exponentialfittinghestonengine.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2020 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
 <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 exponentialfittinghestonengine.cpp
*/
 
#include <ql/functional.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <ql/math/integrals/gaussianquadratures.hpp>
#include <ql/math/integrals/gausslobattointegral.hpp>
#include <ql/math/interpolations/lagrangeinterpolation.hpp>
#include <ql/pricingengines/vanilla/exponentialfittinghestonengine.hpp>
 
namespace QuantLib {
 
    namespace {
        const double values4[][129] = {
                { 0.0, 234.8095791713261, 218.0318519353285, 204.6720284850595, 193.1511360370731, 182.8582046914314, 173.4749468364244, 164.8086026551506, 156.7310751326711, 149.1516659000495, 142.0031214899315, 135.2337879495259, 128.8028787692377, 122.6774602685386, 116.8304450513065, 111.2392075244396, 105.8845994688, 100.750231969514, 95.82194001552078, 91.08737561313309, 86.53569334945649, 82.15730377831932, 77.94367743446313, 73.8871872324829, 69.98098037714679, 66.21887325124759, 62.59526440015139, 59.10506191901711, 55.74362241327837, 52.50669934134626, 49.3903990256247, 46.39114297861616, 43.5056354664215, 40.73083544445857, 38.06393216564644, 35.50232389114117, 33.04359923643779, 30.68552076752596, 28.42601052750101, 26.26313722711847, 24.19510487593323, 22.22024266595088, 20.33699594873022, 18.5439181708592, 16.83966365264874, 15.22298111152472, 13.6927078455475, 12.24776450424429, 10.88715038388637, 9.60993919279611, 8.415275239483032, 7.302370002587396, 6.270499046923647, 5.318999254496381, 4.447266343313092, 3.654752650207289, 2.940965156725249, 2.305463739307505, 1.747859626059435, 1.267814040775252, 0.8650370046481092, 0.5392862212279848, 0.290365744018042, 0.11812251209679, 0.02241587414672291, 19.7904730415389, 14.64287849684275, 12.29787550435821, 10.83820345905683, 9.798443299108831, 8.999307532256775, 8.354314484533429, 7.815638985966243, 7.354263948608144, 6.951358017695886, 6.594058135618385, 6.27321659221623, 5.98211240191717, 5.715672861918123, 5.469981785549187, 5.24195701287718, 5.029132122798146, 4.829504600649047, 4.641427702702372, 4.463531827796793, 4.294666286068176, 4.133855463009227, 3.980265333061287, 3.833177538891964, 3.691969085114964, 3.556096255713026, 3.42508174873024, 3.298504289717459, 3.175990175055341, 3.057206332403495, 2.941854584510562, 2.829666875458116, 2.720401272597374, 2.613838598180361, 2.509779575606303, 2.408042398876443, 2.308460652136126, 2.210881520418866, 2.115164243858015, 2.02117877644997, 1.928804617452471, 1.837929789102533, 1.748449938844707, 1.660267547903212, 1.573291230997683, 1.487435114419195, 1.40261828167578, 1.318764277552648, 1.235800662793408, 1.153658612733963, 1.072272554169656, 0.9915798355270596, 0.9115204260895459, 0.8320366406138465, 0.7530728862177118, 0.674575428995979, 0.5964921786168993, 0.5187724907443817, 0.441366991509971, 0.364227443636659, 0.2873067415931395, 0.2105595201900571, 0.1339474500125191, 0.05752803788948557 },
                { 0.05, 234.2683512992485, 217.5652513510042, 204.2608770758455, 192.7849756796624, 182.5300291920975, 173.1795829183935, 164.5420057558895, 156.4899620596637, 148.9332999194404, 141.8051761627553, 135.054255630516, 128.6400062658957, 122.5297019371973, 116.6964275848426, 111.1177028636259, 105.7745035286647, 100.6505476345717, 95.73176333754835, 91.00588445721034, 86.46213794280316, 82.09099875973048, 77.88399510262698, 73.83355176333369, 69.93286283271761, 66.17578724116877, 62.55676228595253, 59.07073147343707, 55.7130838637403, 52.47960273993026, 49.36642189821734, 46.36998821411457, 43.48702941342039, 40.71452618812902, 38.04968796179686, 35.48993173795288, 33.03286356724488, 30.67626225039232, 28.41806495932832, 26.25635451167667, 24.18934807659869, 22.21538712511386, 20.33292846683142, 18.54053623886463, 16.83687473249949, 15.22070195972028, 13.69086387555865, 12.2462891839139, 10.88598466437716, 9.609030965992248, 8.414578821054335, 7.301845638188178, 6.270112439227548, 5.318721108968854, 4.447071930797849, 3.6546213845556, 2.940880185829794, 2.305411548018228, 1.747829649558985, 1.267798287078069, 0.865029684961297, 0.5392833869746307, 0.2903649293765078, 0.11812238095134, 0.02241587037546683, 19.69916274343335, 14.58017388582429, 12.24845416104839, 10.79710829783229, 9.763275690870078, 8.968668805528184, 8.327294608293961, 7.791601365305953, 7.332739711343556, 6.931988251617563, 6.576559758402458, 6.257360936613612, 5.967711123308542, 5.702568297969066, 5.458040145869966, 5.231063435608646, 5.019187002125522, 4.820420803212686, 4.633128420459334, 4.455948896052475, 4.287738847729877, 4.127528894736217, 3.974490372420735, 3.827909567821301, 3.687167536378474, 3.551724117193278, 3.42110514631576, 3.294892133905787, 3.17271385964117, 3.054239476077969, 2.939172808068394, 2.827247608748426, 2.718223586479143, 2.611883057621558, 2.508028110758968, 2.406478191516223, 2.307068035300078, 2.209645889430603, 2.114071977225534, 2.020217165357372, 1.927961802763817, 1.8371947049587, 1.747812262068525, 1.659717652541767, 1.572820147423197, 1.487034492492155, 1.402280357539424, 1.318481843686772, 1.235567041002679, 1.153467629790401, 1.072118519862915, 0.9914575229087829, 0.9114250537247282, 0.8319638566759891, 0.7530187542860148, 0.6745364154297774, 0.596465141400492, 0.5187546697087099, 0.4413559998512321, 0.3642212606638437, 0.2873037066466006, 0.2105583276842426, 0.1339471455650227, 0.05752801551838103 },
                { 0.1, 232.6616279835473, 216.1806101061962, 203.0409996627243, 191.6986529354063, 181.5563838387744, 172.3032201020834, 163.7509038389486, 155.7743725917344, 148.2851042961916, 141.2174782034082, 134.5211079447418, 128.1562179664579, 122.0906985643736, 116.298146028833, 110.7565105958126, 105.4471352263999, 100.3540545689635, 95.46347233134401, 90.76336415475587, 86.24317075960123, 81.89355730823829, 77.70622219186564, 73.673743285077, 69.7894530036334, 66.04733578606166, 62.44194323407706, 58.96832330580525, 55.62196080004967, 52.39872699313946, 49.29483675572285, 46.30681182898199, 43.43144920869808, 40.66579379303607, 38.00711461136637, 35.45288407815874, 33.00075981622926, 30.6485686735149, 28.39429262166695, 26.23605627654957, 24.17211582282957, 22.20084915926591, 20.32074710960723, 18.53040556739845, 16.82851846242974, 15.21387145278349, 13.68533626004034, 12.24186557666808, 10.88248848431603, 9.606306329980236, 8.412489014037567, 7.300271650171452, 6.268951562391603, 5.317885588814585, 4.446487665722357, 3.654226668717093, 2.940624490552334, 2.305254337329934, 1.747739225754234, 1.267750662450325, 0.8650074760724744, 0.5392747280127196, 0.2903624013083418, 0.1181219533036879, 0.02241585257353072, 19.42718031519661, 14.39373856919362, 12.10168617784474, 10.67516752160333, 9.658985192010958, 8.877846847619767, 8.247222882374721, 7.720380243268126, 7.268971531644766, 6.874604276997105, 6.524717945902563, 6.210381807219462, 5.925035571103697, 5.663728737701915, 5.422640138170565, 5.198762903932961, 4.989691255635626, 4.7934722209592, 4.608500040590655, 4.433439396985166, 4.267168565027318, 4.108736621179749, 3.957330758966992, 3.81225099163693, 3.672890336264371, 3.538719121118826, 3.409272433509946, 3.284139987004636, 3.162957872124423, 3.045401787571403, 2.931181445688388, 2.820035916979011, 2.711729731425256, 2.606049594111934, 2.50280160285089, 2.401808878610175, 2.302909537400565, 2.205954946162037, 2.110808216083759, 2.01734289539004, 1.925441830458653, 1.834996169603027, 1.74590448824573, 1.65807201776635, 1.571409963197856, 1.485834897307841, 1.401268220540341, 1.317635677893176, 1.234866925130263, 1.152895137830144, 1.071656657692984, 0.9910906713032496, 0.9111389172047534, 0.8317454177197424, 0.7528562324755021, 0.6744192311673117, 0.5963838838759056, 0.5187010688415302, 0.4413229019707581, 0.3642026077250811, 0.2872945188119721, 0.2105546891305471, 0.1339461934036071, 0.05752793175097446 },
                { 0.11, 232.2162524384619, 215.7969393963619, 202.7030409321226, 191.397711549136, 181.2866519852657, 172.0604207307601, 163.5317009218791, 155.576063633773, 148.1054405720773, 141.0545509713773, 134.3732720695177, 128.0220382826102, 121.9689108315041, 116.1876276645253, 110.656258197417, 105.356246948308, 100.2717160610699, 95.38894534644033, 90.69597719402554, 86.18231130027293, 81.83866527741461, 77.65678443464872, 73.62928883524543, 69.74954900887522, 66.0115839721048, 62.40997681630143, 58.93980427533277, 55.59657752545848, 52.3761920899415, 49.27488518437013, 46.28919918899815, 43.41595020198845, 40.65220083382199, 37.99523656375259, 35.44254510525165, 32.99179832711543, 30.64083635638588, 28.38765355302058, 26.23038609777186, 24.16730097661579, 22.19678617931318, 20.31734195783706, 18.52757301366996, 16.82618150230464, 15.21196075941869, 13.68378966672644, 12.24062758691387, 10.88150980670946, 9.605543435342695, 8.41190371263693, 7.299830686976213, 6.268626228536939, 5.317651347615923, 4.446323791715681, 3.654115898330527, 2.940552683122748, 2.305210145273273, 1.747713772780544, 1.26773722878545, 0.8650011897091167, 0.5392722610651034, 0.2903616705876975, 0.1181218242669378, 0.02241584582606895, 19.35154106463813, 14.34198355580624, 12.06098980763912, 10.64138233650857, 9.630106600767101, 8.852707782336678, 8.22506540237696, 7.700675208959914, 7.251330028477834, 6.858729226452035, 6.510375523693677, 6.197383518048268, 5.913226459415846, 5.652979328440462, 5.412840747865736, 5.189819514926439, 4.981522453993296, 4.786006877980649, 4.601675526455473, 4.427200183101984, 4.261465115508268, 4.10352450287276, 3.952569919109812, 3.807905165755469, 3.668926558475897, 3.53510731582238, 3.405985072399795, 3.281151798989279, 3.160245596452524, 3.042943962516838, 2.928958226710235, 2.81802891947642, 2.709921894143024, 2.604425059986309, 2.501345614664984, 2.400507687290084, 2.301750321153593, 2.20492573895737, 2.109897844218787, 2.016540921084025, 1.924738501578589, 1.834382374761332, 1.745371716621387, 1.657612323094572, 1.571015931451726, 1.485499617661406, 1.400985259258511, 1.317399054841275, 1.234671092636599, 1.152734961669707, 1.071527399990294, 0.9909879751782293, 0.9110587930079389, 0.8316842307227538, 0.752810691899847, 0.6743863804497366, 0.5963610920819143, 0.518686023150645, 0.4413136011678289, 0.3641973566416527, 0.2872919236705703, 0.2105536537528967, 0.1339459162513727, 0.05752790377099955 },
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        };
    }
 
    std::vector<Real> ExponentialFittingHestonEngine::moneyness_;
 
    ExponentialFittingHestonEngine::ExponentialFittingHestonEngine(
        const ext::shared_ptr<HestonModel>& model,
        ControlVariate cv,
        Real scaling, Real alpha)
    : GenericModelEngine<HestonModel,
                         VanillaOption::arguments,
                         VanillaOption::results>(model),
      cv_(cv),
      scaling_(scaling),
      alpha_(alpha),
      analyticEngine_(ext::make_shared<AnalyticHestonEngine>(model, 1)) {
 
        if (moneyness_.empty()) {
            const Size n = sizeof(values4)/sizeof(values4[0]);
            moneyness_.reserve(n);
 
            for (const auto& i : values4)
                moneyness_.push_back(i[0]);
        }
    }
 
    void ExponentialFittingHestonEngine::calculate() const {
        QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
                   "not an European option");
 
        const Date maturityDate = arguments_.exercise->lastDate();
 
        const ext::shared_ptr<PlainVanillaPayoff> payoff =
            ext::dynamic_pointer_cast<PlainVanillaPayoff>(arguments_.payoff);
        QL_REQUIRE(payoff, "non plain vanilla payoff given");
 
        const Real strike = payoff->strike();
 
        const ext::shared_ptr<HestonProcess> process = model_->process();
 
        const Time t = process->time(maturityDate);
 
        const DiscountFactor rd
            = process->riskFreeRate()->discount(maturityDate);
        const DiscountFactor dd
            = process->dividendYield()->discount(maturityDate);
 
        const Real spot = process->s0()->value();
        QL_REQUIRE(spot > 0.0, "negative or null underlying given");
 
        const Real freq = std::log(spot) - std::log(rd/dd) - std::log(strike);
 
        const Real fwd = spot * dd / rd;
 
        const Real v0    = model_->v0();
        const Real kappa = model_->kappa();
        const Real theta = model_->theta();
        const Real sigma = model_->sigma();
        const Real rho   = model_->rho();
 
        QL_REQUIRE(cv_ != ControlVariate::Gatheral && cv_ != ControlVariate::BranchCorrection,
            "Gatheral and Branch-Correction are not supported as control-variate");
 
        const AnalyticHestonEngine::ComplexLogFormula analyticCV =
            (cv_ == ControlVariate::OptimalCV)
            ? AnalyticHestonEngine::optimalControlVariate(t, v0, kappa, theta, sigma, rho)
            : cv_;
 
        const AnalyticHestonEngine::AP_Helper helper(
            t, fwd, strike, analyticCV, analyticEngine_.get(), alpha_);
 
        const Real vAvg = (1-std::exp(-kappa*t))*(v0-theta)/(kappa*t) + theta;
 
        const Real scalingFactor = (scaling_ == Null<Real>())
            ? (analyticCV != AnalyticHestonEngine::AsymptoticChF)
                    ? std::max(0.25, std::min(1000.0, 0.25/std::sqrt(0.5*vAvg*t)))
                    : Real(1.0)
            : scaling_;
 
        Size n;
        Real u;
        if (std::fabs(freq) < 0.1) {
            n = 0;
            u = scalingFactor;
        }
        else {
            const Real lookup = std::fabs(scalingFactor*freq);
            n = std::min(Size(moneyness_.size() - 1),
                    Size(std::distance(moneyness_.begin(),
                        std::lower_bound(
                            moneyness_.begin(),
                            moneyness_.end(), lookup))));
 
            if (n > 0 && std::fabs(lookup - moneyness_[n])
                            > std::fabs(lookup - moneyness_[n-1])) {
                --n;
            }
 
            const Real omega = moneyness_[n];
            u = std::fabs(omega / freq);
        }
        const Size order = (sizeof(values4[0]) / sizeof(values4[0][0]) - 1) / 2;
 
        Real s = 0.0;
        for (Size i=0; i < order; ++i) {
            const Real x_i = values4[n][i+1];
            const Real w_i = values4[n][order + 1 +i];
 
            s += w_i*u*helper(u*x_i);
        }
 
        const Real h_cv = s * fwd/M_PI;
        const Real cvValue = helper.controlVariateValue();
 
        switch (payoff->optionType())
        {
          case Option::Call:
              results_.value = (cvValue + h_cv)*rd;
            break;
          case Option::Put:
              results_.value = (cvValue + h_cv - (fwd - strike))*rd;
            break;
          default:
            QL_FAIL("unknown option type");
        }
    }
}