mirror of
https://github.com/boostorg/math.git
synced 2026-01-19 04:22:09 +00:00
350 lines
30 KiB
C++
350 lines
30 KiB
C++
// Copyright Matthew Pulver 2018 - 2019.
|
||
// Distributed under the Boost Software License, Version 1.0.
|
||
// (See accompanying file LICENSE_1_0.txt or copy at
|
||
// https://www.boost.org/LICENSE_1_0.txt)
|
||
|
||
#include "test_autodiff.hpp"
|
||
|
||
BOOST_AUTO_TEST_SUITE(test_autodiff_4)
|
||
|
||
struct round_and_trunc_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
using std::round;
|
||
using std::trunc;
|
||
constexpr int m = 3;
|
||
constexpr float cx = 3.25;
|
||
auto x = make_fvar<T,m>(cx);
|
||
auto y = round(x);
|
||
BOOST_REQUIRE(y.derivative(0) == round(cx));
|
||
BOOST_REQUIRE(y.derivative(1) == 0.0);
|
||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||
y = trunc(x);
|
||
BOOST_REQUIRE(y.derivative(0) == trunc(cx));
|
||
BOOST_REQUIRE(y.derivative(1) == 0.0);
|
||
BOOST_REQUIRE(y.derivative(2) == 0.0);
|
||
BOOST_REQUIRE(y.derivative(3) == 0.0);
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(round_and_trunc)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, round_and_trunc_test());
|
||
boost::fusion::for_each(multiprecision_float_types, round_and_trunc_test());
|
||
}
|
||
|
||
struct iround_and_itrunc_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
using namespace boost::math;
|
||
constexpr int m = 3;
|
||
constexpr float cx = 3.25;
|
||
auto x = make_fvar<T,m>(cx);
|
||
int y = iround(x);
|
||
BOOST_REQUIRE(y == iround(cx));
|
||
y = itrunc(x);
|
||
BOOST_REQUIRE(y == itrunc(cx));
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(iround_and_itrunc)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, iround_and_itrunc_test());
|
||
boost::fusion::for_each(multiprecision_float_types, iround_and_itrunc_test());
|
||
}
|
||
|
||
struct lambert_w0_test_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
const T eps = 1000*std::numeric_limits<T>::epsilon(); // percent
|
||
constexpr int m = 10;
|
||
const T cx = 3;
|
||
// Mathematica: N[Table[D[ProductLog[x], {x, n}], {n, 0, 10}] /. x -> 3, 52]
|
||
const char* const answers[m+1] {
|
||
"1.049908894964039959988697070552897904589466943706341",
|
||
"0.1707244807388472968312949774415522047470762509741737",
|
||
"-0.04336545501146252734105411312976167858858970875797718",
|
||
"0.02321456264324789334313200360870492961288748451791104",
|
||
"-0.01909049778427783072663170526188353869136655225133878",
|
||
"0.02122935002563637629500975949987796094687564718834156",
|
||
"-0.02979093848448877259041971538394953658978044986784643",
|
||
"0.05051290266216717699803334605370337985567016837482099",
|
||
"-0.1004503154972645060971099914384090562800544486549660",
|
||
"0.2292464437392250211967939182075930820454464472006425",
|
||
"-0.5905839053125614593682763387470654123192290838719517"};
|
||
auto x = make_fvar<T,m>(cx);
|
||
auto y = lambert_w0(x);
|
||
for (int i=0 ; i<=m ; ++i)
|
||
{
|
||
const T answer = boost::lexical_cast<T>(answers[i]);
|
||
BOOST_REQUIRE_CLOSE(y.derivative(i), answer, eps);
|
||
}
|
||
//const T cx0 = -1 / boost::math::constants::e<T>();
|
||
//auto edge = lambert_w0(make_fvar<T,m>(cx0));
|
||
//std::cout << "edge = " << edge << std::endl;
|
||
//edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
|
||
//edge = depth(1)(-1,inf,-inf,inf,-inf,inf,-inf,inf,-inf,inf,-inf)
|
||
//edge = depth(1)(-1,3.68935e+19,-9.23687e+57,4.62519e+96,-2.89497e+135,2.02945e+174,-1.52431e+213,1.19943e+252,-9.75959e+290,8.14489e+329,-6.93329e+368)
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(lambert_w0_test)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, lambert_w0_test_test());
|
||
boost::fusion::for_each(multiprecision_float_types, lambert_w0_test_test());
|
||
}
|
||
|
||
struct lround_llround_truncl_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
using std::lround;
|
||
using std::llround;
|
||
//using std::truncl; // truncl not supported by boost::multiprecision types.
|
||
constexpr int m = 3;
|
||
const T cx = 3.25;
|
||
auto x = make_fvar<T,m>(cx);
|
||
long yl = lround(x);
|
||
BOOST_REQUIRE(yl == lround(cx));
|
||
long long yll = llround(x);
|
||
BOOST_REQUIRE(yll == llround(cx));
|
||
//long double yld = truncl(x);
|
||
//BOOST_REQUIRE(yld == truncl(cx));
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(lround_llround_truncl)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, lround_llround_truncl_test());
|
||
boost::fusion::for_each(multiprecision_float_types, lround_llround_truncl_test());
|
||
}
|
||
|
||
struct mixed_partials_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
const T eps = 20000e2*std::numeric_limits<T>::epsilon(); // percent
|
||
// Derivatives calculated from symbolic differentiation by Mathematica for comparison.
|
||
const char* const answers[] = {"19878.40628980434922342465374997798674242532797789489","20731.74838274939517275508122761443159515217855975002","14667.60767623939014840117674691707821648144188283774","1840.559936449813118734351750381849294157477519107602","-9219.318005237072129605008516120710807803827373819700","-7272.300634012811783845589472196110804386170683300081","-2135.296370062283924160196772166043360841114107521292","3095.081027251846799545897828297310835169325417217168","4249.026762908615627428402369471953790564918480025345","2063.989061062734416582172072883742097425754355167541","-885.5284114876496084068555333811894392182458751895290","-1962.133420441743158021558423645064067562765178375508","-1846.899830787084518564013512948598850243350915531775","-160.9590127603295755195950112199107484483554942817846","1091.039412341633994110997652976585409621806446647794","452.4395574345229946707651998323417632800605985181691","666.4013922727704990031159406121675703174518834914461","-415.6464114333629107803309520898363153301435468382605","-625.1464179039986361267627631122900331946746137220517","369.9491669772617110087494756677334192842413470837587","-24330.89613849389343130420303653062335840497802221681","-18810.41605175626752065686192937776868736029049989926","-4890.406122702359099863022925593448420259414896197252","8833.005054768976417065486877649473665597894570245307","8484.350739681613747819854384228795938450532463850094","3097.204151240398893507362023543393154680147349049848","-3255.045136783440612110181337652522080890693968833148","-4342.778553332193097878812792875447018366988006584840","-2407.987237906523486012534085031032446996713414362131","861.1173916470300084261504495377425043024739914571554","2436.743725763308619092960749816106318692933687303014","-19.24649610733827783846392798978023489104363382129689","187.7855148870511714395275130898958731897480766620821","-1259.466063335212195169531010871023748854744563232277","-709.6860523972158261343923419671629587637051060458295","1423.000558608604536932163648918899935569543711292466","484.9208133389233959103861107714757012185008046446372","763.9746885074453180462508029718247316712990115789154","-327.4162918228055568224139277603073169658358026440432","-1122.337707248494521123614369562896901904418640152220","23973.06007192346989337502250398494874845408708506720","8840.543151778796869949670401421984604862699128880003","-9082.571033221549378277312292526023838132689941236879","-12270.27378289258717737657881957466807305650429436397","-4320.434071420599854743576892819691675331049612545664","3281.351967707280898543984556670710235259118405463698","5880.336263083418767219493592767818708317492833223933","-1288.482785219706549809211085113790275109642879331959","-803.9713537626580526627976840414468844364935388365037","-2986.387245331698390346145949708414455858834967096376","-586.7316859822658306283656047992829723003491823675739","3929.073189280739356198769778905960586080418779863615","1453.728280983826630077825553258703050898056317382483","1037.878071685953829685046234106860743366780050925514","-1482.745805277401336553926171580259185140208053329753","-1877.134792933828810602377451370316364621357891989679","-931.7138710369298207131581126980851620513905805624544","254.6565590420322632851077818917210811815919344882311","1391.248064745611663849820246430123214796614030838600","-431.4820563154137955051720207563800896297257103310465","16975.34005365179555009050533000516107937041784876054","19662.60356303341709846238790020024593550984564081068","15765.85130704020004301064240357947656083104783442825","3972.155036195937013764185795634749937308876197976202","-8681.748539789720512499473840242996096730194203989543","-7703.183042460387656743498394861780784700076575106134","-3049.708696569518774040135942468704911634779352213044","2971.469685992270876159892302788930292108129670398058","4370.196499857550025657084783894747734031876677385611","2524.632473357435670756946837415389227139966527203701","-656.6080000236679071742450437463693211275208125750923","-2423.452917325258132591368397957959217829861665178601","-2074.987664204263204162199830716851483704870169031179","-381.2253794988132984501358802316138392247470857452486","1219.507245791997351017860252538035146744682380716428","805.3802239840836877339667281819652171888443003165988","838.4004190058912380470543219448821914235443115661655","-390.6125197108983831575656956558201636111305409512701","-828.2085489298235758253219930356006757081473789845849","293.8999854454994790079171865082094494146506490533363","-22965.85985843951977785883587223006628792405076928067","-20026.69101529929621743747554537576887048069629325374","-7316.092745063355996548975300169565482331369744607021","8632.466133972614659252310985982644793465043032940318","8987.046882870452266200748127338744248816756004290490","4199.925399536137541108783465785304128965582292174062","-2958.429850896062893179851696175634522187021390095560","-5665.563891218624062243686482808197054863235184904433","-2945.404552250341615883104643651287431663294281737652","555.6566272478262524735403145861484390537770707372992","2936.796403550079139218970638242013974322758744804216","651.5191650747110008135060635556227666232180743487328","444.7629427486155148584918602702161457622049333694568","-1390.989671799095801316658971275073184600067187023729","-1142.861468946763860859271224968631944511098747155437","1541.978723117340843491920690654997335632919116206279","455.7146063293814470171599782651235242129856311098151","998.7943503940357037260061331795191352937661538946216","-204.8485581981121295383497187536442450324011940647949","-1560.354115460478786113711476250386112014306509906244","25278.29450605247223516529112562423587288781657290275","11873.22337179046469888005044109378787446671408425048","-8242.187303368878103323785658604027555126374435611949","-15939.98056417465751946455567789306872745912255628512","-5648.833539698031486810309720694416837861242341227280","2751.513926122717118525029734574022921057261239749143","7349.432002479077129245930487320138527887196396579062","194.9972545980371127390142753318206783334452047502143","-402.8156857682688265622049800462325595907987257153782","-3518.871908683063371167722463713374376552181380727802","-1494.304793474682619087166400375396721307777439607909","4640.927509426080087451995953783429589632369803588940","1585.757705203227141964561144798400703219894640413562","1565.169992404407137888592924342582799362959736185298","-1513.259809733540018859089666188672238777297615451800","-2974.437872674680092826212901753475972242208819679978","-1203.236292653823441598437153564865951527142648802876","72.52425949879153384040698301599842998884036742649047","1871.625274253419949517250818647194858608124560073483","-2.489984337379681666361341362948045621969765070197429","14462.74423518633102580192225823524237502860825596609","18367.74740916432711689913219912502810575714860430297","16565.76324499673961400925630526921000337443450249297","6054.315252651102952034254100792777051580892954459740","-8084.981271982030146065497115893934803061545998433631","-7988.314359128201297240919364015959817416101519999194","-3989.319346941492698525859335371231602272119870228687","2616.721186534649016680934493970036169897788778926434","4420.859270970486562095630193355634655337290952862363","2973.033519764547909146474824627687039969488363657908","-324.1453016982713707989332262410969595194473127209825","-2843.242039958969221918101261762794653424879358390111","-2281.461806143289517702658392470195144560150025832652","-642.9353229582055924928927665183236308235598082837497","1299.287274176955358490409470855361289523321919337117","1238.597083372069762230817383681570828675426312803376","1021.334042770848165110529668635291528449691525937968","-329.0529345069271079573348500899329811170455711610811","-1046.254301544052075124857362060924818517694048905299","134.7343039554480655186788228552325941588620079791654","-21431.41643507661192392650726158493697457993678274754","-20856.88281479015784660571401663659059349708627445067","-9829.261970591930907585958999196966814861251125275804","7806.858647077811827981774785577363365546600234846335","9319.700085649568180114405924685286453652118439999060","5319.898768025758256383579171601100187435481641933401","-2387.954826466841736373447020403170264502066930376059","-6958.298525165359760665355886221309296550746152109847","-3468.539106391972560670887295398968213297736424267559","130.4167253342709401698825285623058661085645012029873","3371.139930235175987370940343096776588915600470241960","1569.232678004908105313880673484968847566948896728142","750.0912101179065245750415609380442359608197763310413","-1462.257209626597452197736652121394535208578921869658","-1661.577809630240615684355192771059515041884351493459","1509.628528603869133250456671040505284128185908768108","383.8950902580816259502239917715884779698864996879279","1248.051096343638013308778159911906703363730187986273","17.18569564265260274901760034571610990094333217519021","-2038.024598002604853054532645991188063394308018947374","26118.98132017823514803387529120810044029492871875474","14943.61943482227903328457116850255971625430735856355","-6650.686262276131072415580833374348889422387492668440","-19519.81529547404067945704333355155941895199228108631","-6983.190236500848647457042860591724089812405118922223","1899.297502873688983038424995203515277346497811783168","8715.003652642963488202943622358986745434720576722170","2368.150690681864301926962120618658083737878227231428","136.8920793093482831910443246272238406481527839521448","-3954.732706163417141961077488373290331419627965482785","-2673.556440231186786375595871506657802723673830409989","5078.483935249043594670125721926702845818403229980691","1643.459143721204817182772630730123271413273760820347","2182.216979506380293664703833586468523416961563720645","-1345.838830963620501537777318021157952722412472356094","-4309.285350629108413525304135326225818270616857298235","-1488.050869922417817689426519211523527088509094291312","-228.0584943070343720919835603886532454450555855354340","2373.398940425709177876367020236623713151456855728138","773.8481328103928058186643458500631723389600248582833","12294.40387737855548614823173849184004455244840062464","16977.34966571858301862913845572077593071467784570724","17057.17475622503175013658695220988017704387344177727","8121.189758511830935868344768490586007624092305459885","-7458.443541406284389918808653948439156033975014107187","-8134.131160882738058651976911725365291142418949378248","-4912.881158613784419581465435995807691111897279859302","2030.653136098933717888434825960516061206391833398177","4407.490527709412730881592594976776779312299897714205","3392.434568825892752350943548729559313328141534290860","104.0372355841506198680609232049783930050635078746762","-3180.817620484463214391157460812371170723810181051096","-2460.523987075069437321629265332968914260047631079537","-938.2209314069133432825590545267820890922150850657831","1315.246905571876456706320919211807375254975062430487","1735.862392405992188189147617586418269768276241147998","1209.759657223166954850207025399731503326968841680649","-227.3320054566642297128407910803774238020746116287390","-1266.126209991929259396966729664100401813091860201682","-123.0794572338149156803989321165094334755661021559442","-19806.90794333834685506732819834090525250045748665845","-21314.81635440575229337844631555492486744407550254908","-12317.58384430130805020250005527399703840208659666608","6349.418659888281474363154227419204673663621492760982","9489.819687696527735093973063679592839666155440941289","6409.538948456309994399374417972222747225748405617373","-1550.281799013125267606263057621300789555474258987989","-8109.711199785217512061886243157800006692908759687186","-3957.840330296874877742767473517819198882831790006004","-404.0796555836667858753163727999380679499192203780272","3693.614351301181980145006883746936633676934626580499","2716.146658322790064799415509615557123789406209068981","1094.591086641398900496318896947912437274250932576747","-1456.269645549946420883827817869876763706452982413420","-2244.380608735636962338392373719455877272151458411079","1268.593891556261871090883000459505759446497182073132","265.2206730327749346649809229271069944357537135668622","1496.091578778639488439197917198148587432113387871024","354.6137351047722781932932090799444060236757625488818","-2508.477110048684129181005769771219369377836598443263","26517.86140875157324686379805134248778305979287686214","17922.98387741915144079932445041215068937644694653527","-4328.259142127668040873054918170572859673703425721293","-22704.70245940080949074466622805971940616027152354999","-8268.613747173738971390434576274225941735552759965376","740.4056074392611464740778308961471299437619012164253","9848.900182836035080973766381422758538530595451048714","5213.598341476210337710365441072904970861063876340963","801.2462923723508233330997243930793458484750729415321","-4241.870133920767845856621968904769727964770527614244","-4092.241355868550570635569815488217469506874233892269","5074.435909206083943809967780457349942315503368249477","1607.765329254820915989772546102530187884674235100928","2861.155651116567526208762405651011317435252198548496","-918.9310546317296090214320737728927500362088478158839","-5803.211323646092019259074499814222806376618363553826","-1767.541897994477314401145980308432268207111761980100","-663.0646207520075726320417301262932382663072876188661","2837.903194613938414496183429129769829434890424213252","1976.319600747797717779881875290418720908121189218755"};
|
||
constexpr int Nw=3;
|
||
constexpr int Nx=2;
|
||
constexpr int Ny=4;
|
||
constexpr int Nz=3;
|
||
const auto w = make_fvar<T,Nw>(11);
|
||
const auto x = make_fvar<T,0,Nx>(12);
|
||
const auto y = make_fvar<T,0,0,Ny>(13);
|
||
const auto z = make_fvar<T,0,0,0,Nz>(14);
|
||
const auto v = mixed_partials_f(w,x,y,z); // auto = autodiff_fvar<double,Nw,Nx,Ny,Nz>
|
||
int ia=0;
|
||
for (int iw=0 ; iw<=Nw ; ++iw)
|
||
for (int ix=0 ; ix<=Nx ; ++ix)
|
||
for (int iy=0 ; iy<=Ny ; ++iy)
|
||
for (int iz=0 ; iz<=Nz ; ++iz)
|
||
{
|
||
const T answer = boost::lexical_cast<T>(answers[ia++]);
|
||
BOOST_REQUIRE_CLOSE(v.derivative(iw,ix,iy,iz), answer, eps);
|
||
}
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(mixed_partials)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, mixed_partials_test());
|
||
}
|
||
|
||
struct multiprecision_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
const T eps = 600*std::numeric_limits<T>::epsilon(); // percent
|
||
constexpr int Nw=3;
|
||
constexpr int Nx=2;
|
||
constexpr int Ny=4;
|
||
constexpr int Nz=3;
|
||
const auto w = make_fvar<T,Nw>(11);
|
||
const auto x = make_fvar<T,0,Nx>(12);
|
||
const auto y = make_fvar<T,0,0,Ny>(13);
|
||
const auto z = make_fvar<T,0,0,0,Nz>(14);
|
||
const auto v = mixed_partials_f(w,x,y,z); // auto = autodiff_fvar<T,Nw,Nx,Ny,Nz>
|
||
// Calculated from Mathematica symbolic differentiation.
|
||
const T answer = boost::lexical_cast<T>("1976.3196007477977177798818752904187209081211892187"
|
||
"5499076582535951111845769110560421820940516423255314");
|
||
// BOOST_REQUIRE_CLOSE(v.derivative(Nw,Nx,Ny,Nz), answer, eps); // Doesn't work for cpp_dec_float
|
||
using std::fabs;
|
||
const double relative_error = static_cast<double>(fabs(v.derivative(Nw,Nx,Ny,Nz)/answer-1));
|
||
BOOST_REQUIRE(100*relative_error < eps);
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(multiprecision)
|
||
{
|
||
//multiprecision_test()(boost::multiprecision::cpp_bin_float_50());
|
||
boost::fusion::for_each(bin_float_types, mixed_partials_test());
|
||
}
|
||
|
||
struct black_scholes_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
//const T eps = 2725*std::numeric_limits<T>::epsilon(); // percent
|
||
const T eps = 2600e2*std::numeric_limits<T>::epsilon(); // percent - requied by OSX
|
||
const double K = 100.0; // Strike price
|
||
const auto S = make_fvar<T,3>(105); // Stock price.
|
||
const auto sigma = make_fvar<T,0,3>(5); // Volatility.
|
||
const auto tau = make_fvar<T,0,0,1>(T(30.0)/365); // Time to expiration in years. (30 days).
|
||
const auto r = make_fvar<T,0,0,0,1>(T(1.25)/100); // Interest rate.
|
||
const auto call_price = black_scholes_option_price(call, K, S, sigma, tau, r);
|
||
const auto put_price = black_scholes_option_price(put, K, S, sigma, tau, r);
|
||
// Compare automatically calculated greeks by autodiff with formulas for greeks.
|
||
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
|
||
const T d1 = static_cast<T>((log(S/K) + (r+sigma*sigma/2)*tau) / (sigma*sqrt(tau)));
|
||
const T d2 = static_cast<T>((log(S/K) + (r-sigma*sigma/2)*tau) / (sigma*sqrt(tau)));
|
||
const T Phi_pd1 = Phi(d1);
|
||
// intermediate cpp_dec_float calculation can't go to template function as it can't be implicitly cast back to T.
|
||
const T Phi_nd1 = Phi(static_cast<T>(-d1));
|
||
const T Phi_pd2 = Phi(d2);
|
||
const T Phi_nd2 = Phi(static_cast<T>(-d2));
|
||
//const T formula_call_delta = +Phi(+d1);
|
||
const T formula_call_delta = +Phi_pd1;
|
||
//const T formula_put_delta = -Phi(-d1);
|
||
const T formula_put_delta = -Phi_nd1;
|
||
const T formula_vega = static_cast<T>(S*phi(d1)*sqrt(tau));
|
||
//const T formula_call_theta = static_cast<T>(-S*phi(d1)*sigma/(2*sqrt(tau))-r*K*exp(-r*tau)*Phi(+d2));
|
||
const T formula_call_theta = static_cast<T>(-S*phi(d1)*sigma/(2*sqrt(tau))-r*K*exp(-r*tau)*Phi_pd2);
|
||
//const T formula_put_theta = static_cast<T>(-S*phi(d1)*sigma/(2*sqrt(tau))+r*K*exp(-r*tau)*Phi(-d2));
|
||
const T formula_put_theta = static_cast<T>(-S*phi(d1)*sigma/(2*sqrt(tau))+r*K*exp(-r*tau)*Phi_nd2);
|
||
//const T formula_call_rho = static_cast<T>(+K*tau*exp(-r*tau)*Phi(+d2));
|
||
const T formula_call_rho = static_cast<T>(+K*tau*exp(-r*tau)*Phi_pd2);
|
||
//const T formula_put_rho = static_cast<T>(-K*tau*exp(-r*tau)*Phi(-d2));
|
||
const T formula_put_rho = static_cast<T>(-K*tau*exp(-r*tau)*Phi_nd2);
|
||
const T formula_gamma = static_cast<T>(phi(d1)/(S*sigma*sqrt(tau)));
|
||
const T formula_vanna = static_cast<T>(-phi(d1)*d2/sigma);
|
||
const T formula_charm = static_cast<T>(phi(d1)*(d2*sigma*sqrt(tau)-2*r*tau)/(2*tau*sigma*sqrt(tau)));
|
||
const T formula_vomma = static_cast<T>(S*phi(d1)*sqrt(tau)*d1*d2/sigma);
|
||
const T formula_veta = static_cast<T>(-S*phi(d1)*sqrt(tau)*(r*d1/(sigma*sqrt(tau))-(1+d1*d2)/(2*tau)));
|
||
const T formula_speed = static_cast<T>(-phi(d1)*(d1/(sigma*sqrt(tau))+1)/(S*S*sigma*sqrt(tau)));
|
||
const T formula_zomma = static_cast<T>(phi(d1)*(d1*d2-1)/(S*sigma*sigma*sqrt(tau)));
|
||
const T formula_color =
|
||
static_cast<T>(-phi(d1)/(2*S*tau*sigma*sqrt(tau))*(1+(2*r*tau-d2*sigma*sqrt(tau))*d1/(sigma*sqrt(tau))));
|
||
const T formula_ultima = -formula_vega*static_cast<T>((d1*d2*(1-d1*d2)+d1*d1+d2*d2)/(sigma*sigma));
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(1,0,0,0), formula_call_delta, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(0,1,0,0), formula_vega, eps);
|
||
BOOST_REQUIRE_CLOSE(-call_price.derivative(0,0,1,0), formula_call_theta, eps); // minus sign from tau = T-time
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(0,0,0,1), formula_call_rho, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(1,0,0,0), formula_put_delta, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(0,1,0,0), formula_vega, eps);
|
||
BOOST_REQUIRE_CLOSE( -put_price.derivative(0,0,1,0), formula_put_theta, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(0,0,0,1), formula_put_rho, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(2,0,0,0), formula_gamma, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(2,0,0,0), formula_gamma, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(1,1,0,0), formula_vanna, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(1,1,0,0), formula_vanna, eps);
|
||
BOOST_REQUIRE_CLOSE(-call_price.derivative(1,0,1,0), formula_charm, eps);
|
||
BOOST_REQUIRE_CLOSE( -put_price.derivative(1,0,1,0), formula_charm, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(0,2,0,0), formula_vomma, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(0,2,0,0), formula_vomma, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(0,1,1,0), formula_veta, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(0,1,1,0), formula_veta, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(3,0,0,0), formula_speed, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(3,0,0,0), formula_speed, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(2,1,0,0), formula_zomma, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(2,1,0,0), formula_zomma, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(2,0,1,0), formula_color, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(2,0,1,0), formula_color, eps);
|
||
BOOST_REQUIRE_CLOSE( call_price.derivative(0,3,0,0), formula_ultima, eps);
|
||
BOOST_REQUIRE_CLOSE( put_price.derivative(0,3,0,0), formula_ultima, eps);
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(black_scholes)
|
||
{
|
||
boost::fusion::for_each(bin_float_types, black_scholes_test());
|
||
}
|
||
|
||
/*
|
||
// Compilation tests for boost special functions.
|
||
struct boost_special_functions_test
|
||
{
|
||
template<typename T>
|
||
void operator()(const T&) const
|
||
{
|
||
using namespace boost;
|
||
constexpr int m = 3;
|
||
BOOST_REQUIRE(math::acosh(make_fvar<T,m>(1.5)) == math::acosh(static_cast<T>(1.5)));
|
||
// Policy parameter prevents proper ADL for autodiff_fvar objects. E.g. iround(v,pol) instead of iround(v).
|
||
// In cyl_bessel_j_imp() call is made to iround(v, pol) with v of type autodiff_fvar. It it were just iround(v)
|
||
// then autodiff's iround would properly be called via ADL.
|
||
//BOOST_REQUIRE(math::airy_ai(make_fvar<T,m>(1)) == math::airy_ai(static_cast<T>(1)));
|
||
//BOOST_REQUIRE(math::airy_bi(make_fvar<T,m>(1)) == math::airy_bi(static_cast<T>(1)));
|
||
//BOOST_REQUIRE(math::airy_ai_prime(make_fvar<T,m>(1)) == math::airy_ai_prime(static_cast<T>(1)));
|
||
//BOOST_REQUIRE(math::airy_bi_prime(make_fvar<T,m>(1)) == math::airy_bi_prime(static_cast<T>(1)));
|
||
BOOST_REQUIRE(math::asinh(make_fvar<T,m>(0.5)) == math::asinh(static_cast<T>(0.5)));
|
||
BOOST_REQUIRE(math::atanh(make_fvar<T,m>(0.5)) == math::atanh(static_cast<T>(0.5)));
|
||
// Policy parameter prevents ADL.
|
||
//BOOST_REQUIRE(math::cyl_bessel_j(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_j(0,static_cast<T>(0.5)));
|
||
//BOOST_REQUIRE(math::cyl_neumann(0,make_fvar<T,m>(0.5)) == math::cyl_neumann(0,static_cast<T>(0.5)));
|
||
//BOOST_REQUIRE(math::cyl_bessel_j_zero(make_fvar<T,m>(0.5),0) == math::cyl_bessel_j_zero(static_cast<T>(0.5),0));
|
||
//BOOST_REQUIRE(math::cyl_neumann_zero(make_fvar<T,m>(0.5),0) == math::cyl_neumann_zero(static_cast<T>(0.5),0));
|
||
// Required sinh() (added) but then has policy parameter ADL issue.
|
||
//BOOST_REQUIRE(math::cyl_bessel_i(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_i(0,static_cast<T>(0.5)));
|
||
BOOST_REQUIRE(math::cyl_bessel_k(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_k(0,static_cast<T>(0.5)));
|
||
// Policy parameter prevents ADL.
|
||
//BOOST_REQUIRE(math::sph_bessel(0,make_fvar<T,m>(0.5)) == math::sph_bessel(0,static_cast<T>(0.5)));
|
||
// Required fmod() but then has policy parameter ADL issue.
|
||
//BOOST_REQUIRE(math::sph_neumann(0,make_fvar<T,m>(0.5)) == math::sph_neumann(0,static_cast<T>(0.5)));
|
||
// Policy parameter prevents ADL.
|
||
//BOOST_REQUIRE(math::cyl_bessel_j_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_j_prime(0,static_cast<T>(0.5)));
|
||
//BOOST_REQUIRE(math::cyl_neumann_prime(0,make_fvar<T,m>(0.5)) == math::cyl_neumann_prime(0,static_cast<T>(0.5)));
|
||
//BOOST_REQUIRE(math::cyl_bessel_i_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_i_prime(0,static_cast<T>(0.5)));
|
||
BOOST_REQUIRE(math::cyl_bessel_k_prime(0,make_fvar<T,m>(0.5)) == math::cyl_bessel_k_prime(0,static_cast<T>(0.5)));
|
||
// Policy parameter prevents ADL.
|
||
//BOOST_REQUIRE(math::sph_bessel_prime(0,make_fvar<T,m>(0.5)) == math::sph_bessel_prime(0,static_cast<T>(0.5)));
|
||
//BOOST_REQUIRE(math::sph_neumann_prime(0,make_fvar<T,m>(0.5)) == math::sph_neumann_prime(0,static_cast<T>(0.5)));
|
||
// Per docs: "the functions can only be instantiated on types float, double and long double."
|
||
//BOOST_REQUIRE(math::cyl_hankel_1(0,make_fvar<T,m>(0.5)).real() == math::cyl_hankel_1(0,static_cast<T>(0.5)).real());
|
||
//BOOST_REQUIRE(math::cyl_hankel_2(0,make_fvar<T,m>(0.5)).real() == math::cyl_hankel_2(0,static_cast<T>(0.5)).real());
|
||
//BOOST_REQUIRE(math::sph_hankel_1(0,make_fvar<T,m>(0.5)).real() == math::sph_hankel_1(0,static_cast<T>(0.5)).real());
|
||
//BOOST_REQUIRE(math::sph_hankel_2(0,make_fvar<T,m>(0.5)).real() == math::sph_hankel_2(0,static_cast<T>(0.5)).real());
|
||
// Compiles, but compares 0.74868571757768376251 == 0.74868571757768354047 which is false.
|
||
// BOOST_REQUIRE(static_cast<T>(math::beta(make_fvar<T,m>(1.1),make_fvar<T,m>(1.2))) == static_cast<T>(math::beta(static_cast<T>(1.1),static_cast<T>(1.2))));
|
||
// Skipped other beta functions.
|
||
std::cout.precision(20);
|
||
// Compiles, but compares 0.7937005259840996807 == 0.79370052598409979172 which is false.
|
||
//BOOST_REQUIRE(math::cbrt(make_fvar<T,m>(0.5)) == math::cbrt(static_cast<T>(0.5)));
|
||
//Skipping other Basic Functions
|
||
BOOST_REQUIRE(math::chebyshev_next(make_fvar<T,m>(0.5),make_fvar<T,m>(0.5),make_fvar<T,m>(0.5)) ==
|
||
math::chebyshev_next(static_cast<T>(0.5),static_cast<T>(0.5),static_cast<T>(0.5)));
|
||
// Requires acosh() (added)
|
||
BOOST_REQUIRE(math::chebyshev_t(0,make_fvar<T,m>(0.5)) == math::chebyshev_t(0,static_cast<T>(0.5)));
|
||
BOOST_REQUIRE(math::chebyshev_u(0,make_fvar<T,m>(0.5)) == math::chebyshev_u(0,static_cast<T>(0.5)));
|
||
BOOST_REQUIRE(math::chebyshev_t_prime(0,make_fvar<T,m>(0.5)) == math::chebyshev_t_prime(0,static_cast<T>(0.5)));
|
||
{
|
||
std::array<double,4> c{14.2, -13.7, 82.3, 96};
|
||
// /usr/include/boost/math/special_functions/chebyshev.hpp:164:40: error: cannot convert ‘boost::math::differentiation::autodiff_v1::detail::fvar<double, 3>’ to ‘double’ in return
|
||
//BOOST_REQUIRE(math::chebyshev_clenshaw_recurrence(c.data(),c.size(),make_fvar<T,m>(0.5)) == math::chebyshev_clenshaw_recurrence(c.data(),c.size(),static_cast<T>(0.5)));
|
||
}
|
||
// TODO Continue alphabetically through <boost/math/special_functions.hpp>
|
||
}
|
||
};
|
||
|
||
BOOST_AUTO_TEST_CASE(boost_special_functions)
|
||
{
|
||
boost_special_functions_test()(static_cast<double>(0));
|
||
//boost::fusion::for_each(bin_float_types, boost_special_functions_test());
|
||
//boost::fusion::for_each(multiprecision_float_types, boost_special_functions_test());
|
||
}
|
||
*/
|
||
|
||
BOOST_AUTO_TEST_SUITE_END()
|