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|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 RiskMap srl
Copyright (C) 2004, 2005, 2006, 2007, 2008 StatPro Italia srl
Copyright (C) 2019 Wojciech Ślusarski
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.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/instruments/capfloor.hpp>
#include <ql/instruments/vanillaswap.hpp>
#include <ql/cashflows/cashflowvectors.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/zerospreadedtermstructure.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/pricingengines/capfloor/blackcapfloorengine.hpp>
#include <ql/pricingengines/capfloor/bacheliercapfloorengine.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/math/matrix.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/schedule.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/cashflows/cashflows.hpp>
#include <ql/cashflows/couponpricer.hpp>
#include <ql/quotes/simplequote.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(CapFloorTests)
struct CommonVars {
// common data
Date settlement;
std::vector<Real> nominals;
BusinessDayConvention convention;
Frequency frequency;
ext::shared_ptr<IborIndex> index;
Calendar calendar;
Natural fixingDays;
RelinkableHandle<YieldTermStructure> termStructure;
// setup
CommonVars()
: nominals(1,100) {
frequency = Semiannual;
index = ext::shared_ptr<IborIndex>(new Euribor6M(termStructure));
calendar = index->fixingCalendar();
convention = ModifiedFollowing;
Date today = Settings::instance().evaluationDate();
Natural settlementDays = 2;
fixingDays = 2;
settlement = calendar.advance(today,settlementDays,Days);
termStructure.linkTo(flatRate(settlement,0.05,
ActualActual(ActualActual::ISDA)));
}
// utilities
Leg makeLeg(const Date& startDate, Integer length) const {
Date endDate = calendar.advance(startDate,length*Years,convention);
Schedule schedule(startDate, endDate, Period(frequency), calendar,
convention, convention,
DateGeneration::Forward, false);
return IborLeg(schedule, index)
.withNotionals(nominals)
.withPaymentDayCounter(index->dayCounter())
.withPaymentAdjustment(convention)
.withFixingDays(fixingDays);
}
ext::shared_ptr<PricingEngine> makeEngine(Volatility volatility) const {
Handle<Quote> vol(ext::shared_ptr<Quote>(new SimpleQuote(volatility)));
return ext::shared_ptr<PricingEngine>(
new BlackCapFloorEngine(termStructure, vol));
}
ext::shared_ptr<PricingEngine> makeBachelierEngine(Volatility volatility) const {
Handle<Quote> vol(ext::shared_ptr<Quote>(new SimpleQuote(volatility)));
return ext::shared_ptr<PricingEngine>(
new BachelierCapFloorEngine(termStructure, vol));
}
ext::shared_ptr<CapFloor> makeCapFloor(CapFloor::Type type,
const Leg& leg,
Rate strike,
Volatility volatility,
bool isLogNormal = true) const {
ext::shared_ptr<CapFloor> result;
switch (type) {
case CapFloor::Cap:
result = ext::shared_ptr<CapFloor>(
new Cap(leg, std::vector<Rate>(1, strike)));
break;
case CapFloor::Floor:
result = ext::shared_ptr<CapFloor>(
new Floor(leg, std::vector<Rate>(1, strike)));
break;
default:
QL_FAIL("unknown cap/floor type");
}
if(isLogNormal){
result->setPricingEngine(makeEngine(volatility));
} else {
result->setPricingEngine(makeBachelierEngine(volatility));
}
return result;
}
};
bool checkAbsError(Real x1, Real x2, Real tolerance){
return std::fabs(x1 - x2) < tolerance;
}
std::string typeToString(CapFloor::Type type) {
switch (type) {
case CapFloor::Cap:
return "cap";
case CapFloor::Floor:
return "floor";
case CapFloor::Collar:
return "collar";
default:
QL_FAIL("unknown cap/floor type");
}
}
BOOST_AUTO_TEST_CASE(testVega) {
BOOST_TEST_MESSAGE("Testing cap/floor vega...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 30 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Rate strikes[] = { 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 };
CapFloor::Type types[] = { CapFloor::Cap, CapFloor::Floor};
Date startDate = vars.termStructure->referenceDate();
static const Real shift = 1e-8;
static const Real tolerance = 0.005;
for (int length : lengths) {
for (Real vol : vols) {
for (Real strike : strikes) {
for (auto& type : types) {
Leg leg = vars.makeLeg(startDate, length);
ext::shared_ptr<CapFloor> capFloor = vars.makeCapFloor(type, leg, strike, vol);
ext::shared_ptr<CapFloor> shiftedCapFloor2 =
vars.makeCapFloor(type, leg, strike, vol + shift);
ext::shared_ptr<CapFloor> shiftedCapFloor1 =
vars.makeCapFloor(type, leg, strike, vol - shift);
Real value1 = shiftedCapFloor1->NPV();
Real value2 = shiftedCapFloor2->NPV();
Real numericalVega = (value2 - value1) / (2*shift);
if (numericalVega>1.0e-4) {
Real analyticalVega = capFloor->result<Real>("vega");
Real discrepancy =
std::fabs(numericalVega - analyticalVega);
discrepancy /= numericalVega;
if (discrepancy > tolerance)
BOOST_FAIL("failed to compute cap/floor vega:"
<< "\n lengths: " << length * Years
<< "\n strike: " << io::rate(strike) <<
//"\n types: " << types[h] <<
std::fixed << std::setprecision(12) << "\n calculated: "
<< analyticalVega << "\n expected: " << numericalVega
<< "\n discrepancy: " << io::rate(discrepancy)
<< "\n tolerance: " << io::rate(tolerance));
}
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testStrikeDependency) {
BOOST_TEST_MESSAGE("Testing cap/floor dependency on strike...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Rate strikes[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Date startDate = vars.termStructure->referenceDate();
for (int& length : lengths) {
for (Real vol : vols) {
// store the results for different strikes...
std::vector<Real> cap_values, floor_values;
for (Real strike : strikes) {
Leg leg = vars.makeLeg(startDate, length);
ext::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap, leg, strike, vol);
cap_values.push_back(cap->NPV());
ext::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor, leg, strike, vol);
floor_values.push_back(floor->NPV());
}
// and check that they go the right way
auto it = std::adjacent_find(cap_values.begin(), cap_values.end(), std::less<>());
if (it != cap_values.end()) {
Size n = it - cap_values.begin();
BOOST_FAIL("NPV is increasing with the strike in a cap: \n"
<< std::setprecision(2) << " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " value: " << cap_values[n]
<< " at strike: " << io::rate(strikes[n]) << "\n"
<< " value: " << cap_values[n + 1]
<< " at strike: " << io::rate(strikes[n + 1]));
}
// same for floors
it = std::adjacent_find(floor_values.begin(), floor_values.end(), std::greater<>());
if (it != floor_values.end()) {
Size n = it - floor_values.begin();
BOOST_FAIL("NPV is decreasing with the strike in a floor: \n"
<< std::setprecision(2) << " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " value: " << floor_values[n]
<< " at strike: " << io::rate(strikes[n]) << "\n"
<< " value: " << floor_values[n + 1]
<< " at strike: " << io::rate(strikes[n + 1]));
}
}
}
}
BOOST_AUTO_TEST_CASE(testConsistency) {
BOOST_TEST_MESSAGE("Testing consistency between cap, floor and collar...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate cap_rates[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Rate floor_rates[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (int& length : lengths) {
for (Real& cap_rate : cap_rates) {
for (Real& floor_rate : floor_rates) {
for (Real vol : vols) {
Leg leg = vars.makeLeg(startDate, length);
ext::shared_ptr<CapFloor> cap =
vars.makeCapFloor(CapFloor::Cap, leg, cap_rate, vol);
ext::shared_ptr<CapFloor> floor =
vars.makeCapFloor(CapFloor::Floor, leg, floor_rate, vol);
Collar collar(leg, std::vector<Rate>(1, cap_rate),
std::vector<Rate>(1, floor_rate));
collar.setPricingEngine(vars.makeEngine(vol));
if (std::fabs((cap->NPV() - floor->NPV()) - collar.NPV()) > 1e-10) {
BOOST_FAIL("inconsistency between cap, floor and collar:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rate) << "\n"
<< " floor value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rate) << "\n"
<< " collar value: " << collar.NPV());
// test re-composition by optionlets, N.B. two per year
Real capletsNPV = 0.0;
std::vector<ext::shared_ptr<CapFloor> > caplets;
for (Integer m = 0; m < length * 2; m++) {
caplets.push_back(cap->optionlet(m));
caplets[m]->setPricingEngine(vars.makeEngine(vol));
capletsNPV += caplets[m]->NPV();
}
if (std::fabs(cap->NPV() - capletsNPV) > 1e-10) {
BOOST_FAIL("sum of caplet NPVs does not equal cap NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rate) << "\n"
<< " sum of caplets value: " << capletsNPV
<< " at strike (first): "
<< io::rate(caplets[0]->capRates()[0]) << "\n");
}
Real floorletsNPV = 0.0;
std::vector<ext::shared_ptr<CapFloor> > floorlets;
for (Integer m = 0; m < length * 2; m++) {
floorlets.push_back(floor->optionlet(m));
floorlets[m]->setPricingEngine(vars.makeEngine(vol));
floorletsNPV += floorlets[m]->NPV();
}
if (std::fabs(floor->NPV() - floorletsNPV) > 1e-10) {
BOOST_FAIL("sum of floorlet NPVs does not equal floor NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rate) << "\n"
<< " sum of floorlets value: " << floorletsNPV
<< " at strike (first): "
<< io::rate(floorlets[0]->floorRates()[0]) << "\n");
}
Real collarletsNPV = 0.0;
std::vector<ext::shared_ptr<CapFloor> > collarlets;
for (Integer m = 0; m < length * 2; m++) {
collarlets.push_back(collar.optionlet(m));
collarlets[m]->setPricingEngine(vars.makeEngine(vol));
collarletsNPV += collarlets[m]->NPV();
}
if (std::fabs(collar.NPV() - collarletsNPV) > 1e-10) {
BOOST_FAIL("sum of collarlet NPVs does not equal floor NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << collar.NPV()
<< " at strike floor: " << io::rate(floor_rate)
<< " at strike cap: " << io::rate(cap_rate) << "\n"
<< " sum of collarlets value: " << collarletsNPV
<< " at strike floor (first): "
<< io::rate(collarlets[0]->floorRates()[0])
<< " at strike cap (first): "
<< io::rate(collarlets[0]->capRates()[0]) << "\n");
}
}
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testParity) {
BOOST_TEST_MESSAGE("Testing cap/floor parity...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate strikes[] = { 0., 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (int& length : lengths) {
for (Real strike : strikes) {
for (Real vol : vols) {
Leg leg = vars.makeLeg(startDate, length);
ext::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap, leg, strike, vol);
ext::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor, leg, strike, vol);
Date maturity = vars.calendar.advance(startDate, length, Years, vars.convention);
Schedule schedule(startDate, maturity, Period(vars.frequency), vars.calendar,
vars.convention, vars.convention, DateGeneration::Forward, false);
VanillaSwap swap(Swap::Payer, vars.nominals[0], schedule, strike,
vars.index->dayCounter(), schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(
ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(vars.termStructure)));
if (std::fabs((cap->NPV() - floor->NPV()) - swap.NPV()) > 1.0e-10) {
BOOST_FAIL("put/call parity violated:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " strike: " << io::rate(strike) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV());
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testATMRate) {
BOOST_TEST_MESSAGE("Testing cap/floor ATM rate...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate strikes[] = { 0., 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (int& length : lengths) {
Leg leg = vars.makeLeg(startDate, length);
Date maturity = vars.calendar.advance(startDate, length, Years, vars.convention);
Schedule schedule(startDate,maturity,
Period(vars.frequency),vars.calendar,
vars.convention,vars.convention,
DateGeneration::Forward,false);
for (Real strike : strikes) {
for (Real vol : vols) {
ext::shared_ptr<CapFloor> cap = vars.makeCapFloor(CapFloor::Cap, leg, strike, vol);
ext::shared_ptr<CapFloor> floor =
vars.makeCapFloor(CapFloor::Floor, leg, strike, vol);
Rate capATMRate = cap->atmRate(**vars.termStructure);
Rate floorATMRate = floor->atmRate(**vars.termStructure);
if (!checkAbsError(floorATMRate, capATMRate, 1.0e-10))
BOOST_FAIL("Cap ATM Rate and floor ATM Rate should be equal :\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " strike: " << io::rate(strike) << "\n"
<< " cap ATM rate: " << capATMRate << "\n"
<< " floor ATM rate:" << floorATMRate << "\n"
<< " relative Error:"
<< relativeError(capATMRate, floorATMRate, capATMRate) * 100 << "%");
VanillaSwap swap(Swap::Payer, vars.nominals[0],
schedule, floorATMRate,
vars.index->dayCounter(),
schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(ext::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(vars.termStructure)));
Real swapNPV = swap.NPV();
if (!checkAbsError(swapNPV, 0, 1.0e-10))
BOOST_FAIL("the NPV of a Swap struck at ATM rate "
"should be equal to 0:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " ATM rate: " << io::rate(floorATMRate) << "\n"
<< " swap NPV: " << swapNPV);
}
}
}
}
BOOST_AUTO_TEST_CASE(testImpliedVolatility) {
BOOST_TEST_MESSAGE("Testing implied term volatility for cap and floor...");
CommonVars vars;
Size maxEvaluations = 100;
Real tolerance = 1.0e-8;
CapFloor::Type types[] = { CapFloor::Cap, CapFloor::Floor };
Rate strikes[] = { 0.02, 0.03, 0.04 };
Integer lengths[] = { 1, 5, 10 };
// test data
Rate rRates[] = { 0.02, 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.20, 0.30, 0.70, 0.90 };
for (int& length : lengths) {
Leg leg = vars.makeLeg(vars.settlement, length);
for (auto& type : types) {
for (Real strike : strikes) {
ext::shared_ptr<CapFloor> capfloor = vars.makeCapFloor(type, leg, strike, 0.0);
for (Real r : rRates) {
for (Real v : vols) {
vars.termStructure.linkTo(flatRate(vars.settlement, r, Actual360()));
capfloor->setPricingEngine(vars.makeEngine(v));
Real value = capfloor->NPV();
Volatility implVol = 0.0;
try {
implVol =
capfloor->impliedVolatility(value,
vars.termStructure,
0.10,
tolerance,
maxEvaluations,
10.0e-7, 4.0,
ShiftedLognormal, 0.0);
} catch (std::exception& e) {
// couldn't bracket?
capfloor->setPricingEngine(vars.makeEngine(0.0));
Real value2 = capfloor->NPV();
if (std::fabs(value-value2) < tolerance) {
// ok, just skip:
continue;
}
// otherwise, report error
BOOST_ERROR("implied vol failure: "
<< typeToString(type) << "\n strike: "
<< io::rate(strike) << "\n risk-free: " << io::rate(r)
<< "\n length: " << length << "Y"
<< "\n volatility: " << io::volatility(v)
<< "\n price: " << value << "\n"
<< e.what());
}
if (std::fabs(implVol-v) > tolerance) {
// the difference might not matter
capfloor->setPricingEngine(
vars.makeEngine(implVol));
Real value2 = capfloor->NPV();
if (std::fabs(value-value2) > tolerance) {
BOOST_FAIL("implied vol failure: "
<< typeToString(type)
<< "\n strike: " << io::rate(strike)
<< "\n risk-free: " << io::rate(r)
<< "\n length: " << length << "Y"
<< "\n volatility: " << io::volatility(v)
<< "\n price: " << value
<< "\n implied vol: " << io::volatility(implVol)
<< "\n implied price: " << value2);
}
}
}
}
}
}
}
}
BOOST_AUTO_TEST_CASE(testCachedValue) {
BOOST_TEST_MESSAGE("Testing Black cap/floor price against cached values...");
CommonVars vars;
Date cachedToday(14,March,2002),
cachedSettlement(18,March,2002);
Settings::instance().evaluationDate() = cachedToday;
vars.termStructure.linkTo(flatRate(cachedSettlement, 0.05, Actual360()));
Date startDate = vars.termStructure->referenceDate();
Leg leg = vars.makeLeg(startDate,20);
ext::shared_ptr<Instrument> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.07,0.20);
ext::shared_ptr<Instrument> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.03,0.20);
Real cachedCapNPV, cachedFloorNPV ;
if (!IborCoupon::Settings::instance().usingAtParCoupons()) {
// index fixing price
cachedCapNPV = 6.87630307745,
cachedFloorNPV = 2.65796764715;
} else {
// par coupon price
cachedCapNPV = 6.87570026732;
cachedFloorNPV = 2.65812927959;
}
// test Black cap price against cached value
if (std::fabs(cap->NPV()-cachedCapNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached cap value:\n"
<< std::setprecision(12)
<< " calculated: " << cap->NPV() << "\n"
<< " expected: " << cachedCapNPV);
// test Black floor price against cached value
if (std::fabs(floor->NPV()-cachedFloorNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached floor value:\n"
<< std::setprecision(12)
<< " calculated: " << floor->NPV() << "\n"
<< " expected: " << cachedFloorNPV);
}
BOOST_AUTO_TEST_CASE(testCachedValueFromOptionLets) {
BOOST_TEST_MESSAGE("Testing Black cap/floor price as a sum of optionlets prices against cached values...");
CommonVars vars;
Date cachedToday(14,March,2002),
cachedSettlement(18,March,2002);
Settings::instance().evaluationDate() = cachedToday;
ext::shared_ptr<YieldTermStructure> baseCurve = flatRate(cachedSettlement,
0.05, Actual360());
vars.termStructure.linkTo(baseCurve);
Date startDate = vars.termStructure->referenceDate();
Leg leg = vars.makeLeg(startDate,20);
ext::shared_ptr<Instrument> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.07,0.20);
ext::shared_ptr<Instrument> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.03,0.20);
Real calculatedCapletsNPV = 0.0,
calculatedFloorletsNPV = 0.0;
Real cachedCapNPV, cachedFloorNPV;
if (IborCoupon::Settings::instance().usingAtParCoupons()) {
cachedCapNPV = 6.87570026732;
cachedFloorNPV = 2.65812927959;
} else {
cachedCapNPV = 6.87630307745;
cachedFloorNPV = 2.65796764715;
}
// test Black floor price against cached value
std::vector<Real> capletPrices;
std::vector<Real> floorletPrices;
capletPrices = cap->result<std::vector<Real> >("optionletsPrice");
floorletPrices = floor->result<std::vector<Real> >("optionletsPrice");
if (capletPrices.size() != 40)
BOOST_ERROR(
"failed to produce prices for all caplets:\n"
<< " calculated: " << capletPrices.size() << " caplet prices\n"
<< " expected: " << 40);
for (Real capletPrice : capletPrices) {
calculatedCapletsNPV += capletPrice;
}
for (Real floorletPrice : floorletPrices) {
calculatedFloorletsNPV += floorletPrice;
}
if (std::fabs(calculatedCapletsNPV-cachedCapNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached cap value from its caplets' values:\n"
<< std::setprecision(12)
<< " calculated: " << calculatedCapletsNPV << "\n"
<< " expected: " << cachedCapNPV);
// test Black floor price against cached value
if (std::fabs(calculatedFloorletsNPV-cachedFloorNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached floor value from its floorlets' values:\n"
<< std::setprecision(12)
<< " calculated: " << calculatedFloorletsNPV << "\n"
<< " expected: " << cachedFloorNPV);
}
BOOST_AUTO_TEST_CASE(testOptionLetsDelta) {
BOOST_TEST_MESSAGE("Testing Black caplet/floorlet delta coefficients against finite difference values...");
CommonVars vars;
Date cachedToday(14,March,2002),
cachedSettlement(18,March,2002);
Settings::instance().evaluationDate() = cachedToday;
ext::shared_ptr<YieldTermStructure> baseCurve = flatRate(cachedSettlement,
0.05, Actual360());
RelinkableHandle<YieldTermStructure> baseCurveHandle(baseCurve);
// Define spreaded curve with eps as spread used for FD sensitivities
Real eps = 1.0e-6;
ext::shared_ptr<SimpleQuote> spread(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> spreadCurve(new ZeroSpreadedTermStructure(
baseCurveHandle,
Handle<Quote>(spread),
Continuous,
Annual,
Actual360()));
vars.termStructure.linkTo(spreadCurve);
Date startDate = vars.termStructure->referenceDate();
Leg leg = vars.makeLeg(startDate,20);
ext::shared_ptr<CapFloor> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.05,0.20);
ext::shared_ptr<CapFloor> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.05,0.20);
//so far tests pass, now try to get additional results and it will fail
Size capletsNum = cap->capRates().size();
std::vector<Real> capletUpPrices,
capletDownPrices,
capletAnalyticDelta,
capletDiscountFactorsUp,
capletDiscountFactorsDown,
capletForwardsUp,
capletForwardsDown,
capletFDDelta(capletsNum, 0.0);
Size floorletNum = floor->floorRates().size();
std::vector<Real> floorletUpPrices,
floorletDownPrices,
floorletAnalyticDelta,
floorletDiscountFactorsUp,
floorletDiscountFactorsDown,
floorletForwardsUp,
floorletForwardsDown,
floorletFDDelta(floorletNum, 0.0);
capletAnalyticDelta = cap->result<std::vector<Real> >("optionletsDelta");
floorletAnalyticDelta = floor->result<std::vector<Real> >("optionletsDelta");
spread->setValue(eps);
capletUpPrices = cap->result<std::vector<Real> >("optionletsPrice");
floorletUpPrices = floor->result<std::vector<Real> >("optionletsPrice");
capletDiscountFactorsUp = cap->result<std::vector<Real> >("optionletsDiscountFactor");
floorletDiscountFactorsUp = floor->result<std::vector<Real> >("optionletsDiscountFactor");
capletForwardsUp = cap->result<std::vector<Real> >("optionletsAtmForward");
floorletForwardsUp = floor->result<std::vector<Real> >("optionletsAtmForward");
spread->setValue(-eps);
capletDownPrices = cap->result<std::vector<Real> >("optionletsPrice");
floorletDownPrices = floor->result<std::vector<Real> >("optionletsPrice");
capletDiscountFactorsDown = cap->result<std::vector<Real> >("optionletsDiscountFactor");
floorletDiscountFactorsDown = floor->result<std::vector<Real> >("optionletsDiscountFactor");
capletForwardsDown = cap->result<std::vector<Real> >("optionletsAtmForward");
floorletForwardsDown = floor->result<std::vector<Real> >("optionletsAtmForward");
Real accrualFactor;
Leg capLeg = cap->floatingLeg();
Leg floorLeg = floor->floatingLeg();
for (Size n=1; n < capletUpPrices.size(); n++){
// calculating only caplet's FD sensitivity w.r.t. forward rate
// without the effect of sensitivity related to changed discount factor
ext::shared_ptr<FloatingRateCoupon> c = ext::dynamic_pointer_cast<FloatingRateCoupon>(capLeg[n]);
accrualFactor = c->nominal() * c->accrualPeriod() * c->gearing();
capletFDDelta[n] = (capletUpPrices[n] / capletDiscountFactorsUp[n]
- capletDownPrices[n] / capletDiscountFactorsDown[n])
/ (capletForwardsUp[n] - capletForwardsDown[n])
/ accrualFactor;
}
for (Size n=0; n<floorletUpPrices.size(); n++){
// calculating only caplet's FD sensitivity w.r.t. forward rate
// without the effect of sensitivity related to changed discount factor
ext::shared_ptr<FloatingRateCoupon> c = ext::dynamic_pointer_cast<FloatingRateCoupon>(floorLeg[n]);
accrualFactor = c->nominal() * c->accrualPeriod() * c->gearing();
floorletFDDelta[n] = (floorletUpPrices[n] / floorletDiscountFactorsUp[n]
- floorletDownPrices[n] / floorletDiscountFactorsDown[n])
/ (floorletForwardsUp[n] - floorletForwardsDown[n])
/ accrualFactor;
}
for (Size n=0; n<capletAnalyticDelta.size(); n++){
if (std::fabs(capletAnalyticDelta[n]-capletFDDelta[n]) > 1.0e-6)
BOOST_ERROR(
"failed to compare analytical and finite difference caplet delta:\n"
<< "caplet number:\t" << n << "\n"
<< std::setprecision(12)
<< " finite difference: " << capletFDDelta[n]<< "\n"
<< " analytical value: " << capletAnalyticDelta[n] << "\n"
<< " resulting ratio: " << capletFDDelta[n] / capletAnalyticDelta[n]);
}
for (Size n=0; n<floorletAnalyticDelta.size(); n++){
if (std::fabs(floorletAnalyticDelta[n]-floorletFDDelta[n]) > 1.0e-6)
BOOST_ERROR(
"failed to compare analytical and finite difference floorlet delta:\n"
<< "floorlet number:\t" << n << "\n"
<< std::setprecision(12)
<< " finite difference: " << floorletFDDelta[n]<< "\n"
<< " analytical value: " << floorletAnalyticDelta[n] << "\n"
<< " resulting ratio: " << floorletFDDelta[n] / floorletAnalyticDelta[n]);
}
}
BOOST_AUTO_TEST_CASE(testBachelierOptionLetsDelta) {
BOOST_TEST_MESSAGE("Testing Bachelier caplet/floorlet delta coefficients against finite difference values...");
CommonVars vars;
Date cachedToday(14,March,2002),
cachedSettlement(18,March,2002);
Settings::instance().evaluationDate() = cachedToday;
ext::shared_ptr<YieldTermStructure> baseCurve = flatRate(cachedSettlement,
0.05, Actual360());
RelinkableHandle<YieldTermStructure> baseCurveHandle(baseCurve);
// Define spreaded curve with eps as spread used for FD sensitivities
Real eps = 1.0e-6;
ext::shared_ptr<SimpleQuote> spread(new SimpleQuote(0.0));
ext::shared_ptr<YieldTermStructure> spreadCurve(new ZeroSpreadedTermStructure(
baseCurveHandle,
Handle<Quote>(spread),
Continuous,
Annual,
Actual360()));
vars.termStructure.linkTo(spreadCurve);
Date startDate = vars.termStructure->referenceDate();
Leg leg = vars.makeLeg(startDate,20);
// Use normal model (BachelierCapFloorEngine)
bool isLogNormal = false;
ext::shared_ptr<CapFloor> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.05, 0.01, isLogNormal);
ext::shared_ptr<CapFloor> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.05, 0.01, isLogNormal);
//so far tests pass, now try to get additional results and it will fail
Size capletsNum = cap->capRates().size();
std::vector<Real> capletUpPrices,
capletDownPrices,
capletAnalyticDelta,
capletDiscountFactorsUp,
capletDiscountFactorsDown,
capletForwardsUp,
capletForwardsDown,
capletFDDelta(capletsNum, 0.0);
Size floorletNum = floor->floorRates().size();
std::vector<Real> floorletUpPrices,
floorletDownPrices,
floorletAnalyticDelta,
floorletDiscountFactorsUp,
floorletDiscountFactorsDown,
floorletForwardsUp,
floorletForwardsDown,
floorletFDDelta(floorletNum, 0.0);
capletAnalyticDelta = cap->result<std::vector<Real> >("optionletsDelta");
floorletAnalyticDelta = floor->result<std::vector<Real> >("optionletsDelta");
spread->setValue(eps);
capletUpPrices = cap->result<std::vector<Real> >("optionletsPrice");
floorletUpPrices = floor->result<std::vector<Real> >("optionletsPrice");
capletDiscountFactorsUp = cap->result<std::vector<Real> >("optionletsDiscountFactor");
floorletDiscountFactorsUp = floor->result<std::vector<Real> >("optionletsDiscountFactor");
capletForwardsUp = cap->result<std::vector<Real> >("optionletsAtmForward");
floorletForwardsUp = floor->result<std::vector<Real> >("optionletsAtmForward");
spread->setValue(-eps);
capletDownPrices = cap->result<std::vector<Real> >("optionletsPrice");
floorletDownPrices = floor->result<std::vector<Real> >("optionletsPrice");
capletDiscountFactorsDown = cap->result<std::vector<Real> >("optionletsDiscountFactor");
floorletDiscountFactorsDown = floor->result<std::vector<Real> >("optionletsDiscountFactor");
capletForwardsDown = cap->result<std::vector<Real> >("optionletsAtmForward");
floorletForwardsDown = floor->result<std::vector<Real> >("optionletsAtmForward");
Real accrualFactor;
Leg capLeg = cap->floatingLeg();
Leg floorLeg = floor->floatingLeg();
for (Size n=1; n < capletUpPrices.size(); n++){
// calculating only caplet's FD sensitivity w.r.t. forward rate
// without the effect of sensitivity related to changed discount factor
ext::shared_ptr<FloatingRateCoupon> c = ext::dynamic_pointer_cast<FloatingRateCoupon>(capLeg[n]);
accrualFactor = c->nominal() * c->accrualPeriod() * c->gearing();
capletFDDelta[n] = (capletUpPrices[n] / capletDiscountFactorsUp[n]
- capletDownPrices[n] / capletDiscountFactorsDown[n])
/ (capletForwardsUp[n] - capletForwardsDown[n])
/ accrualFactor;
}
for (Size n=0; n<floorletUpPrices.size(); n++){
// calculating only caplet's FD sensitivity w.r.t. forward rate
// without the effect of sensitivity related to changed discount factor
ext::shared_ptr<FloatingRateCoupon> c = ext::dynamic_pointer_cast<FloatingRateCoupon>(floorLeg[n]);
accrualFactor = c->nominal() * c->accrualPeriod() * c->gearing();
floorletFDDelta[n] = (floorletUpPrices[n] / floorletDiscountFactorsUp[n]
- floorletDownPrices[n] / floorletDiscountFactorsDown[n])
/ (floorletForwardsUp[n] - floorletForwardsDown[n])
/ accrualFactor;
}
for (Size n=0; n<capletAnalyticDelta.size(); n++){
if (std::fabs(capletAnalyticDelta[n]-capletFDDelta[n]) > 1.0e-6)
BOOST_ERROR(
"failed to compare analytical and finite difference caplet delta:\n"
<< "caplet number:\t" << n << "\n"
<< std::setprecision(12)
<< " finite difference: " << capletFDDelta[n]<< "\n"
<< " analytical value: " << capletAnalyticDelta[n] << "\n"
<< " resulting ratio: " << capletFDDelta[n] / capletAnalyticDelta[n]);
}
for (Size n=0; n<floorletAnalyticDelta.size(); n++){
if (std::fabs(floorletAnalyticDelta[n]-floorletFDDelta[n]) > 1.0e-6)
BOOST_ERROR(
"failed to compare analytical and finite difference floorlet delta:\n"
<< "floorlet number:\t" << n << "\n"
<< std::setprecision(12)
<< " finite difference: " << floorletFDDelta[n]<< "\n"
<< " analytical value: " << floorletAnalyticDelta[n] << "\n"
<< " resulting ratio: " << floorletFDDelta[n] / floorletAnalyticDelta[n]);
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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