext::shared_ptr<PricingEngine>(
                        new BinomialVanillaEngine<Trigeorgis>(stochProcess,
                                                              binomialSteps));
        break;
      case TIAN:
        engine = ext::shared_ptr<PricingEngine>(
                new BinomialVanillaEngine<Tian>(stochProcess, binomialSteps));
        break;
      case LR:
        engine = ext::shared_ptr<PricingEngine>(
                      new BinomialVanillaEngine<LeisenReimer>(stochProcess,
                                                              binomialSteps));
        break;
      case JOSHI:
        engine = ext::shared_ptr<PricingEngine>(
              new BinomialVanillaEngine<Joshi4>(stochProcess, binomialSteps));
        break;
      case FiniteDifferences:
        engine = ext::shared_ptr<PricingEngine>(
                            new FdBlackScholesVanillaEngine(stochProcess,
                                                            binomialSteps,
                                                            samples));
        break;
      case Integral:
        engine = ext::shared_ptr<PricingEngine>(
                                            new IntegralEngine(stochProcess));
        break;
      case PseudoMonteCarlo:
        engine = MakeMCEuropeanEngine<PseudoRandom>(stochProcess)
            .withSteps(1)
            .withSamples(samples)
            .withSeed(42);
        break;
      case QuasiMonteCarlo:
        engine = MakeMCEuropeanEngine<LowDiscrepancy>(stochProcess)
            .withSteps(1)
            .withSamples(samples);
        break;
      case FFT:
        engine = ext::shared_ptr<PricingEngine>(
                                          new FFTVanillaEngine(stochProcess));
        break;
      default:
        QL_FAIL("unknown engine type");
    }

    ext::shared_ptr<VanillaOption> option(
            new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    return option;
}

void testEngineConsistency(EngineType engine,
                           Size binomialSteps,
                           Size samples,
                           std::map<std::string,Real> tolerance,
                           bool testGreeks = false) {

    std::map<std::string,Real> calculated, expected;

    // test options
    Option::Type types[] = { Option::Call, Option::Put };
    Real strikes[] = { 75.0, 100.0, 125.0 };
    Integer lengths[] = { 1 };

    // test data
    Real underlyings[] = { 100.0 };
    Rate qRates[] = { 0.00, 0.05 };
    Rate rRates[] = { 0.01, 0.05, 0.15 };
    Volatility vols[] = { 0.11, 0.50, 1.20 };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today,vol,dc);
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today,qRate,dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today,rRate,dc);

    for (auto& type : types) {
        for (Real strike : strikes) {
            for (int length : lengths) {
                Date exDate = today + length * 360;
                ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
                ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
                // reference option
                ext::shared_ptr<VanillaOption> refOption =
                    makeOption(payoff, exercise, spot, qTS, rTS, volTS, Analytic, Null<Size>(),
                               Null<Size>());
                // option to check
                ext::shared_ptr<VanillaOption> option = makeOption(
                    payoff, exercise, spot, qTS, rTS, volTS, engine, binomialSteps, samples);

                for (Real u : underlyings) {
                    for (Real m : qRates) {
                        for (Real n : rRates) {
                            for (Real v : vols) {
                                Rate q = m, r = n;
                                spot->setValue(u);
                                qRate->setValue(q);
                                rRate->setValue(r);
                                vol->setValue(v);

                                expected.clear();
                                calculated.clear();

                                expected["value"] = refOption->NPV();
                                calculated["value"] = option->NPV();

                                if (testGreeks && option->NPV() > spot->value() * 1.0e-5) {
                                    expected["delta"] = refOption->delta();
                                    expected["gamma"] = refOption->gamma();
                                    expected["theta"] = refOption->theta();
                                    calculated["delta"] = option->delta();
                                    calculated["gamma"] = option->gamma();
                                    calculated["theta"] = option->theta();
                                }
                                std::map<std::string, Real>::iterator it;
                                for (it = calculated.begin(); it != calculated.end(); ++it) {
                                    std::string greek = it->first;
                                    Real expct = expected[greek], calcl = calculated[greek],
                                         tol = tolerance[greek];
                                    Real error = relativeError(expct, calcl, u);
                                    if (error > tol) {
                                        REPORT_FAILURE(greek, payoff, exercise, u, q, r, today,
                                                       v, expct, calcl, error, tol);
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}


BOOST_AUTO_TEST_CASE(testValues) {

    BOOST_TEST_MESSAGE("Testing European option values...");

    /* The data below are from
       "Option pricing formulas", E.G. Haug, McGraw-Hill 1998
    */
    EuropeanOptionData values[] = {
      // pag 2-8
      //        type, strike,   spot,    q,    r,    t,  vol,   value,    tol
      { Option::Call,  65.00,  60.00, 0.00, 0.08, 0.25, 0.30,  2.1334, 1.0e-4},
      { Option::Put,   95.00, 100.00, 0.05, 0.10, 0.50, 0.20,  2.4648, 1.0e-4},
      { Option::Put,   19.00,  19.00, 0.10, 0.10, 0.75, 0.28,  1.7011, 1.0e-4},
      { Option::Call,  19.00,  19.00, 0.10, 0.10, 0.75, 0.28,  1.7011, 1.0e-4},
      { Option::Call,   1.60,   1.56, 0.08, 0.06, 0.50, 0.12,  0.0291, 1.0e-4},
      { Option::Put,   70.00,  75.00, 0.05, 0.10, 0.50, 0.35,  4.0870, 1.0e-4},
      // pag 24
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.10, 0.15,  0.0205, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.15,  1.8734, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.15,  9.9413, 1.0e-4},
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.10, 0.25,  0.3150, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.25,  3.1217, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.25, 10.3556, 1.0e-4},
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.10, 0.35,  0.9474, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.10, 0.35,  4.3693, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.10, 0.35, 11.1381, 1.0e-4},
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.50, 0.15,  0.8069, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.15,  4.0232, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.15, 10.5769, 1.0e-4},
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.50, 0.25,  2.7026, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.25,  6.6997, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.25, 12.7857, 1.0e-4},
      { Option::Call, 100.00,  90.00, 0.10, 0.10, 0.50, 0.35,  4.9329, 1.0e-4},
      { Option::Call, 100.00, 100.00, 0.10, 0.10, 0.50, 0.35,  9.3679, 1.0e-4},
      { Option::Call, 100.00, 110.00, 0.10, 0.10, 0.50, 0.35, 15.3086, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.10, 0.15,  9.9210, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.10, 0.15,  1.8734, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.10, 0.15,  0.0408, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.10, 0.25, 10.2155, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.10, 0.25,  3.1217, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.10, 0.25,  0.4551, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.10, 0.35, 10.8479, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.10, 0.35,  4.3693, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.10, 0.35,  1.2376, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.50, 0.15, 10.3192, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.50, 0.15,  4.0232, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.50, 0.15,  1.0646, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.50, 0.25, 12.2149, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.50, 0.25,  6.6997, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.50, 0.25,  3.2734, 1.0e-4},
      { Option::Put,  100.00,  90.00, 0.10, 0.10, 0.50, 0.35, 14.4452, 1.0e-4},
      { Option::Put,  100.00, 100.00, 0.10, 0.10, 0.50, 0.35,  9.3679, 1.0e-4},
      { Option::Put,  100.00, 110.00, 0.10, 0.10, 0.50, 0.35,  5.7963, 1.0e-4},
      // pag 27
      { Option::Call,  40.00,  42.00, 0.08, 0.04, 0.75, 0.35,  5.0975, 1.0e-4}
    };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);

    for (auto& value : values) {

        ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(value.type, value.strike));
        Date exDate = today + timeToDays(value.t);
        ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));

        spot->setValue(value.s);
        qRate->setValue(value.q);
        rRate->setValue(value.r);
        vol->setValue(value.v);

        ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new
            BlackScholesMertonProcess(Handle<Quote>(spot),
                                      Handle<YieldTermStructure>(qTS),
                                      Handle<YieldTermStructure>(rTS),
                                      Handle<BlackVolTermStructure>(volTS)));
        ext::shared_ptr<PricingEngine> engine(
                                    new AnalyticEuropeanEngine(stochProcess));

        EuropeanOption option(payoff, exercise);
        option.setPricingEngine(engine);

        Real calculated = option.NPV();
        Real error = std::fabs(calculated - value.result);
        Real tolerance = value.tol;
        if (error>tolerance) {
            REPORT_FAILURE("value", payoff, exercise, value.s, value.q, value.r, today, value.v,
                           value.result, calculated, error, tolerance);
        }

        engine = ext::shared_ptr<PricingEngine>(
                    new FdBlackScholesVanillaEngine(stochProcess,200,400));
        option.setPricingEngine(engine);

        calculated = option.NPV();
        error = std::fabs(calculated - value.result);
        tolerance = 1.0e-3;
        if (error>tolerance) {
            REPORT_FAILURE("value", payoff, exercise, value.s, value.q, value.r, today, value.v,
                           value.result, calculated, error, tolerance);
        }
    }
}

BOOST_AUTO_TEST_CASE(testGreekValues) {

    BOOST_TEST_MESSAGE("Testing European option greek values...");

    /* The data below are from
       "Option pricing formulas", E.G. Haug, McGraw-Hill 1998
       pag 11-16
    */
    EuropeanOptionData values[] = {
      //        type, strike,   spot,    q,    r,        t,  vol,  value
      // delta
      { Option::Call, 100.00, 105.00, 0.10, 0.10, 0.500000, 0.36,  0.5946, 0 },
      { Option::Put,  100.00, 105.00, 0.10, 0.10, 0.500000, 0.36, -0.3566, 0 },
      // elasticity
      { Option::Put,  100.00, 105.00, 0.10, 0.10, 0.500000, 0.36, -4.8775, 0 },
      // gamma
      { Option::Call,  60.00,  55.00, 0.00, 0.10, 0.750000, 0.30,  0.0278, 0 },
      { Option::Put,   60.00,  55.00, 0.00, 0.10, 0.750000, 0.30,  0.0278, 0 },
      // vega
      { Option::Call,  60.00,  55.00, 0.00, 0.10, 0.750000, 0.30, 18.9358, 0 },
      { Option::Put,   60.00,  55.00, 0.00, 0.10, 0.750000, 0.30, 18.9358, 0 },
      // theta
      { Option::Put,  405.00, 430.00, 0.05, 0.07, 1.0/12.0, 0.20,-31.1924, 0 },
      // theta per day
      { Option::Put,  405.00, 430.00, 0.05, 0.07, 1.0/12.0, 0.20, -0.0855, 0 },
      // rho
      { Option::Call,  75.00,  72.00, 0.00, 0.09, 1.000000, 0.19, 38.7325, 0 },
      // dividendRho
      { Option::Put,  490.00, 500.00, 0.05, 0.08, 0.250000, 0.15, 42.2254, 0 }
    };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
    ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new
        BlackScholesMertonProcess(Handle<Quote>(spot),
                                  Handle<YieldTermStructure>(qTS),
                                  Handle<YieldTermStructure>(rTS),
                                  Handle<BlackVolTermStructure>(volTS)));
    ext::shared_ptr<PricingEngine> engine(
                                    new AnalyticEuropeanEngine(stochProcess));

    ext::shared_ptr<StrikedTypePayoff> payoff;
    Date exDate;
    ext::shared_ptr<Exercise> exercise;
    ext::shared_ptr<VanillaOption> option;
    Real calculated;

    Integer i = -1;

    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->delta();
    Real error = std::fabs(calculated-values[i].result);
    Real tolerance = 1e-4;
    if (error>tolerance)
        REPORT_FAILURE("delta", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);

    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->delta();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("delta", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);

    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->elasticity();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("elasticity", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->gamma();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("gamma", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);

    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->gamma();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("gamma", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->vega();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("vega", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->vega();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("vega", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->theta();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("theta", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->thetaPerDay();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("thetaPerDay", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->rho();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("rho", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);


    i++;
    payoff = ext::shared_ptr<StrikedTypePayoff>(new
        PlainVanillaPayoff(values[i].type, values[i].strike));
    exDate = today + timeToDays(values[i].t);
    exercise = ext::shared_ptr<Exercise>(new EuropeanExercise(exDate));
    spot ->setValue(values[i].s);
    qRate->setValue(values[i].q);
    rRate->setValue(values[i].r);
    vol  ->setValue(values[i].v);
    option = ext::shared_ptr<VanillaOption>(
                                        new EuropeanOption(payoff, exercise));
    option->setPricingEngine(engine);
    calculated = option->dividendRho();
    error = std::fabs(calculated-values[i].result);
    if (error>tolerance)
        REPORT_FAILURE("dividendRho", payoff, exercise, values[i].s,
                       values[i].q, values[i].r, today,
                       values[i].v, values[i].result, calculated,
                       error, tolerance);

}

BOOST_AUTO_TEST_CASE(testGreeks) {

    BOOST_TEST_MESSAGE("Testing analytic European option greeks...");

    std::map<std::string,Real> calculated, expected, tolerance;
    tolerance["delta"]  = 1.0e-5;
    tolerance["gamma"]  = 1.0e-5;
    tolerance["theta"]  = 1.0e-5;
    tolerance["rho"]    = 1.0e-5;
    tolerance["divRho"] = 1.0e-5;
    tolerance["vega"]   = 1.0e-5;

    Option::Type types[] = { Option::Call, Option::Put };
    Real strikes[] = { 50.0, 99.5, 100.0, 100.5, 150.0 };
    Real underlyings[] = { 100.0 };
    Rate qRates[] = { 0.04, 0.05, 0.06 };
    Rate rRates[] = { 0.01, 0.05, 0.15 };
    Time residualTimes[] = { 1.0, 2.0 };
    Volatility vols[] = { 0.11, 0.50, 1.20 };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();
    Settings::instance().evaluationDate() = today;

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    Handle<YieldTermStructure> qTS(flatRate(qRate, dc));
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    Handle<YieldTermStructure> rTS(flatRate(rRate, dc));
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    Handle<BlackVolTermStructure> volTS(flatVol(vol, dc));

    ext::shared_ptr<StrikedTypePayoff> payoff;

    for (auto& type : types) {
        for (Real strike : strikes) {
            for (Real residualTime : residualTimes) {
                Date exDate = today + timeToDays(residualTime);
                ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
                for (Size kk = 0; kk < 4; kk++) {
                    // option to check
                    if (kk == 0) {
                        payoff = ext::shared_ptr<StrikedTypePayoff>(
                            new PlainVanillaPayoff(type, strike));
                    } else if (kk == 1) {
                        payoff = ext::shared_ptr<StrikedTypePayoff>(
                            new CashOrNothingPayoff(type, strike, 100.0));
                    } else if (kk == 2) {
                        payoff = ext::shared_ptr<StrikedTypePayoff>(
                            new AssetOrNothingPayoff(type, strike));
                    } else if (kk == 3) {
                        payoff =
                            ext::shared_ptr<StrikedTypePayoff>(new GapPayoff(type, strike, 100.0));
                    }

                    ext::shared_ptr<BlackScholesMertonProcess> stochProcess(
                        new BlackScholesMertonProcess(Handle<Quote>(spot), qTS, rTS, volTS));
                    ext::shared_ptr<PricingEngine> engine(new AnalyticEuropeanEngine(stochProcess));
                    EuropeanOption option(payoff, exercise);
                    option.setPricingEngine(engine);

                    for (Real u : underlyings) {
                        for (Real m : qRates) {
                            for (Real n : rRates) {
                                for (Real v : vols) {
                                    Rate q = m, r = n;
                                    spot->setValue(u);
                                    qRate->setValue(q);
                                    rRate->setValue(r);
                                    vol->setValue(v);

                                    Real value = option.NPV();
                                    calculated["delta"] = option.delta();
                                    calculated["gamma"] = option.gamma();
                                    calculated["theta"] = option.theta();
                                    calculated["rho"] = option.rho();
                                    calculated["divRho"] = option.dividendRho();
                                    calculated["vega"] = option.vega();

                                    if (value > spot->value() * 1.0e-5) {
                                        // perturb spot and get delta and gamma
                                        Real du = u * 1.0e-4;
                                        spot->setValue(u + du);
                                        Real value_p = option.NPV(), delta_p = option.delta();
                                        spot->setValue(u - du);
                                        Real value_m = option.NPV(), delta_m = option.delta();
                                        spot->setValue(u);
                                        expected["delta"] = (value_p - value_m) / (2 * du);
                                        expected["gamma"] = (delta_p - delta_m) / (2 * du);

                                        // perturb rates and get rho and dividend rho
                                        Spread dr = r * 1.0e-4;
                                        rRate->setValue(r + dr);
                                        value_p = option.NPV();
                                        rRate->setValue(r - dr);
                                        value_m = option.NPV();
                                        rRate->setValue(r);
                                        expected["rho"] = (value_p - value_m) / (2 * dr);

                                        Spread dq = q * 1.0e-4;
                                        qRate->setValue(q + dq);
                                        value_p = option.NPV();
                                        qRate->setValue(q - dq);
                                        value_m = option.NPV();
                                        qRate->setValue(q);
                                        expected["divRho"] = (value_p - value_m) / (2 * dq);

                                        // perturb volatility and get vega
                                        Volatility dv = v * 1.0e-4;
                                        vol->setValue(v + dv);
                                        value_p = option.NPV();
                                        vol->setValue(v - dv);
                                        value_m = option.NPV();
                                        vol->setValue(v);
                                        expected["vega"] = (value_p - value_m) / (2 * dv);

                                        // perturb date and get theta
                                        Time dT = dc.yearFraction(today - 1, today + 1);
                                        Settings::instance().evaluationDate() = today - 1;
                                        value_m = option.NPV();
                                        Settings::instance().evaluationDate() = today + 1;
                                        value_p = option.NPV();
                                        Settings::instance().evaluationDate() = today;
                                        expected["theta"] = (value_p - value_m) / dT;

                                        // compare
                                        std::map<std::string, Real>::iterator it;
                                        for (it = calculated.begin(); it != calculated.end();
                                             ++it) {
                                            std::string greek = it->first;
                                            Real expct = expected[greek], calcl = calculated[greek],
                                                 tol = tolerance[greek];
                                            Real error = relativeError(expct, calcl, u);
                                            if (error > tol) {
                                                REPORT_FAILURE(greek, payoff, exercise, u, q, r,
                                                               today, v, expct, calcl, error, tol);
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}

BOOST_AUTO_TEST_CASE(testImpliedVol) {

    BOOST_TEST_MESSAGE("Testing European option implied volatility...");

    Size maxEvaluations = 100;
    Real tolerance = 1.0e-6;

    // test options
    Option::Type types[] = { Option::Call, Option::Put };
    Real strikes[] = { 90.0, 99.5, 100.0, 100.5, 110.0 };
    Integer lengths[] = { 36, 180, 360, 1080 };

    // test data
    Real underlyings[] = { 90.0, 95.0, 99.9, 100.0, 100.1, 105.0, 110.0 };
    Rate qRates[] = { 0.01, 0.05, 0.10 };
    Rate rRates[] = { 0.01, 0.05, 0.10 };
    Volatility vols[] = { 0.01, 0.20, 0.30, 0.70, 0.90 };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);

    for (auto& type : types) {
        for (Real& strike : strikes) {
            for (int length : lengths) {
                // option to check
                Date exDate = today + length;
                ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
                ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
                ext::shared_ptr<VanillaOption> option = makeOption(
                    payoff, exercise, spot, qTS, rTS, volTS, Analytic, Null<Size>(), Null<Size>());

                ext::shared_ptr<GeneralizedBlackScholesProcess> process =
                    makeProcess(spot, qTS, rTS, volTS);

                for (Real u : underlyings) {
                    for (Real m : qRates) {
                        for (Real n : rRates) {
                            for (Real v : vols) {
                                Rate q = m, r = n;
                                spot->setValue(u);
                                qRate->setValue(q);
                                rRate->setValue(r);
                                vol->setValue(v);

                                Real value = option->NPV();
                                Volatility implVol = 0.0; // just to remove a warning...
                                if (value != 0.0) {
                                    // shift guess somehow
                                    vol->setValue(v * 0.5);
                                    if (std::fabs(value - option->NPV()) <= 1.0e-12) {
                                        // flat price vs vol --- pointless (and
                                        // numerically unstable) to solve
                                        continue;
                                    }
                                    try {
                                        implVol = option->impliedVolatility(
                                            value, process, tolerance, maxEvaluations);
                                    } catch (std::exception& e) {
                                        BOOST_ERROR("\nimplied vol calculation failed:"
                                                    << "\n   option:         " << type
                                                    << "\n   strike:         " << strike
                                                    << "\n   spot value:     " << u
                                                    << "\n   dividend yield: " << io::rate(q)
                                                    << "\n   risk-free rate: " << io::rate(r)
                                                    << "\n   today:          " << today
                                                    << "\n   maturity:       " << exDate
                                                    << "\n   volatility:     " << io::volatility(v)
                                                    << "\n   option value:   " << value << "\n"
                                                    << e.what());
                                    }
                                    if (std::fabs(implVol - v) > tolerance) {
                                        // the difference might not matter
                                        vol->setValue(implVol);
                                        Real value2 = option->NPV();
                                        Real error = relativeError(value, value2, u);
                                        if (error > tolerance) {
                                            BOOST_ERROR(
                                                type
                                                << " option :\n"
                                                << "    spot value:          " << u << "\n"
                                                << "    strike:              " << strike << "\n"
                                                << "    dividend yield:      " << io::rate(q)
                                                << "\n"
                                                << "    risk-free rate:      " << io::rate(r)
                                                << "\n"
                                                << "    maturity:            " << exDate << "\n\n"
                                                << "    original volatility: " << io::volatility(v)
                                                << "\n"
                                                << "    price:               " << value << "\n"
                                                << "    implied volatility:  "
                                                << io::volatility(implVol) << "\n"
                                                << "    corresponding price: " << value2 << "\n"
                                                << "    error:               " << error);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}

BOOST_AUTO_TEST_CASE(testImpliedVolWithDividends) {

    BOOST_TEST_MESSAGE("Testing European option implied volatility with dividends...");

    Size maxEvaluations = 100;
    Real tolerance = 1.0e-6;

    // test options
    Option::Type types[] = { Option::Call, Option::Put };
    Real strikes[] = { 90.0, 99.5, 100.0, 100.5, 110.0 };
    Integer lengths[] = { 36, 180, 360, 1080 };

    // test data
    Real underlyings[] = { 90.0, 95.0, 99.9, 100.0, 100.1, 105.0, 110.0 };
    Rate qRates[] = { 0.01, 0.05, 0.10 };
    Rate rRates[] = { 0.01, 0.05, 0.10 };
    Volatility vols[] = { 0.01, 0.20, 0.30, 0.70, 0.90 };

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(0.0));
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.0));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.0));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);

    for (auto& type : types) {
        for (Real& strike : strikes) {
            for (int length : lengths) {
                // option to check
                Date exDate = today + length;
                ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
                ext::shared_ptr<StrikedTypePayoff> payoff(new PlainVanillaPayoff(type, strike));
                auto process = makeProcess(spot, qTS, rTS, volTS);
                auto dividends = DividendVector({ today + length/2 }, { 1.0 });
                auto option = makeOption(
                    payoff, exercise, spot, qTS, rTS, volTS, Analytic, Null<Size>(), Null<Size>());
                auto divEngine = ext::make_shared<AnalyticDividendEuropeanEngine>(process, dividends);
                option->setPricingEngine(divEngine);

                for (Real u : underlyings) {
                    for (Real m : qRates) {
                        for (Real n : rRates) {
                            for (Real v : vols) {
                                Rate q = m, r = n;
                                spot->setValue(u);
                                qRate->setValue(q);
                                rRate->setValue(r);
                                vol->setValue(v);

                                Real value = option->NPV();
                                Volatility implVol = 0.0; // just to remove a warning...
                                if (value != 0.0) {
                                    // shift guess somehow
                                    vol->setValue(v * 0.5);
                                    if (std::fabs(value - option->NPV()) <= 1.0e-12) {
                                        // flat price vs vol --- pointless (and
                                        // numerically unstable) to solve
                                        continue;
                                    }
                                    try {
                                        implVol = option->impliedVolatility(
                                            value, process, dividends, tolerance, maxEvaluations);
                                    } catch (std::exception& e) {
                                        BOOST_ERROR("\nimplied vol calculation failed:"
                                                    << "\n   option:         " << type
                                                    << "\n   strike:         " << strike
                                                    << "\n   spot value:     " << u
                                                    << "\n   dividend yield: " << io::rate(q)
                                                    << "\n   risk-free rate: " << io::rate(r)
                                                    << "\n   today:          " << today
                                                    << "\n   maturity:       " << exDate
                                                    << "\n   volatility:     " << io::volatility(v)
                                                    << "\n   option value:   " << value << "\n"
                                                    << e.what());
                                    }
                                    if (std::fabs(implVol - v) > tolerance) {
                                        // the difference might not matter
                                        vol->setValue(implVol);
                                        Real value2 = option->NPV();
                                        Real error = relativeError(value, value2, u);
                                        if (error > tolerance) {
                                            BOOST_ERROR(
                                                type
                                                << " option :\n"
                                                << "    spot value:          " << u << "\n"
                                                << "    strike:              " << strike << "\n"
                                                << "    dividend yield:      " << io::rate(q)
                                                << "\n"
                                                << "    risk-free rate:      " << io::rate(r)
                                                << "\n"
                                                << "    maturity:            " << exDate << "\n\n"
                                                << "    original volatility: " << io::volatility(v)
                                                << "\n"
                                                << "    price:               " << value << "\n"
                                                << "    implied volatility:  "
                                                << io::volatility(implVol) << "\n"
                                                << "    corresponding price: " << value2 << "\n"
                                                << "    error:               " << error);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }
}

BOOST_AUTO_TEST_CASE(testImpliedVolContainment) {

    BOOST_TEST_MESSAGE("Testing self-containment of "
                       "implied volatility calculation...");

    Size maxEvaluations = 100;
    Real tolerance = 1.0e-6;

    // test options

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(100.0));
    Handle<Quote> underlying(spot);
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.05));
    Handle<YieldTermStructure> qTS(flatRate(today, qRate, dc));
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.03));
    Handle<YieldTermStructure> rTS(flatRate(today, rRate, dc));
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.20));
    Handle<BlackVolTermStructure> volTS(flatVol(today, vol, dc));

    Date exerciseDate = today + 1*Years;
    ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exerciseDate));
    ext::shared_ptr<StrikedTypePayoff> payoff(
                                 new PlainVanillaPayoff(Option::Call, 100.0));

    ext::shared_ptr<BlackScholesMertonProcess> process(
                  new BlackScholesMertonProcess(underlying, qTS, rTS, volTS));
    ext::shared_ptr<PricingEngine> engine(
                                        new AnalyticEuropeanEngine(process));
    // link to the same stochastic process, which shouldn't be changed
    // by calling methods of either option

    ext::shared_ptr<VanillaOption> option1(
                                        new EuropeanOption(payoff, exercise));
    option1->setPricingEngine(engine);
    ext::shared_ptr<VanillaOption> option2(
                                        new EuropeanOption(payoff, exercise));
    option2->setPricingEngine(engine);

    // test

    Real refValue = option2->NPV();

    Flag f;
    f.registerWith(option2);

    option1->impliedVolatility(refValue*1.5, process,
                               tolerance, maxEvaluations);

    if (f.isUp())
        BOOST_ERROR("implied volatility calculation triggered a change "
                    "in another instrument");

    option2->recalculate();
    if (std::fabs(option2->NPV() - refValue) >= 1.0e-8)
        BOOST_ERROR("implied volatility calculation changed the value "
                    << "of another instrument: \n"
                    << std::setprecision(8)
                    << "previous value: " << refValue << "\n"
                    << "current value:  " << option2->NPV());

    vol->setValue(vol->value()*1.5);

    if (!f.isUp())
        BOOST_ERROR("volatility change not notified");

    if (std::fabs(option2->NPV() - refValue) <= 1.0e-8)
        BOOST_ERROR("volatility change did not cause the value to change");

}

BOOST_AUTO_TEST_CASE(testJRBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing JR binomial European engines "
                       "against analytic results...");

    EngineType engine = JR;
    Size steps = 251;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.002;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testCRRBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing CRR binomial European engines "
                       "against analytic results...");

    EngineType engine = CRR;
    Size steps = 501;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.02;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testEQPBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing EQP binomial European engines "
                       "against analytic results...");

    EngineType engine = EQP;
    Size steps = 501;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.02;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testTGEOBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing TGEO binomial European engines "
                       "against analytic results...");

    EngineType engine = TGEO;
    Size steps = 251;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.002;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testTIANBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing TIAN binomial European engines "
                       "against analytic results...");

    EngineType engine = TIAN;
    Size steps = 251;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.002;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testLRBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing LR binomial European engines "
                       "against analytic results...");

    EngineType engine = LR;
    Size steps = 251;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 1.0e-6;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testJOSHIBinomialEngines) {

    BOOST_TEST_MESSAGE("Testing Joshi binomial European engines "
                       "against analytic results...");

    EngineType engine = JOSHI;
    Size steps = 251;
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 1.0e-7;
    relativeTol["delta"] = 1.0e-3;
    relativeTol["gamma"] = 1.0e-4;
    relativeTol["theta"] = 0.03;
    testEngineConsistency(engine,steps,samples,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testFdEngines) {

    BOOST_TEST_MESSAGE("Testing finite-difference European engines "
                       "against analytic results...");

    EngineType engine = FiniteDifferences;
    Size timeSteps = 500;
    Size gridPoints = 500;
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 1.0e-4;
    relativeTol["delta"] = 1.0e-6;
    relativeTol["gamma"] = 1.0e-6;
    relativeTol["theta"] = 1.0e-3;
    testEngineConsistency(engine,timeSteps,gridPoints,relativeTol,true);
}

BOOST_AUTO_TEST_CASE(testIntegralEngines) {

    BOOST_TEST_MESSAGE("Testing integral engines against analytic results...");

    EngineType engine = Integral;
    Size timeSteps = 300;
    Size gridPoints = 300;
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.0001;
    testEngineConsistency(engine,timeSteps,gridPoints,relativeTol);
}

BOOST_AUTO_TEST_CASE(testMcEngines) {

    BOOST_TEST_MESSAGE("Testing Monte Carlo European engines "
                       "against analytic results...");

    EngineType engine = PseudoMonteCarlo;
    Size steps = Null<Size>();
    Size samples = 40000;
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.01;
    testEngineConsistency(engine,steps,samples,relativeTol);
}

BOOST_AUTO_TEST_CASE(testQmcEngines) {

    BOOST_TEST_MESSAGE("Testing Quasi Monte Carlo European engines "
                       "against analytic results...");

    EngineType engine = QuasiMonteCarlo;
    Size steps = Null<Size>();
    Size samples = 4095; // 2^12-1
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.01;
    testEngineConsistency(engine,steps,samples,relativeTol);
}

BOOST_AUTO_TEST_CASE(testLocalVolatility) {
    BOOST_TEST_MESSAGE("Testing finite-differences with local volatility...");

    const Date settlementDate(5, July, 2002);
    Settings::instance().evaluationDate() = settlementDate;

    const DayCounter dayCounter = Actual365Fixed();
    const Calendar calendar = TARGET();

    Integer t[] = { 13, 41, 75, 165, 256, 345, 524, 703 };
    Rate r[] = { 0.0357,0.0349,0.0341,0.0355,0.0359,0.0368,0.0386,0.0401 };

    std::vector<Rate> rates(1, 0.0357);
    std::vector<Date> dates(1, settlementDate);
    for (Size i = 0; i < 8; ++i) {
        dates.push_back(settlementDate + t[i]);
        rates.push_back(r[i]);
    }
    const ext::shared_ptr<YieldTermStructure> rTS(
                                   new ZeroCurve(dates, rates, dayCounter));
    const ext::shared_ptr<YieldTermStructure> qTS(
                                   flatRate(settlementDate, 0.0, dayCounter));

    const ext::shared_ptr<Quote> s0(new SimpleQuote(4500.00));
    
    const std::vector<Real> strikes = { 100 ,500 ,2000,3400,3600,3800,4000,4200,4400,4500,
                                        4600,4800,5000,5200,5400,5600,7500,10000,20000,30000 };
    
    Volatility v[] =
      { 1.015873, 1.015873, 1.015873, 0.89729, 0.796493, 0.730914, 0.631335, 0.568895,
        0.711309, 0.711309, 0.711309, 0.641309, 0.635593, 0.583653, 0.508045, 0.463182,
        0.516034, 0.500534, 0.500534, 0.500534, 0.448706, 0.416661, 0.375470, 0.353442,
        0.516034, 0.482263, 0.447713, 0.387703, 0.355064, 0.337438, 0.316966, 0.306859,
        0.497587, 0.464373, 0.430764, 0.374052, 0.344336, 0.328607, 0.310619, 0.301865,
        0.479511, 0.446815, 0.414194, 0.361010, 0.334204, 0.320301, 0.304664, 0.297180,
        0.461866, 0.429645, 0.398092, 0.348638, 0.324680, 0.312512, 0.299082, 0.292785,
        0.444801, 0.413014, 0.382634, 0.337026, 0.315788, 0.305239, 0.293855, 0.288660,
        0.428604, 0.397219, 0.368109, 0.326282, 0.307555, 0.298483, 0.288972, 0.284791,
        0.420971, 0.389782, 0.361317, 0.321274, 0.303697, 0.295302, 0.286655, 0.282948,
        0.413749, 0.382754, 0.354917, 0.316532, 0.300016, 0.292251, 0.284420, 0.281164,
        0.400889, 0.370272, 0.343525, 0.307904, 0.293204, 0.286549, 0.280189, 0.277767,
        0.390685, 0.360399, 0.334344, 0.300507, 0.287149, 0.281380, 0.276271, 0.274588,
        0.383477, 0.353434, 0.327580, 0.294408, 0.281867, 0.276746, 0.272655, 0.271617,
        0.379106, 0.349214, 0.323160, 0.289618, 0.277362, 0.272641, 0.269332, 0.268846,
        0.377073, 0.347258, 0.320776, 0.286077, 0.273617, 0.269057, 0.266293, 0.266265,
        0.399925, 0.369232, 0.338895, 0.289042, 0.265509, 0.255589, 0.249308, 0.249665,
        0.423432, 0.406891, 0.373720, 0.314667, 0.281009, 0.263281, 0.246451, 0.242166,
        0.453704, 0.453704, 0.453704, 0.381255, 0.334578, 0.305527, 0.268909, 0.251367,
        0.517748, 0.517748, 0.517748, 0.416577, 0.364770, 0.331595, 0.287423, 0.264285 };
    
    Matrix blackVolMatrix(strikes.size(), dates.size()-1);
    for (Size i=0; i < strikes.size(); ++i)
        for (Size j=1; j < dates.size(); ++j) {
            blackVolMatrix[i][j-1] = v[i*(dates.size()-1)+j-1];
        }
    
    const ext::shared_ptr<BlackVarianceSurface> volTS(
        new BlackVarianceSurface(settlementDate, calendar,
                                 std::vector<Date>(dates.begin()+1, dates.end()),
                                 strikes, blackVolMatrix,
                                 dayCounter));
    volTS->setInterpolation<Bicubic>();
    const ext::shared_ptr<GeneralizedBlackScholesProcess> process =
                                              makeProcess(s0, qTS, rTS,volTS);
    
    const std::pair<FdmSchemeDesc, std::string> schemeDescs[]= {
        std::make_pair(FdmSchemeDesc::Douglas(), "Douglas"),
        std::make_pair(FdmSchemeDesc::CrankNicolson(), "Crank-Nicolson"),
        std::make_pair(FdmSchemeDesc::ModifiedCraigSneyd(), "Mod. Craig-Sneyd")
    };

    for (Size i=2; i < dates.size(); i+=2) {
        for (Size j=3; j < strikes.size()-5; j+=5) {
            const Date& exDate = dates[i];
            const ext::shared_ptr<StrikedTypePayoff> payoff(new
                                 PlainVanillaPayoff(Option::Call, strikes[j]));
    
            const ext::shared_ptr<Exercise> exercise(
                                                 new EuropeanExercise(exDate));
    
            EuropeanOption option(payoff, exercise);
            option.setPricingEngine(ext::shared_ptr<PricingEngine>(
                                         new AnalyticEuropeanEngine(process)));
             
            const Real tol = 0.001;
            const Real expectedNPV   = option.NPV();
            const Real expectedDelta = option.delta();
            const Real expectedGamma = option.gamma();
            
            option.setPricingEngine(ext::shared_ptr<PricingEngine>(
                         new FdBlackScholesVanillaEngine(process, 200, 400)));
    
            Real calculatedNPV = option.NPV();
            const Real calculatedDelta = option.delta();
            const Real calculatedGamma = option.gamma();
            
            // check implied pricing first
            if (std::fabs(expectedNPV - calculatedNPV) > tol*expectedNPV) {
                BOOST_FAIL("Failed to reproduce option price for "
                           << "\n    strike:     " << payoff->strike()
                           << "\n    maturity:   " << exDate
                           << "\n    calculated: " << calculatedNPV
                           << "\n    expected:   " << expectedNPV);
            }
            if (std::fabs(expectedDelta - calculatedDelta) >tol*expectedDelta) {
                BOOST_FAIL("Failed to reproduce option delta for "
                           << "\n    strike:     " << payoff->strike()
                           << "\n    maturity:   " << exDate
                           << "\n    calculated: " << calculatedDelta
                           << "\n    expected:   " << expectedDelta);
            }
            if (std::fabs(expectedGamma - calculatedGamma) >tol*expectedGamma) {
                BOOST_FAIL("Failed to reproduce option gamma for "
                           << "\n    strike:     " << payoff->strike()
                           << "\n    maturity:   " << exDate
                           << "\n    calculated: " << calculatedGamma
                           << "\n    expected:   " << expectedGamma);
            }
            
            // check local vol pricing
            // delta/gamma are not the same by definition (model implied greeks)
            for (const auto& schemeDesc : schemeDescs) {
                option.setPricingEngine(ext::make_shared<FdBlackScholesVanillaEngine>(
                    process, 25, 100, 0, schemeDesc.first, true, 0.35));

                calculatedNPV = option.NPV();
                if (std::fabs(expectedNPV - calculatedNPV) > tol*expectedNPV) {
                    BOOST_FAIL("Failed to reproduce local vol option price for "
                               << "\n    strike:     " << payoff->strike() << "\n    maturity:   "
                               << exDate << "\n    calculated: " << calculatedNPV
                               << "\n    expected:   " << expectedNPV
                               << "\n    scheme:     " << schemeDesc.second);
                }
            }
        }
    }
}

BOOST_AUTO_TEST_CASE(testAnalyticEngineDiscountCurve) {
    BOOST_TEST_MESSAGE(
        "Testing separate discount curve for analytic European engine...");

    DayCounter dc = Actual360();
    Date today = Date::todaysDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(1000.0));
    ext::shared_ptr<SimpleQuote> qRate(new SimpleQuote(0.01));
    ext::shared_ptr<YieldTermStructure> qTS = flatRate(today, qRate, dc);
    ext::shared_ptr<SimpleQuote> rRate(new SimpleQuote(0.015));
    ext::shared_ptr<YieldTermStructure> rTS = flatRate(today, rRate, dc);
    ext::shared_ptr<SimpleQuote> vol(new SimpleQuote(0.02));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today, vol, dc);
    ext::shared_ptr<SimpleQuote> discRate(new SimpleQuote(0.015));
    ext::shared_ptr<YieldTermStructure> discTS = flatRate(today, discRate, dc);

    ext::shared_ptr<BlackScholesMertonProcess> stochProcess(new
        BlackScholesMertonProcess(Handle<Quote>(spot),
            Handle<YieldTermStructure>(qTS),
            Handle<YieldTermStructure>(rTS),
            Handle<BlackVolTermStructure>(volTS)));
    ext::shared_ptr<PricingEngine> engineSingleCurve(
        new AnalyticEuropeanEngine(stochProcess));
    ext::shared_ptr<PricingEngine> engineMultiCurve(
        new AnalyticEuropeanEngine(stochProcess,
            Handle<YieldTermStructure>(discTS)));

    ext::shared_ptr<StrikedTypePayoff> payoff(new
        PlainVanillaPayoff(Option::Call, 1025.0));
    Date exDate = today + Period(1, Years);
    ext::shared_ptr<Exercise> exercise(new EuropeanExercise(exDate));
    EuropeanOption option(payoff, exercise);
    Real npvSingleCurve, npvMultiCurve;
    option.setPricingEngine(engineSingleCurve);
    npvSingleCurve = option.NPV();
    option.setPricingEngine(engineMultiCurve);
    npvMultiCurve = option.NPV();
    // check that NPV is the same regardless of engine interface
    BOOST_CHECK_EQUAL(npvSingleCurve, npvMultiCurve);
    // check that NPV changes if discount rate is changed
    discRate->setValue(0.023);
    npvMultiCurve = option.NPV();
    BOOST_CHECK_NE(npvSingleCurve, npvMultiCurve);
}

BOOST_AUTO_TEST_CASE(testPDESchemes) {
    BOOST_TEST_MESSAGE("Testing different PDE schemes to solve Black-Scholes PDEs...");

    const DayCounter dc = Actual365Fixed();
    const Date today = Date(18, February, 2018);

    Settings::instance().evaluationDate() = today;

    const Handle<Quote> spot(ext::make_shared<SimpleQuote>(100.0));
    const Handle<YieldTermStructure> qTS(flatRate(today, 0.06, dc));
    const Handle<YieldTermStructure> rTS(flatRate(today, 0.10, dc));
    const Handle<BlackVolTermStructure> volTS(flatVol(today, 0.35, dc));

    const Date maturity = today + Period(6, Months);

    const ext::shared_ptr<BlackScholesMertonProcess> process =
        ext::make_shared<BlackScholesMertonProcess>(
            spot, qTS, rTS, volTS);

    const ext::shared_ptr<PricingEngine> analytic =
        ext::make_shared<AnalyticEuropeanEngine>(process);

    // Crank-Nicolson and Douglas scheme are the same in one dimension
    const ext::shared_ptr<PricingEngine> douglas =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 15, 100, 0, FdmSchemeDesc::Douglas());

    const ext::shared_ptr<PricingEngine> crankNicolson =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 15, 100, 0, FdmSchemeDesc::CrankNicolson());

    const ext::shared_ptr<PricingEngine> implicitEuler =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 500, 100, 0, FdmSchemeDesc::ImplicitEuler());

    const ext::shared_ptr<PricingEngine> explicitEuler =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 1000, 100, 0, FdmSchemeDesc::ExplicitEuler());

    const ext::shared_ptr<PricingEngine> methodOfLines =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 1, 100, 0, FdmSchemeDesc::MethodOfLines());

    const ext::shared_ptr<PricingEngine> hundsdorfer =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 10, 100, 0, FdmSchemeDesc::Hundsdorfer());

    const ext::shared_ptr<PricingEngine> craigSneyd =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 10, 100, 0, FdmSchemeDesc::CraigSneyd());

    const ext::shared_ptr<PricingEngine> modCraigSneyd =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 15, 100, 0, FdmSchemeDesc::ModifiedCraigSneyd());

    const ext::shared_ptr<PricingEngine> trBDF2 =
        ext::make_shared<FdBlackScholesVanillaEngine>(
            process, 15, 100, 0, FdmSchemeDesc::TrBDF2());


    const std::pair<ext::shared_ptr<PricingEngine>, std::string> engines[]= {
        std::make_pair(douglas, "Douglas"),
        std::make_pair(crankNicolson, "Crank-Nicolson"),
        std::make_pair(implicitEuler, "Implicit-Euler"),
        std::make_pair(explicitEuler, "Explicit-Euler"),
        std::make_pair(methodOfLines, "Method-of-Lines"),
        std::make_pair(hundsdorfer, "Hundsdorfer"),
        std::make_pair(craigSneyd, "Craig-Sneyd"),
        std::make_pair(modCraigSneyd, "Modified Craig-Sneyd"),
        std::make_pair(trBDF2, "TR-BDF2")
    };

    const ext::shared_ptr<PlainVanillaPayoff> payoff(
        ext::make_shared<PlainVanillaPayoff>(Option::Put, spot->value()));

    const ext::shared_ptr<Exercise> exercise(
        ext::make_shared<EuropeanExercise>(maturity));

    VanillaOption option(payoff, exercise);

    option.setPricingEngine(analytic);
    const Real expected = option.NPV();

    const Real tol = 0.006;
    for (const auto& engine : engines) {
        option.setPricingEngine(engine.first);
        const Real calculated = option.NPV();

        const Real diff = std::fabs(expected - calculated);

        if (diff > tol) {
            BOOST_FAIL("Failed to reproduce European option values with the "
                       << engine.second << " PDE scheme"
                       << "\n    calculated: " << calculated << "\n    expected:   " << expected
                       << "\n    difference: " << diff << "\n    tolerance:  " << tol);
        }
    }
}

BOOST_AUTO_TEST_CASE(testFdEngineWithNonConstantParameters) {
    BOOST_TEST_MESSAGE("Testing finite-difference European engine "
                       "with non-constant parameters...");

    Real u = 190.0;
    Volatility v = 0.20;

    DayCounter dc = Actual360();
    Date today = Settings::instance().evaluationDate();

    ext::shared_ptr<SimpleQuote> spot(new SimpleQuote(u));
    ext::shared_ptr<BlackVolTermStructure> volTS = flatVol(today,v,dc);

    std::vector<Date> dates(5);
    std::vector<Rate> rates(5);
    dates[0] = today;     rates[0] = 0.0;
    dates[1] = today+90;  rates[1] = 0.001;
    dates[2] = today+180; rates[2] = 0.002;
    dates[3] = today+270; rates[3] = 0.005;
    dates[4] = today+360; rates[4] = 0.01;
    ext::shared_ptr<YieldTermStructure> rTS =
        ext::make_shared<ForwardCurve>(dates, rates, dc);
    Rate r = rTS->zeroRate(dates[4], dc, Continuous);

    ext::shared_ptr<BlackScholesProcess> process =
        ext::make_shared<BlackScholesProcess>(Handle<Quote>(spot),
                                              Handle<YieldTermStructure>(rTS),
                                              Handle<BlackVolTermStructure>(volTS));
    
    ext::shared_ptr<Exercise> exercise =
        ext::make_shared<EuropeanExercise>(today + 360);
    ext::shared_ptr<StrikedTypePayoff> payoff =
        ext::make_shared<PlainVanillaPayoff>(Option::Call, 190.0);

    EuropeanOption option(payoff, exercise);

    option.setPricingEngine(ext::make_shared<AnalyticEuropeanEngine>(process));
    Real expected = option.NPV();

    Size timeSteps = 200;
    Size gridPoints = 201;
    option.setPricingEngine(ext::make_shared<FdBlackScholesVanillaEngine>(
                              process, timeSteps, gridPoints));
    Real calculated = option.NPV();

    Real tolerance = 0.01;
    Real error = std::fabs(expected-calculated);
    if (error > tolerance) {
        REPORT_FAILURE("value", payoff, exercise,
                       u, 0.0, r, today, v,
                       expected, calculated,
                       error, tolerance);
    }
}

BOOST_AUTO_TEST_CASE(testDouglasVsCrankNicolson) {
    BOOST_TEST_MESSAGE("Testing Douglas vs Crank-Nicolson scheme "
                        "for finite-difference European PDE engines...");

    const DayCounter dc = Actual365Fixed();
    const Date today = Date(5, October, 2018);

    Settings::instance().evaluationDate() = today;

    const Handle<Quote> spot(ext::make_shared<SimpleQuote>(100.0));
    const Handle<YieldTermStructure> qTS(flatRate(today, 0.02, dc));
    const Handle<YieldTermStructure> rTS(flatRate(today, 0.075, dc));
    const Handle<BlackVolTermStructure> volTS(flatVol(today, 0.25, dc));

    const ext::shared_ptr<BlackScholesMertonProcess> process =
        ext::make_shared<BlackScholesMertonProcess>(
            spot, qTS, rTS, volTS);

    VanillaOption option(
        ext::make_shared<PlainVanillaPayoff>(Option::Put, spot->value()+2),
        ext::make_shared<EuropeanExercise>(today + Period(6, Months)));

    option.setPricingEngine(
        ext::make_shared<AnalyticEuropeanEngine>(process));

    const Real npv = option.NPV();
    const Real schemeTol = 1e-12;
    const Real npvTol = 1e-2;

    for (Real theta = 0.2; theta < 0.81; theta+=0.1) {
        option.setPricingEngine(
            ext::make_shared<FdBlackScholesVanillaEngine>(
                process, 500, 100, 0,
                FdmSchemeDesc(FdmSchemeDesc::CrankNicolsonType, theta, 0.0)));
        const Real crankNicolsonNPV = option.NPV();

        const Real npvDiff = std::fabs(crankNicolsonNPV - npv);
        if (npvDiff > npvTol) {
            BOOST_FAIL("Failed to reproduce european option values "
                    "with the Crank-Nicolson PDE scheme "
                       << "\n    Analytic NPV:       " << npv
                       << "\n    Crank-Nicolson NPV: " << crankNicolsonNPV
                       << "\n    theta:              " << theta
                       << "\n    difference:         " << npvDiff
                       << "\n    tolerance:          " << npvTol);
        }

        option.setPricingEngine(
            ext::make_shared<FdBlackScholesVanillaEngine>(
                process, 500, 100, 0,
                FdmSchemeDesc(FdmSchemeDesc::DouglasType, theta, 0.0)));
        const Real douglasNPV = option.NPV();

        const Real schemeDiff = std::fabs(crankNicolsonNPV - douglasNPV);

        if (schemeDiff > schemeTol) {
            BOOST_FAIL("Failed to reproduce Douglas scheme option values "
                    "with the Crank-Nicolson PDE scheme "
                       << "\n    Dougles NPV:        " << douglasNPV
                       << "\n    Crank-Nicolson NPV: " << crankNicolsonNPV
                       << "\n    difference:         " << schemeDiff
                       << "\n    tolerance:          " << schemeTol);
        }
    }
}

BOOST_AUTO_TEST_CASE(testFFTEngines) {

    BOOST_TEST_MESSAGE("Testing FFT European engines "
                       "against analytic results...");

    EngineType engine = FFT;
    Size steps = Null<Size>();
    Size samples = Null<Size>();
    std::map<std::string,Real> relativeTol;
    relativeTol["value"] = 0.01;
    testEngineConsistency(engine,steps,samples,relativeTol);
}

BOOST_AUTO_TEST_SUITE_END()

BOOST_AUTO_TEST_SUITE_END()
