void SwapTest::testCachedValue() {
BOOST_TEST_MESSAGE("Testing vanilla-swap calculation against cached value...");
CommonVars vars;
vars.today = Date(17,June,2002);
Settings::instance().evaluationDate() = vars.today;
vars.settlement =
vars.calendar.advance(vars.today,vars.settlementDays,Days);
vars.termStructure.linkTo(flatRate(vars.settlement,0.05,Actual365Fixed()));
boost::shared_ptr<VanillaSwap> swap = vars.makeSwap(10, 0.06, 0.001);
#ifndef QL_USE_INDEXED_COUPON
Real cachedNPV = -5.872863313209;
#else
Real cachedNPV = -5.872342992212;
#endif
if (std::fabs(swap->NPV()-cachedNPV) > 1.0e-11)
BOOST_ERROR("failed to reproduce cached swap value:\n"
<< QL_FIXED << std::setprecision(12)
<< " calculated: " << swap->NPV() << "\n"
<< " expected: " << cachedNPV);
}
void OvernightIndexedSwapTest::testSeasonedSwaps() {
BOOST_TEST_MESSAGE("Testing seasoned Eonia-swap calculation...");
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Spread spreads[] = { -0.001, -0.01, 0.0, 0.01, 0.001 };
Date effectiveDate = Date(2, February, 2009);
vars.eoniaIndex->addFixing(Date(2,February,2009), 0.0010); // fake fixing values
vars.eoniaIndex->addFixing(Date(3,February,2009), 0.0011);
vars.eoniaIndex->addFixing(Date(4,February,2009), 0.0012);
vars.eoniaIndex->addFixing(Date(5,February,2009), 0.0013);
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(spreads); j++) {
shared_ptr<OvernightIndexedSwap> swap =
vars.makeSwap(lengths[i],0.0,spreads[j],false,effectiveDate);
shared_ptr<OvernightIndexedSwap> swap2 =
vars.makeSwap(lengths[i],0.0,spreads[j],true,effectiveDate);
if (std::fabs(swap->NPV() - swap2->NPV()) > 1.0e-10) {
BOOST_ERROR("swap npv is different:\n"
<< std::setprecision(2)
<< " length: " << lengths[i] << " \n"
<< " floating spread: "
<< io::rate(spreads[j]) << "\n"
<< " swap value (non telescopic value dates): " << swap->NPV()
<< "\n swap value (telescopic value dates ): " << swap2->NPV());
}
}
}
}
void SwapTest::testFairSpread() {
BOOST_TEST_MESSAGE("Testing vanilla-swap calculation of "
"fair floating spread...");
CommonVars vars;
Integer lengths[] = { 1, 2, 5, 10, 20 };
Rate rates[] = { 0.04, 0.05, 0.06, 0.07 };
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(rates); j++) {
boost::shared_ptr<VanillaSwap> swap =
vars.makeSwap(lengths[i],rates[j],0.0);
swap = vars.makeSwap(lengths[i],rates[j],swap->fairSpread());
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("recalculating with implied spread:\n"
<< std::setprecision(2)
<< " length: " << lengths[i] << " years\n"
<< " fixed rate: " << io::rate(rates[j]) << "\n"
<< " swap value: " << swap->NPV());
}
}
}
}
void CapFloorTest::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 (Size i=0; i<LENGTH(lengths); i++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
Date maturity = vars.calendar.advance(startDate,lengths[i],Years,
vars.convention);
Schedule schedule(startDate,maturity,
Period(vars.frequency),vars.calendar,
vars.convention,vars.convention,
DateGeneration::Forward,false);
for (Size j=0; j<LENGTH(strikes); j++) {
for (Size k=0; k<LENGTH(vols); k++) {
boost::shared_ptr<CapFloor> cap =
vars.makeCapFloor(CapFloor::Cap, leg, strikes[j],vols[k]);
boost::shared_ptr<CapFloor> floor =
vars.makeCapFloor(CapFloor::Floor, leg, strikes[j],vols[k]);
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " cap ATM rate: " << capATMRate << "\n"
<< " floor ATM rate:" << floorATMRate << "\n"
<< " relative Error:"
<< relativeError(capATMRate, floorATMRate,
capATMRate)*100 << "%" );
VanillaSwap swap(VanillaSwap::Payer, vars.nominals[0],
schedule, floorATMRate,
vars.index->dayCounter(),
schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(boost::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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " ATM rate: " << io::rate(floorATMRate) << "\n"
<< " swap NPV: " << swapNPV);
}
}
}
}
void OptionletStripperTest::testFlatTermVolatilityStripping1() {
BOOST_TEST_MESSAGE(
"Testing forward/forward vol stripping from flat term vol "
"surface using OptionletStripper1 class...");
CommonVars vars;
Settings::instance().evaluationDate() = Date(28, October, 2013);
vars.setFlatTermVolSurface();
shared_ptr<IborIndex> iborIndex(new Euribor6M(vars.yieldTermStructure));
boost::shared_ptr<OptionletStripper> optionletStripper1(new
OptionletStripper1(vars.flatTermVolSurface,
iborIndex,
Null<Rate>(),
vars.accuracy));
boost::shared_ptr<StrippedOptionletAdapter> strippedOptionletAdapter(new
StrippedOptionletAdapter(optionletStripper1));
Handle<OptionletVolatilityStructure> vol(strippedOptionletAdapter);
vol->enableExtrapolation();
boost::shared_ptr<BlackCapFloorEngine> strippedVolEngine(new
BlackCapFloorEngine(vars.yieldTermStructure,
vol));
boost::shared_ptr<CapFloor> cap;
for (Size tenorIndex=0; tenorIndex<vars.optionTenors.size(); ++tenorIndex) {
for (Size strikeIndex=0; strikeIndex<vars.strikes.size(); ++strikeIndex) {
cap = MakeCapFloor(CapFloor::Cap,
vars.optionTenors[tenorIndex],
iborIndex,
vars.strikes[strikeIndex],
0*Days)
.withPricingEngine(strippedVolEngine);
Real priceFromStrippedVolatility = cap->NPV();
boost::shared_ptr<PricingEngine> blackCapFloorEngineConstantVolatility(new
BlackCapFloorEngine(vars.yieldTermStructure,
vars.termV[tenorIndex][strikeIndex]));
cap->setPricingEngine(blackCapFloorEngineConstantVolatility);
Real priceFromConstantVolatility = cap->NPV();
Real error = std::fabs(priceFromStrippedVolatility - priceFromConstantVolatility);
if (error>vars.tolerance)
BOOST_FAIL("\noption tenor: " << vars.optionTenors[tenorIndex] <<
"\nstrike: " << io::rate(vars.strikes[strikeIndex]) <<
"\nstripped vol price: " << io::rate(priceFromStrippedVolatility) <<
"\nconstant vol price: " << io::rate(priceFromConstantVolatility) <<
"\nerror: " << io::rate(error) <<
"\ntolerance: " << io::rate(vars.tolerance));
}
}
}
void OvernightIndexedSwapTest::testFairSpread() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation of "
"fair floating spread...");
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Rate rates[] = { 0.04, 0.05, 0.06, 0.07 };
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(rates); j++) {
shared_ptr<OvernightIndexedSwap> swap =
vars.makeSwap(lengths[i], rates[j], 0.0);
Spread fairSpread = swap->fairSpread();
swap = vars.makeSwap(lengths[i], rates[j], fairSpread);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("\nrecalculating with implied spread:" <<
std::setprecision(2) <<
"\n length: " << lengths[i] <<
"\n fixed rate: " << io::rate(rates[j]) <<
"\nfair spread: " << io::rate(fairSpread) <<
"\n swap value: " << swap->NPV());
}
}
}
}
void OvernightIndexedSwapTest::testFairRate() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation of fair fixed rate...");
CommonVars vars;
Period lengths[] = { 1*Years, 2*Years, 5*Years, 10*Years, 20*Years };
Spread spreads[] = { -0.001, -0.01, 0.0, 0.01, 0.001 };
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(spreads); j++) {
shared_ptr<OvernightIndexedSwap> swap =
vars.makeSwap(lengths[i],0.0,spreads[j]);
swap = vars.makeSwap(lengths[i],swap->fairRate(),spreads[j]);
if (std::fabs(swap->NPV()) > 1.0e-10) {
BOOST_ERROR("recalculating with implied rate:\n"
<< std::setprecision(2)
<< " length: " << lengths[i] << " \n"
<< " floating spread: "
<< io::rate(spreads[j]) << "\n"
<< " swap value: " << swap->NPV());
}
}
}
}
void OvernightIndexedSwapTest::testCachedValue() {
BOOST_TEST_MESSAGE("Testing Eonia-swap calculation against cached value...");
CommonVars vars;
Settings::instance().evaluationDate() = vars.today;
vars.settlement =
vars.calendar.advance(vars.today,vars.settlementDays,Days);
Real flat = 0.05;
vars.eoniaTermStructure.linkTo(flatRate(vars.settlement,flat,Actual360()));
Real fixedRate = exp(flat) - 1;
shared_ptr<OvernightIndexedSwap> swap = vars.makeSwap(1*Years, fixedRate, 0.0,false);
shared_ptr<OvernightIndexedSwap> swap2 = vars.makeSwap(1*Years, fixedRate, 0.0,true);
Real cachedNPV = 0.001730450147;
Real tolerance = 1.0e-11;
if (std::fabs(swap->NPV()-cachedNPV) > tolerance)
BOOST_ERROR("\nfailed to reproduce cached swap value (non telescopic value dates):" <<
std::fixed << std::setprecision(12) <<
"\ncalculated: " << swap->NPV() <<
"\n expected: " << cachedNPV <<
"\n tolerance:" << tolerance);
if (std::fabs(swap2->NPV()-cachedNPV) > tolerance)
BOOST_ERROR("\nfailed to reproduce cached swap value (telescopic value dates):" <<
std::fixed << std::setprecision(12) <<
"\ncalculated: " << swap->NPV() <<
"\n expected: " << cachedNPV <<
"\n tolerance:" << tolerance);
}
void SwaptionTest::testCachedValue() {
BOOST_MESSAGE("Testing swaption value against cached value...");
CommonVars vars;
vars.today = Date(13, March, 2002);
vars.settlement = Date(15, March, 2002);
Settings::instance().evaluationDate() = vars.today;
vars.termStructure.linkTo(flatRate(vars.settlement, 0.05, Actual365Fixed()));
Date exerciseDate = vars.calendar.advance(vars.settlement, 5*Years);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays, Days);
boost::shared_ptr<VanillaSwap> swap =
MakeVanillaSwap(10*Years, vars.index, 0.06)
.withEffectiveDate(startDate);
boost::shared_ptr<Swaption> swaption =
vars.makeSwaption(swap, exerciseDate, 0.20);
#ifndef QL_USE_INDEXED_COUPON
Real cachedNPV = 0.036418158579;
#else
Real cachedNPV = 0.036421429684;
#endif
// FLOATING_POINT_EXCEPTION
if (std::fabs(swaption->NPV()-cachedNPV) > 1.0e-12)
BOOST_ERROR("failed to reproduce cached swaption value:\n" <<
QL_FIXED << std::setprecision(12) <<
"\ncalculated: " << swaption->NPV() <<
"\nexpected: " << cachedNPV);
}
void SwaptionVolatilityMatrixTest::testSwaptionVolMatrixCoherence() {
BOOST_TEST_MESSAGE("Testing swaption volatility matrix...");
CommonVars vars;
boost::shared_ptr<SwaptionVolatilityMatrix> vol;
std::string description;
//floating reference date, floating market data
description = "floating reference date, floating market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeCoherenceTest(description, vol);
//fixed reference date, floating market data
description = "fixed reference date, floating market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(Settings::instance().evaluationDate(),
vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeCoherenceTest(description, vol);
// floating reference date, fixed market data
description = "floating reference date, fixed market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeCoherenceTest(description, vol);
// fixed reference date, fixed market data
description = "fixed reference date, fixed market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(Settings::instance().evaluationDate(),
vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeCoherenceTest(description, vol);
}
void CapFloorTest::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 (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(vols); j++) {
for (Size k=0; k<LENGTH(strikes); k++) {
for (Size h=0; h<LENGTH(types); h++) {
Leg leg = vars.makeLeg(startDate, lengths[i]);
boost::shared_ptr<CapFloor> capFloor =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]);
boost::shared_ptr<CapFloor> shiftedCapFloor2 =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]+shift);
boost::shared_ptr<CapFloor> shiftedCapFloor1 =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]-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: " << lengths[j]*Years <<
"\n strike: " << io::rate(strikes[k]) <<
//"\n types: " << types[h] <<
QL_FIXED << std::setprecision(12) <<
"\n calculated: " << analyticalVega <<
"\n expected: " << numericalVega <<
"\n discrepancy: " << io::rate(discrepancy) <<
"\n tolerance: " << io::rate(tolerance));
}
}
}
}
}
}
void OptionletStripperTest::testSwitchStrike() {
BOOST_TEST_MESSAGE("Testing switch strike level and recalibration of level "
"in case of curve relinking...");
CommonVars vars;
Settings::instance().evaluationDate() = Date(28, October, 2013);
vars.setCapFloorTermVolSurface();
RelinkableHandle< YieldTermStructure > yieldTermStructure;
yieldTermStructure.linkTo(boost::shared_ptr< FlatForward >(
new FlatForward(0, vars.calendar, 0.03, vars.dayCounter)));
shared_ptr< IborIndex > iborIndex(new Euribor6M(yieldTermStructure));
boost::shared_ptr< OptionletStripper1 > optionletStripper1(
new OptionletStripper1(vars.capFloorVolSurface, iborIndex,
Null< Rate >(), vars.accuracy));
#if defined(QL_USE_INDEXED_COUPON)
Real expected = 0.02981258;
#else
Real expected = 0.02981223;
#endif
Real error = std::fabs(optionletStripper1->switchStrike() - expected);
if (error > vars.tolerance)
BOOST_FAIL("\nSwitchstrike not correctly computed: "
<< "\nexpected switch strike: " << io::rate(expected)
<< "\ncomputed switch strike: "
<< io::rate(optionletStripper1->switchStrike())
<< "\nerror: " << io::rate(error)
<< "\ntolerance: " << io::rate(vars.tolerance));
yieldTermStructure.linkTo(boost::shared_ptr< FlatForward >(
new FlatForward(0, vars.calendar, 0.05, vars.dayCounter)));
#if defined(QL_USE_INDEXED_COUPON)
expected = 0.0499381;
#else
expected = 0.0499371;
#endif
error = std::fabs(optionletStripper1->switchStrike() - expected);
if (error > vars.tolerance)
BOOST_FAIL("\nSwitchstrike not correctly computed: "
<< "\nexpected switch strike: " << io::rate(expected)
<< "\ncomputed switch strike: "
<< io::rate(optionletStripper1->switchStrike())
<< "\nerror: " << io::rate(error)
<< "\ntolerance: " << io::rate(vars.tolerance));
}
void CapFloorTest::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 (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(strikes); j++) {
for (Size k=0; k<LENGTH(vols); k++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
strikes[j],vols[k]);
boost::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
strikes[j],vols[k]);
Date maturity = vars.calendar.advance(startDate,lengths[i],Years,
vars.convention);
Schedule schedule(startDate,maturity,
Period(vars.frequency),vars.calendar,
vars.convention,vars.convention,
DateGeneration::Forward,false);
VanillaSwap swap(VanillaSwap::Payer, vars.nominals[0],
schedule, strikes[j], vars.index->dayCounter(),
schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(boost::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(vars.termStructure)));
// FLOATING_POINT_EXCEPTION
if (std::fabs((cap->NPV()-floor->NPV()) - swap.NPV()) > 1.0e-10) {
BOOST_FAIL(
"put/call parity violated:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV());
}
}
}
}
}
void CapFloorTest::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);
boost::shared_ptr<Instrument> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.07,0.20);
boost::shared_ptr<Instrument> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.03,0.20);
#ifndef QL_USE_INDEXED_COUPON
// par coupon price
Real cachedCapNPV = 6.87570026732,
cachedFloorNPV = 2.65812927959;
#else
// index fixing price
Real cachedCapNPV = 6.87630307745,
cachedFloorNPV = 2.65796764715;
#endif
// 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);
}
void SwapTest::testSpreadDependency() {
BOOST_TEST_MESSAGE("Testing vanilla-swap dependency on floating spread...");
CommonVars vars;
Integer lengths[] = { 1, 2, 5, 10, 20 };
Rate rates[] = { 0.04, 0.05, 0.06, 0.07 };
Spread spreads[] = { -0.01, -0.002, -0.001, 0.0, 0.001, 0.002, 0.01 };
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(rates); j++) {
// store the results for different spreads...
std::vector<Real> swap_values;
for (Size k=0; k<LENGTH(spreads); k++) {
boost::shared_ptr<VanillaSwap> swap =
vars.makeSwap(lengths[i],rates[j],spreads[k]);
swap_values.push_back(swap->NPV());
}
// and check that they go the right way
std::vector<Real>::iterator it =
std::adjacent_find(swap_values.begin(),swap_values.end(),
std::greater<Real>());
if (it != swap_values.end()) {
Size n = it - swap_values.begin();
BOOST_ERROR(
"NPV is decreasing with the floating spread in a swap: \n"
<< " length: " << lengths[i] << " years\n"
<< " value: " << swap_values[n]
<< " receiving spread: " << io::rate(spreads[n]) << "\n"
<< " value: " << swap_values[n+1]
<< " receiving spread: " << io::rate(spreads[n+1]));
}
}
}
}
double in_arrear_floorlet(const Date& todaysDate_,
double start,
double length,
Rate spot_,
Rate strike,
Volatility volatility
)
{
CommonVars vars;
try{
vars.makeIndex(todaysDate_,spot_);
Leg leg = vars.makeLeg(start,length);
boost::shared_ptr<Instrument> floor = vars.makeCapFloor(CapFloor::Floor, leg, strike, volatility);
return floor->NPV();
}
catch (std::exception& e) {
std::cerr << e.what() << std::endl;
return 1;
}
}
void CapFloorTest::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 (Size k=0; k<LENGTH(lengths); k++) {
Leg leg = vars.makeLeg(vars.settlement, lengths[k]);
for (Size i=0; i<LENGTH(types); i++) {
for (Size j=0; j<LENGTH(strikes); j++) {
boost::shared_ptr<CapFloor> capfloor =
vars.makeCapFloor(types[i], leg, strikes[j], 0.0);
for (Size n=0; n<LENGTH(rRates); n++) {
for (Size m=0; m<LENGTH(vols); m++) {
Rate r = rRates[n];
Volatility v = vols[m];
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, 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(types[i]) <<
"\n strike: " << io::rate(strikes[j]) <<
"\n risk-free: " << io::rate(r) <<
"\n length: " << lengths[k] << "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(types[i]) <<
"\n strike: " << io::rate(strikes[j]) <<
"\n risk-free: " << io::rate(r) <<
"\n length: " << lengths[k] << "Y" <<
"\n volatility: " << io::volatility(v) <<
"\n price: " << value <<
"\n implied vol: " << io::volatility(implVol) <<
"\n implied price: " << value2);
}
}
}
}
}
}
}
}
void SwaptionTest::testCashSettledSwaptions() {
BOOST_MESSAGE("Testing cash settled swaptions modified annuity...");
CommonVars vars;
Rate strike = 0.05;
for (Size i=0; i<LENGTH(exercises); i++) {
for (Size j=0; j<LENGTH(lengths); j++) {
Date exerciseDate = vars.calendar.advance(vars.today,exercises[i]);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays,Days);
Date maturity =
vars.calendar.advance(startDate,lengths[j],
vars.floatingConvention);
Schedule floatSchedule(startDate, maturity, vars.floatingTenor,
vars.calendar,vars.floatingConvention,
vars.floatingConvention,
DateGeneration::Forward, false);
// Swap with fixed leg conventions: Business Days = Unadjusted, DayCount = 30/360
Schedule fixedSchedule_u(startDate, maturity,
Period(vars.fixedFrequency),
vars.calendar, Unadjusted, Unadjusted,
DateGeneration::Forward, true);
boost::shared_ptr<VanillaSwap> swap_u360(
new VanillaSwap(type[0], vars.nominal,
fixedSchedule_u,strike,Thirty360(),
floatSchedule,vars.index,0.0,
vars.index->dayCounter()));
// Swap with fixed leg conventions: Business Days = Unadjusted, DayCount = Act/365
boost::shared_ptr<VanillaSwap> swap_u365(
new VanillaSwap(type[0],vars.nominal,
fixedSchedule_u,strike,Actual365Fixed(),
floatSchedule,vars.index,0.0,
vars.index->dayCounter()));
// Swap with fixed leg conventions: Business Days = Modified Following, DayCount = 30/360
Schedule fixedSchedule_a(startDate,maturity,
Period(vars.fixedFrequency),
vars.calendar,ModifiedFollowing,
ModifiedFollowing,
DateGeneration::Forward, true);
boost::shared_ptr<VanillaSwap> swap_a360(
new VanillaSwap(type[0],vars.nominal,
fixedSchedule_a,strike,Thirty360(),
floatSchedule,vars.index,0.0,
vars.index->dayCounter()));
// Swap with fixed leg conventions: Business Days = Modified Following, DayCount = Act/365
boost::shared_ptr<VanillaSwap> swap_a365(
new VanillaSwap(type[0],vars.nominal,
fixedSchedule_a,strike,Actual365Fixed(),
floatSchedule,vars.index,0.0,
vars.index->dayCounter()));
boost::shared_ptr<PricingEngine> swapEngine(
new DiscountingSwapEngine(vars.termStructure));
swap_u360->setPricingEngine(swapEngine);
swap_a360->setPricingEngine(swapEngine);
swap_u365->setPricingEngine(swapEngine);
swap_a365->setPricingEngine(swapEngine);
const Leg& swapFixedLeg_u360 = swap_u360->fixedLeg();
const Leg& swapFixedLeg_a360 = swap_a360->fixedLeg();
const Leg& swapFixedLeg_u365 = swap_u365->fixedLeg();
const Leg& swapFixedLeg_a365 = swap_a365->fixedLeg();
// FlatForward curves
// FLOATING_POINT_EXCEPTION
Handle<YieldTermStructure> termStructure_u360(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(vars.settlement,swap_u360->fairRate(),
Thirty360(),Compounded,
vars.fixedFrequency)));
Handle<YieldTermStructure> termStructure_a360(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(vars.settlement,swap_a360->fairRate(),
Thirty360(),Compounded,
vars.fixedFrequency)));
Handle<YieldTermStructure> termStructure_u365(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(vars.settlement,swap_u365->fairRate(),
Actual365Fixed(),Compounded,
vars.fixedFrequency)));
Handle<YieldTermStructure> termStructure_a365(
boost::shared_ptr<YieldTermStructure>(
new FlatForward(vars.settlement,swap_a365->fairRate(),
Actual365Fixed(),Compounded,
vars.fixedFrequency)));
// Annuity calculated by swap method fixedLegBPS().
// Fixed leg conventions: Unadjusted, 30/360
Real annuity_u360 = swap_u360->fixedLegBPS() / 0.0001;
annuity_u360 = swap_u360->type()==VanillaSwap::Payer ?
-annuity_u360 : annuity_u360;
// Fixed leg conventions: ModifiedFollowing, act/365
Real annuity_a365 = swap_a365->fixedLegBPS() / 0.0001;
annuity_a365 = swap_a365->type()==VanillaSwap::Payer ?
-annuity_a365 : annuity_a365;
// Fixed leg conventions: ModifiedFollowing, 30/360
Real annuity_a360 = swap_a360->fixedLegBPS() / 0.0001;
annuity_a360 = swap_a360->type()==VanillaSwap::Payer ?
-annuity_a360 : annuity_a360;
// Fixed leg conventions: Unadjusted, act/365
Real annuity_u365 = swap_u365->fixedLegBPS() / 0.0001;
annuity_u365 = swap_u365->type()==VanillaSwap::Payer ?
-annuity_u365 : annuity_u365;
// Calculation of Modified Annuity (cash settlement)
// Fixed leg conventions of swap: unadjusted, 30/360
Real cashannuity_u360 = 0.;
Size i;
for (i=0; i<swapFixedLeg_u360.size(); i++) {
cashannuity_u360 += swapFixedLeg_u360[i]->amount()/strike
* termStructure_u360->discount(
swapFixedLeg_u360[i]->date());
}
// Fixed leg conventions of swap: unadjusted, act/365
Real cashannuity_u365 = 0.;
for (i=0; i<swapFixedLeg_u365.size(); i++) {
cashannuity_u365 += swapFixedLeg_u365[i]->amount()/strike
* termStructure_u365->discount(
swapFixedLeg_u365[i]->date());
}
// Fixed leg conventions of swap: modified following, 30/360
Real cashannuity_a360 = 0.;
for (i=0; i<swapFixedLeg_a360.size(); i++) {
cashannuity_a360 += swapFixedLeg_a360[i]->amount()/strike
* termStructure_a360->discount(
swapFixedLeg_a360[i]->date());
}
// Fixed leg conventions of swap: modified following, act/365
Real cashannuity_a365 = 0.;
for (i=0; i<swapFixedLeg_a365.size(); i++) {
cashannuity_a365 += swapFixedLeg_a365[i]->amount()/strike
* termStructure_a365->discount(
swapFixedLeg_a365[i]->date());
}
// Swaptions: underlying swap fixed leg conventions:
// unadjusted, 30/360
// Physical settled swaption
boost::shared_ptr<Swaption> swaption_p_u360 =
vars.makeSwaption(swap_u360,exerciseDate,0.20);
Real value_p_u360 = swaption_p_u360->NPV();
// Cash settled swaption
boost::shared_ptr<Swaption> swaption_c_u360 =
vars.makeSwaption(swap_u360,exerciseDate,0.20,
Settlement::Cash);
Real value_c_u360 = swaption_c_u360->NPV();
// the NPV's ratio must be equal to annuities ratio
Real npv_ratio_u360 = value_c_u360 / value_p_u360;
Real annuity_ratio_u360 = cashannuity_u360 / annuity_u360;
// Swaptions: underlying swap fixed leg conventions:
// modified following, act/365
// Physical settled swaption
boost::shared_ptr<Swaption> swaption_p_a365 =
vars.makeSwaption(swap_a365,exerciseDate,0.20);
Real value_p_a365 = swaption_p_a365->NPV();
// Cash settled swaption
boost::shared_ptr<Swaption> swaption_c_a365 =
vars.makeSwaption(swap_a365,exerciseDate,0.20,
Settlement::Cash);
Real value_c_a365 = swaption_c_a365->NPV();
// the NPV's ratio must be equal to annuities ratio
Real npv_ratio_a365 = value_c_a365 / value_p_a365;
Real annuity_ratio_a365 = cashannuity_a365 / annuity_a365;
// Swaptions: underlying swap fixed leg conventions:
// modified following, 30/360
// Physical settled swaption
boost::shared_ptr<Swaption> swaption_p_a360 =
vars.makeSwaption(swap_a360,exerciseDate,0.20);
Real value_p_a360 = swaption_p_a360->NPV();
// Cash settled swaption
boost::shared_ptr<Swaption> swaption_c_a360 =
vars.makeSwaption(swap_a360,exerciseDate,0.20,
Settlement::Cash);
Real value_c_a360 = swaption_c_a360->NPV();
// the NPV's ratio must be equal to annuities ratio
Real npv_ratio_a360 = value_c_a360 / value_p_a360;
Real annuity_ratio_a360 = cashannuity_a360 / annuity_a360;
// Swaptions: underlying swap fixed leg conventions:
// unadjusted, act/365
// Physical settled swaption
boost::shared_ptr<Swaption> swaption_p_u365 =
vars.makeSwaption(swap_u365,exerciseDate,0.20);
Real value_p_u365 = swaption_p_u365->NPV();
// Cash settled swaption
boost::shared_ptr<Swaption> swaption_c_u365 =
vars.makeSwaption(swap_u365,exerciseDate,0.20,
Settlement::Cash);
Real value_c_u365 = swaption_c_u365->NPV();
// the NPV's ratio must be equal to annuities ratio
Real npv_ratio_u365 = value_c_u365 / value_p_u365;
Real annuity_ratio_u365 = cashannuity_u365 / annuity_u365;
if (std::fabs(annuity_ratio_u360-npv_ratio_u360)>1e-10 ) {
BOOST_ERROR("\n" <<
" The npv's ratio must be equal to " <<
" annuities ratio" << "\n"
" Swaption " <<
exercises[i].units() << "y x " << lengths[j].units() << "y" <<
" (underlying swap fixed leg Unadjusted, 30/360)" << "\n" <<
" Today : " <<
vars.today << "\n" <<
" Settlement date : " <<
vars.settlement << "\n" <<
" Exercise date : " <<
exerciseDate << "\n" <<
" Swap start date : " <<
startDate << "\n" <<
" Swap end date : " <<
maturity << "\n" <<
" physical delivered swaption npv : " <<
value_p_u360 << "\t\t\t" <<
" annuity : " <<
annuity_u360 << "\n" <<
" cash delivered swaption npv : " <<
value_c_u360 << "\t\t\t" <<
" annuity : " <<
cashannuity_u360 << "\n" <<
" npv ratio : " <<
npv_ratio_u360 << "\n" <<
" annuity ratio : " <<
annuity_ratio_u360 << "\n" <<
" difference : " <<
(annuity_ratio_u360-npv_ratio_u360) );
}
if (std::fabs(annuity_ratio_a365-npv_ratio_a365)>1e-10) {
BOOST_ERROR("\n" <<
" The npv's ratio must be equal to " <<
" annuities ratio" << "\n"
" Swaption " <<
exercises[i].units() << "y x " << lengths[j].units() << "y" <<
" (underlying swap fixed leg Modified Following, act/365" << "\n" <<
" Today : " <<
vars.today << "\n" <<
" Settlement date : " <<
vars.settlement << "\n" <<
" Exercise date : " <<
exerciseDate << "\n" <<
" Swap start date : " <<
startDate << "\n" <<
" Swap end date : " <<
maturity << "\n" <<
" physical delivered swaption npv : " <<
value_p_a365 << "\t\t\t" <<
" annuity : " <<
annuity_a365 << "\n" <<
" cash delivered swaption npv : " <<
value_c_a365 << "\t\t\t" <<
" annuity : " <<
cashannuity_a365 << "\n" <<
" npv ratio : " <<
npv_ratio_a365 << "\n" <<
" annuity ratio : " <<
annuity_ratio_a365 << "\n" <<
" difference : " <<
(annuity_ratio_a365-npv_ratio_a365) );
}
if (std::fabs(annuity_ratio_a360-npv_ratio_a360)>1e-10) {
BOOST_ERROR("\n" <<
" The npv's ratio must be equal to " <<
" annuities ratio" << "\n"
" Swaption " <<
exercises[i].units() << "y x " << lengths[j].units() << "y" <<
" (underlying swap fixed leg Unadjusted, 30/360)" << "\n" <<
" Today : " <<
vars.today << "\n" <<
" Settlement date : " <<
vars.settlement << "\n" <<
" Exercise date : " <<
exerciseDate << "\n" <<
" Swap start date : " <<
startDate << "\n" <<
" Swap end date : " <<
maturity << "\n" <<
" physical delivered swaption npv : " <<
value_p_a360 << "\t\t\t" <<
" annuity : " <<
annuity_a360 << "\n" <<
" cash delivered swaption npv : " <<
value_c_a360 << "\t\t\t" <<
" annuity : " <<
cashannuity_a360 << "\n" <<
" npv ratio : " <<
npv_ratio_a360 << "\n" <<
" annuity ratio : " <<
annuity_ratio_a360 << "\n" <<
" difference : " <<
(annuity_ratio_a360-npv_ratio_a360) );
}
if (std::fabs(annuity_ratio_u365-npv_ratio_u365)>1e-10) {
BOOST_ERROR("\n" <<
" The npv's ratio must be equal to " <<
" annuities ratio" << "\n"
" Swaption " <<
exercises[i].units() << "y x " << lengths[j].units() << "y" <<
" (underlying swap fixed leg Unadjusted, act/365)" << "\n" <<
" Today : " <<
vars.today << "\n" <<
" Settlement date : " <<
vars.settlement << "\n" <<
" Exercise date : " <<
exerciseDate << "\n" <<
" Swap start date : " <<
startDate << "\n" <<
" Swap end date : " <<
maturity << "\n" <<
" physical delivered swaption npv : " <<
value_p_u365 << "\t\t\t" <<
" annuity : " <<
annuity_u365 << "\n" <<
" cash delivered swaption npv : " <<
value_c_u365 << "\t\t\t" <<
" annuity : " <<
cashannuity_u365 << "\n" <<
" npv ratio : " <<
npv_ratio_u365 << "\n" <<
" annuity ratio : " <<
annuity_ratio_u365 << "\n" <<
" difference : " <<
(annuity_ratio_u365-npv_ratio_u365) );
}
}
}
}
void SwaptionTest::testVega() {
BOOST_MESSAGE("Testing swaption vega...");
CommonVars vars;
Settlement::Type types[] = { Settlement::Physical, Settlement::Cash };
Rate strikes[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.20, 0.30, 0.70, 0.90 };
Volatility shift = 1e-8;
for (Size i=0; i<LENGTH(exercises); i++) {
Date exerciseDate = vars.calendar.advance(vars.today, exercises[i]);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays*Days);
for (Size j=0; j<LENGTH(lengths); j++) {
for (Size t=0; t<LENGTH(strikes); t++) {
for (Size h=0; h<LENGTH(type); h++) {
boost::shared_ptr<VanillaSwap> swap =
MakeVanillaSwap(lengths[j], vars.index, strikes[t])
.withEffectiveDate(startDate)
.withFloatingLegSpread(0.0)
.withType(type[h]);
for (Size u=0; u<LENGTH(vols); u++) {
boost::shared_ptr<Swaption> swaption =
vars.makeSwaption(swap, exerciseDate,
vols[u], types[h]);
// FLOATING_POINT_EXCEPTION
boost::shared_ptr<Swaption> swaption1 =
vars.makeSwaption(swap, exerciseDate,
vols[u]-shift, types[h]);
boost::shared_ptr<Swaption> swaption2 =
vars.makeSwaption(swap, exerciseDate,
vols[u]+shift, types[h]);
Real swaptionNPV = swaption->NPV();
Real numericalVegaPerPoint =
(swaption2->NPV()-swaption1->NPV())/(200.0*shift);
// check only relevant vega
if (numericalVegaPerPoint/swaptionNPV>1.0e-7) {
Real analyticalVegaPerPoint =
swaption->result<Real>("vega")/100.0;
Real discrepancy = std::fabs(analyticalVegaPerPoint
- numericalVegaPerPoint);
discrepancy /= numericalVegaPerPoint;
Real tolerance = 0.015;
if (discrepancy > tolerance)
BOOST_FAIL("failed to compute swaption vega:" <<
"\n option tenor: " << exercises[i] <<
"\n volatility: " << io::rate(vols[u]) <<
"\n option type: " << swaption->type() <<
"\n swap tenor: " << lengths[j] <<
"\n strike: " << io::rate(strikes[t]) <<
"\n settlement: " << types[h] <<
"\n nominal: " << swaption->underlyingSwap()->nominal() <<
"\n npv: " << swaptionNPV <<
"\n calculated vega: " << analyticalVegaPerPoint <<
"\n expected vega: " << numericalVegaPerPoint <<
"\n discrepancy: " << io::rate(discrepancy) <<
"\n tolerance: " << io::rate(tolerance));
}
}
}
}
}
}
}
void OvernightIndexedSwapTest::testBootstrap() {
BOOST_TEST_MESSAGE("Testing Eonia-swap curve building...");
CommonVars vars;
std::vector<shared_ptr<RateHelper> > eoniaHelpers;
std::vector<shared_ptr<RateHelper> > swap3mHelpers;
shared_ptr<IborIndex> euribor3m(new Euribor3M);
shared_ptr<Eonia> eonia(new Eonia);
for (Size i = 0; i < LENGTH(depositData); i++) {
Real rate = 0.01 * depositData[i].rate;
shared_ptr<SimpleQuote> simple = shared_ptr<SimpleQuote>(new SimpleQuote(rate));
shared_ptr<Quote> quote (simple);
Period term = depositData[i].n * depositData[i].unit;
shared_ptr<RateHelper> helper(new
DepositRateHelper(Handle<Quote>(quote),
term,
depositData[i].settlementDays,
euribor3m->fixingCalendar(),
euribor3m->businessDayConvention(),
euribor3m->endOfMonth(),
euribor3m->dayCounter()));
if (term <= 2*Days)
eoniaHelpers.push_back(helper);
if (term <= 3*Months)
swap3mHelpers.push_back(helper);
}
for (Size i = 0; i < LENGTH(fraData); i++) {
Real rate = 0.01 * fraData[i].rate;
shared_ptr<SimpleQuote> simple = shared_ptr<SimpleQuote>(new SimpleQuote(rate));
shared_ptr<Quote> quote (simple);
shared_ptr<RateHelper> helper(new
FraRateHelper(Handle<Quote>(quote),
fraData[i].nExpiry,
fraData[i].nMaturity,
fraData[i].settlementDays,
euribor3m->fixingCalendar(),
euribor3m->businessDayConvention(),
euribor3m->endOfMonth(),
euribor3m->dayCounter()));
swap3mHelpers.push_back(helper);
}
for (Size i = 0; i < LENGTH(eoniaSwapData); i++) {
Real rate = 0.01 * eoniaSwapData[i].rate;
shared_ptr<SimpleQuote> simple = shared_ptr<SimpleQuote>(new SimpleQuote(rate));
shared_ptr<Quote> quote (simple);
Period term = eoniaSwapData[i].n * eoniaSwapData[i].unit;
shared_ptr<RateHelper> helper(new
OISRateHelper(eoniaSwapData[i].settlementDays,
term,
Handle<Quote>(quote),
eonia));
eoniaHelpers.push_back(helper);
}
for (Size i = 0; i < LENGTH(swapData); i++) {
Real rate = 0.01 * swapData[i].rate;
shared_ptr<SimpleQuote> simple = shared_ptr<SimpleQuote>(new SimpleQuote(rate));
shared_ptr<Quote> quote (simple);
Period tenor = swapData[i].nIndexUnits * swapData[i].indexUnit;
Period term = swapData[i].nTermUnits * swapData[i].termUnit;
shared_ptr<RateHelper> helper(new SwapRateHelper(
Handle<Quote>(quote),
term,
vars.calendar,
vars.fixedSwapFrequency,
vars.fixedSwapConvention,
vars.fixedSwapDayCount,
euribor3m));
if (tenor == 3*Months)
swap3mHelpers.push_back(helper);
}
shared_ptr<PiecewiseFlatForward> eoniaTS(new
PiecewiseFlatForward (vars.today, eoniaHelpers, Actual365Fixed()));
shared_ptr<PiecewiseFlatForward> swapTS(new
PiecewiseFlatForward (vars.today, swap3mHelpers, Actual365Fixed()));
vars.eoniaTermStructure.linkTo(eoniaTS);
/*
std::cout.setf (std::ios::fixed, std::ios::floatfield);
std::cout.setf (std::ios::showpoint);
*/
// test curve consistency
Real tolerance = 1.0e-8;
for (Size i = 0; i < LENGTH(eoniaSwapData); i++) {
Rate expected = eoniaSwapData[i].rate;
Period term = eoniaSwapData[i].n * eoniaSwapData[i].unit;
shared_ptr<OvernightIndexedSwap> swap = vars.makeSwap(term, 0.0, 0.0);
Rate calculated = 100.0 * swap->fairRate();
Rate error = std::fabs(expected-calculated);
if (error>tolerance)
BOOST_FAIL("curve inconsistency:" << std::setprecision(10) <<
"\n swap length: " << term <<
"\n quoted rate: " << expected <<
"\n calculated rate: " << calculated <<
"\n error: " << error <<
"\n tolerance: " << tolerance);
}
// zero spread
/*
std::cout << "zero spread:" << std::endl;
std::cout << "years date zero3m/% zero1d/% spread/bp" << std::endl;
DayCounter dc = Actual365Fixed();
for (Size i = 1; i <= 10; i++) {
Date d = vars.today + i*Years;
Rate zero1d = eoniaTS->zeroRate(d, dc, Continuous, Annual,false).rate();
Rate zero3m = swapTS->zeroRate(d, dc, Continuous, Annual,false).rate();
std::cout << std::setw(2) << i << "y " << io::iso_date(d) << " "
<< std::setprecision(3)
<< zero3m * 100.0 << " "
<< zero1d * 100.0 << " "
<< std::setprecision(1)
<< (zero3m - zero1d) * 10000.0 << std::endl;
}
*/
}
void SwaptionVolatilityMatrixTest::testSwaptionVolMatrixObservability() {
BOOST_TEST_MESSAGE("Testing swaption volatility matrix observability...");
CommonVars vars;
boost::shared_ptr<SwaptionVolatilityMatrix> vol;
std::string description;
//floating reference date, floating market data
description = "floating reference date, floating market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeObservabilityTest(description, vol, true, true);
//fixed reference date, floating market data
description = "fixed reference date, floating market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(Settings::instance().evaluationDate(),
vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeObservabilityTest(description, vol, true, false);
// floating reference date, fixed market data
description = "floating reference date, fixed market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeObservabilityTest(description, vol, false, true);
// fixed reference date, fixed market data
description = "fixed reference date, fixed market data";
vol = boost::shared_ptr<SwaptionVolatilityMatrix>(new
SwaptionVolatilityMatrix(Settings::instance().evaluationDate(),
vars.conventions.calendar,
vars.conventions.optionBdc,
vars.atm.tenors.options,
vars.atm.tenors.swaps,
vars.atm.volsHandle,
vars.conventions.dayCounter));
vars.makeObservabilityTest(description, vol, false, false);
// fixed reference date and fixed market data, option dates
//SwaptionVolatilityMatrix(const Date& referenceDate,
// const std::vector<Date>& exerciseDates,
// const std::vector<Period>& swapTenors,
// const Matrix& volatilities,
// const DayCounter& dayCounter);
}
void BermudanSwaptionTest::testCachedValues() {
BOOST_MESSAGE("Testing Bermudan swaption against cached values...");
CommonVars vars;
vars.today = Date(15, February, 2002);
Settings::instance().evaluationDate() = vars.today;
vars.settlement = Date(19, February, 2002);
// flat yield term structure impling 1x5 swap at 5%
vars.termStructure.linkTo(flatRate(vars.settlement,
0.04875825,
Actual365Fixed()));
Rate atmRate = vars.makeSwap(0.0)->fairRate();
boost::shared_ptr<VanillaSwap> itmSwap = vars.makeSwap(0.8*atmRate);
boost::shared_ptr<VanillaSwap> atmSwap = vars.makeSwap(atmRate);
boost::shared_ptr<VanillaSwap> otmSwap = vars.makeSwap(1.2*atmRate);
Real a = 0.048696, sigma = 0.0058904;
boost::shared_ptr<ShortRateModel> model(new HullWhite(vars.termStructure,
a, sigma));
std::vector<Date> exerciseDates;
const Leg& leg = atmSwap->fixedLeg();
for (Size i=0; i<leg.size(); i++) {
boost::shared_ptr<Coupon> coupon =
boost::dynamic_pointer_cast<Coupon>(leg[i]);
exerciseDates.push_back(coupon->accrualStartDate());
}
boost::shared_ptr<Exercise> exercise(new BermudanExercise(exerciseDates));
boost::shared_ptr<PricingEngine> engine(new TreeSwaptionEngine(model, 50));
#if defined(QL_USE_INDEXED_COUPON)
Real itmValue = 42.2413, atmValue = 12.8789, otmValue = 2.4759;
#else
Real itmValue = 42.2470, atmValue = 12.8826, otmValue = 2.4769;
#endif
Real tolerance = 1.0e-4;
Swaption swaption(itmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-itmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached in-the-money swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << itmValue);
swaption = Swaption(atmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-atmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached at-the-money swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << atmValue);
swaption = Swaption(otmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-otmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached out-of-the-money "
<< "swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << otmValue);
for (Size j=0; j<exerciseDates.size(); j++)
exerciseDates[j] = vars.calendar.adjust(exerciseDates[j]-10);
exercise =
boost::shared_ptr<Exercise>(new BermudanExercise(exerciseDates));
#if defined(QL_USE_INDEXED_COUPON)
itmValue = 42.1917; atmValue = 12.7788; otmValue = 2.4388;
#else
itmValue = 42.1974; atmValue = 12.7825; otmValue = 2.4399;
#endif
swaption = Swaption(itmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-itmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached in-the-money swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << itmValue);
swaption = Swaption(atmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-atmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached at-the-money swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << atmValue);
swaption = Swaption(otmSwap, exercise);
swaption.setPricingEngine(engine);
if (std::fabs(swaption.NPV()-otmValue) > tolerance)
BOOST_ERROR("failed to reproduce cached out-of-the-money "
<< "swaption value:\n"
<< "calculated: " << swaption.NPV() << "\n"
<< "expected: " << otmValue);
}
void SwaptionTest::testImpliedVolatility() {
BOOST_MESSAGE("Testing implied volatility for swaptions...");
CommonVars vars;
Size maxEvaluations = 100;
Real tolerance = 1.0e-08;
Settlement::Type types[] = { Settlement::Physical, Settlement::Cash };
// test data
Rate strikes[] = { 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 (Size i=0; i<LENGTH(exercises); i++) {
for (Size j=0; j<LENGTH(lengths); j++) {
Date exerciseDate = vars.calendar.advance(vars.today,exercises[i]);
Date startDate = vars.calendar.advance(exerciseDate,
vars.settlementDays, Days);
for (Size t=0; t<LENGTH(strikes); t++) {
for (Size k=0; k<LENGTH(type); k++) {
boost::shared_ptr<VanillaSwap> swap =
MakeVanillaSwap(lengths[j], vars.index, strikes[t])
.withEffectiveDate(startDate)
.withFloatingLegSpread(0.0)
.withType(type[k]);
for (Size h=0; h<LENGTH(types); h++) {
for (Size u=0; u<LENGTH(vols); u++) {
boost::shared_ptr<Swaption> swaption =
vars.makeSwaption(swap, exerciseDate,
vols[u], types[h]);
// Black price
Real value = swaption->NPV();
Volatility implVol = 0.0;
try {
implVol =
swaption->impliedVolatility(value,
vars.termStructure,
0.10,
tolerance,
maxEvaluations);
} catch (std::exception& e) {
// couldn't bracket?
swaption->setPricingEngine(vars.makeEngine(0.0));
Real value2 = swaption->NPV();
if (std::fabs(value-value2) < tolerance) {
// ok, just skip:
continue;
}
// otherwise, report error
BOOST_ERROR("implied vol failure: " <<
exercises[i] << "x" << lengths[j] << " " << type[k] <<
"\nsettlement: " << types[h] <<
"\nstrike " << strikes[t] <<
"\natm level: " << io::rate(swap->fairRate()) <<
"\nvol: " << io::volatility(vols[u]) <<
"\nprice: " << value <<
"\n" << e.what());
}
if (std::fabs(implVol-vols[u]) > tolerance) {
// the difference might not matter
swaption->setPricingEngine(vars.makeEngine(implVol));
Real value2 = swaption->NPV();
if (std::fabs(value-value2) > tolerance) {
BOOST_ERROR("implied vol failure: " <<
exercises[i] << "x" << lengths[j] << " " << type[k] <<
"\nsettlement: " << types[h] <<
"\nstrike " << strikes[t] <<
"\natm level: " << io::rate(swap->fairRate()) <<
"\nvol: " << io::volatility(vols[u]) <<
"\nprice: " << value <<
"\nimplied vol: " << io::volatility(implVol) <<
"\nimplied price: " << value2);
}
}
}
}
}
}
}
}
}
void OptionletStripperTest::testTermVolatilityStripping2() {
BOOST_TEST_MESSAGE(
"Testing forward/forward vol stripping from non-flat term vol "
"surface using OptionletStripper2 class...");
CommonVars vars;
Settings::instance().evaluationDate() = Date::todaysDate();
vars.setCapFloorTermVolCurve();
vars.setCapFloorTermVolSurface();
shared_ptr<IborIndex> iborIndex(new Euribor6M(vars.yieldTermStructure));
// optionletstripper1
boost::shared_ptr<OptionletStripper1> optionletStripper1(new
OptionletStripper1(vars.capFloorVolSurface,
iborIndex,
Null<Rate>(),
vars.accuracy));
boost::shared_ptr<StrippedOptionletAdapter> strippedOptionletAdapter1 =
boost::shared_ptr<StrippedOptionletAdapter>(new
StrippedOptionletAdapter(optionletStripper1));
Handle<OptionletVolatilityStructure> vol1(strippedOptionletAdapter1);
vol1->enableExtrapolation();
// optionletstripper2
boost::shared_ptr<OptionletStripper> optionletStripper2(new
OptionletStripper2(optionletStripper1,
vars.capFloorVolCurve));
boost::shared_ptr<StrippedOptionletAdapter> strippedOptionletAdapter2(new
StrippedOptionletAdapter(optionletStripper2));
Handle<OptionletVolatilityStructure> vol2(strippedOptionletAdapter2);
vol2->enableExtrapolation();
// consistency check: diff(stripped vol1-stripped vol2)
for (Size strikeIndex=0; strikeIndex<vars.strikes.size(); ++strikeIndex) {
for (Size tenorIndex=0; tenorIndex<vars.optionTenors.size(); ++tenorIndex) {
Volatility strippedVol1 = vol1->volatility(vars.optionTenors[tenorIndex],
vars.strikes[strikeIndex], true);
Volatility strippedVol2 = vol2->volatility(vars.optionTenors[tenorIndex],
vars.strikes[strikeIndex], true);
// vol from flat vol surface (for comparison only)
Volatility flatVol = vars.capFloorVolSurface->volatility(vars.optionTenors[tenorIndex],
vars.strikes[strikeIndex], true);
Real error = std::fabs(strippedVol1-strippedVol2);
if (error>vars.tolerance)
BOOST_FAIL("\noption tenor: " << vars.optionTenors[tenorIndex] <<
"\nstrike: " << io::rate(vars.strikes[strikeIndex]) <<
"\nstripped vol1: " << io::rate(strippedVol1) <<
"\nstripped vol2: " << io::rate(strippedVol2) <<
"\nflat vol: " << io::rate(flatVol) <<
"\nerror: " << io::rate(error) <<
"\ntolerance: " << io::rate(vars.tolerance));
}
}
}
void CapFloorTest::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 (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(vols); j++) {
// store the results for different strikes...
std::vector<Real> cap_values, floor_values;
for (Size k=0; k<LENGTH(strikes); k++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
strikes[k],vols[j]);
cap_values.push_back(cap->NPV());
boost::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
strikes[k],vols[j]);
floor_values.push_back(floor->NPV());
}
// and check that they go the right way
std::vector<Real>::iterator it =
std::adjacent_find(cap_values.begin(),cap_values.end(),
std::less<Real>());
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[j]) << "\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<Real>());
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[j]) << "\n"
<< " value: " << floor_values[n]
<< " at strike: " << io::rate(strikes[n]) << "\n"
<< " value: " << floor_values[n+1]
<< " at strike: " << io::rate(strikes[n+1]));
}
}
}
}
void OptionletStripperTest::testTermVolatilityStrippingShiftedLogNormalVol() {
BOOST_TEST_MESSAGE(
"Testing forward/forward vol stripping from non-flat normal vol term "
"vol surface for normal vol setup using OptionletStripper1 class...");
CommonVars vars;
Real shift = 0.03;
Settings::instance().evaluationDate() = Date(30, April, 2015);
vars.setRealCapFloorTermVolSurface();
shared_ptr< IborIndex > iborIndex(new Euribor6M(vars.forwardingYTS));
boost::shared_ptr< OptionletStripper > optionletStripper1(
new OptionletStripper1(vars.capFloorVolRealSurface, iborIndex,
Null< Rate >(), vars.accuracy, 100,
vars.discountingYTS, ShiftedLognormal, shift,
true));
boost::shared_ptr< StrippedOptionletAdapter > strippedOptionletAdapter =
boost::shared_ptr< StrippedOptionletAdapter >(
new StrippedOptionletAdapter(optionletStripper1));
Handle< OptionletVolatilityStructure > vol(strippedOptionletAdapter);
vol->enableExtrapolation();
boost::shared_ptr< BlackCapFloorEngine > strippedVolEngine(
new BlackCapFloorEngine(vars.discountingYTS, vol));
boost::shared_ptr< CapFloor > cap;
for (Size strikeIndex = 0; strikeIndex < vars.strikes.size();
++strikeIndex) {
for (Size tenorIndex = 0; tenorIndex < vars.optionTenors.size();
++tenorIndex) {
cap = MakeCapFloor(CapFloor::Cap, vars.optionTenors[tenorIndex],
iborIndex, vars.strikes[strikeIndex],
0 * Days).withPricingEngine(strippedVolEngine);
Real priceFromStrippedVolatility = cap->NPV();
boost::shared_ptr< PricingEngine >
blackCapFloorEngineConstantVolatility(new BlackCapFloorEngine(
vars.discountingYTS, vars.termV[tenorIndex][strikeIndex],
vars.capFloorVolRealSurface->dayCounter(), shift));
cap->setPricingEngine(blackCapFloorEngineConstantVolatility);
Real priceFromConstantVolatility = cap->NPV();
Real error = std::fabs(priceFromStrippedVolatility -
priceFromConstantVolatility);
if (error > vars.tolerance)
BOOST_FAIL(
"\noption tenor: "
<< vars.optionTenors[tenorIndex] << "\nstrike: "
<< io::rate(vars.strikes[strikeIndex])
<< "\nstripped vol price: "
<< io::rate(priceFromStrippedVolatility)
<< "\nconstant vol price: "
<< io::rate(priceFromConstantVolatility)
<< "\nerror: " << io::rate(error)
<< "\ntolerance: " << io::rate(vars.tolerance));
}
}
}
void CapFloorTest::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 (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(cap_rates); j++) {
for (Size k=0; k<LENGTH(floor_rates); k++) {
for (Size l=0; l<LENGTH(vols); l++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<CapFloor> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
cap_rates[j],vols[l]);
boost::shared_ptr<CapFloor> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
floor_rates[k],vols[l]);
Collar collar(leg,std::vector<Rate>(1,cap_rates[j]),
std::vector<Rate>(1,floor_rates[k]));
collar.setPricingEngine(vars.makeEngine(vols[l]));
if (std::fabs((cap->NPV()-floor->NPV())-collar.NPV()) > 1e-10) {
BOOST_FAIL(
"inconsistency between cap, floor and collar:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[l]) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rates[j]) << "\n"
<< " floor value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rates[k]) << "\n"
<< " collar value: " << collar.NPV());
// test re-composition by optionlets, N.B. two per year
Real capletsNPV = 0.0;
std::vector<boost::shared_ptr<CapFloor> > caplets;
for (Integer m=0; m<lengths[i]*2; m++) {
caplets.push_back(cap->optionlet(m));
caplets[m]->setPricingEngine(vars.makeEngine(vols[l]));
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[l]) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rates[j]) << "\n"
<< " sum of caplets value: " << capletsNPV
<< " at strike (first): " << io::rate(caplets[0]->capRates()[0]) << "\n"
);
}
Real floorletsNPV = 0.0;
std::vector<boost::shared_ptr<CapFloor> > floorlets;
for (Integer m=0; m<lengths[i]*2; m++) {
floorlets.push_back(floor->optionlet(m));
floorlets[m]->setPricingEngine(vars.makeEngine(vols[l]));
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[l]) << "\n"
<< " cap value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rates[j]) << "\n"
<< " sum of floorlets value: " << floorletsNPV
<< " at strike (first): " << io::rate(floorlets[0]->floorRates()[0]) << "\n"
);
}
Real collarletsNPV = 0.0;
std::vector<boost::shared_ptr<CapFloor> > collarlets;
for (Integer m=0; m<lengths[i]*2; m++) {
collarlets.push_back(collar.optionlet(m));
collarlets[m]->setPricingEngine(vars.makeEngine(vols[l]));
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: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[l]) << "\n"
<< " cap value: " << collar.NPV()
<< " at strike floor: " << io::rate(floor_rates[j])
<< " at strike cap: " << io::rate(cap_rates[j]) << "\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"
);
}
}
}
}
}
}
}
void InflationCapFlooredCouponTest::testInstrumentEquality() {
BOOST_MESSAGE("Testing inflation capped/floored coupon against inflation capfloor instrument...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
Rate strikes[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
// yoy inflation vol is generally very low
Volatility vols[] = { 0.001, 0.005, 0.010, 0.015, 0.020 };
// this is model independent
// capped coupon = fwd - cap, and fwd = swap(0)
// floored coupon = fwd + floor
for (Size whichPricer = 0; whichPricer < 3; whichPricer++) {
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(strikes); j++) {
for (Size k=0; k<LENGTH(vols); k++) {
Leg leg = vars.makeYoYLeg(vars.evaluationDate,lengths[i]);
boost::shared_ptr<Instrument> cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,
leg, strikes[j], vols[k], whichPricer);
boost::shared_ptr<Instrument> floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,
leg, strikes[j], vols[k], whichPricer);
Date from = vars.nominalTS->referenceDate();
Date to = from+lengths[i]*Years;
Schedule yoySchedule = MakeSchedule().from(from).to(to)
.withTenor(1*Years)
.withCalendar(UnitedKingdom())
.withConvention(Unadjusted)
.backwards()
;
YearOnYearInflationSwap swap(YearOnYearInflationSwap::Payer,
1000000.0,
yoySchedule,//fixed schedule, but same as yoy
0.0,//strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
0.0, //spread on index
vars.dc,
UnitedKingdom());
Handle<YieldTermStructure> hTS(vars.nominalTS);
boost::shared_ptr<PricingEngine> sppe(new DiscountingSwapEngine(hTS));
swap.setPricingEngine(sppe);
Leg leg2 = vars.makeYoYCapFlooredLeg(whichPricer, from,
lengths[i],
std::vector<Rate>(lengths[i],strikes[j]),//cap
std::vector<Rate>(),//floor
vols[k],
1.0, // gearing
0.0);// spread
Leg leg3 = vars.makeYoYCapFlooredLeg(whichPricer, from,
lengths[i],
std::vector<Rate>(),// cap
std::vector<Rate>(lengths[i],strikes[j]),//floor
vols[k],
1.0, // gearing
0.0);// spread
// N.B. nominals are 10e6
Real capped = CashFlows::npv(leg2,(**vars.nominalTS),false);
if ( fabs(capped - (swap.NPV() - cap->NPV())) > 1.0e-6) {
BOOST_FAIL(
"capped coupon != swap(0) - cap:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " swap value: " << swap.NPV() << "\n"
<< " capped coupon " << capped);
}
// N.B. nominals are 10e6
Real floored = CashFlows::npv(leg3,(**vars.nominalTS),false);
if ( fabs(floored - (swap.NPV() + floor->NPV())) > 1.0e-6) {
BOOST_FAIL(
"floored coupon != swap(0) + floor :\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV() << "\n"
<< " floored coupon " << floored);
}
}
}
}
}
}
void InflationCapFlooredCouponTest::testDecomposition() {
BOOST_MESSAGE("Testing collared coupon against its decomposition...");
CommonVars vars;
Real tolerance = 1e-10;
Real npvVanilla,npvCappedLeg,npvFlooredLeg,npvCollaredLeg,npvCap,npvFloor,npvCollar;
Real error;
Rate floorstrike = 0.05;
Rate capstrike = 0.10;
std::vector<Rate> caps(vars.length,capstrike);
std::vector<Rate> caps0 = std::vector<Rate>();
std::vector<Rate> floors(vars.length,floorstrike);
std::vector<Rate> floors0 = std::vector<Rate>();
Rate gearing_p = Rate(0.5);
Spread spread_p = Spread(0.002);
Rate gearing_n = Rate(-1.5);
Spread spread_n = Spread(0.12);
// fixed leg with zero rate
Leg fixedLeg =
vars.makeFixedLeg(vars.startDate,vars.length);
// floating leg with gearing=1 and spread=0
Leg floatLeg =
vars.makeYoYLeg(vars.startDate,vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
Leg floatLeg_p =
vars.makeYoYLeg(vars.startDate,vars.length,gearing_p,spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
Leg floatLeg_n =
vars.makeYoYLeg(vars.startDate,vars.length,gearing_n,spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg(fixedLeg,floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p(fixedLeg,floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n(fixedLeg,floatLeg_n);
boost::shared_ptr<PricingEngine> engine(
new DiscountingSwapEngine(vars.nominalTS));
vanillaLeg.setPricingEngine(engine); // here use the autoset feature
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
// CAPPED coupon - Decomposition of payoff
// Payoff = Nom * Min(rate,strike) * accrualperiod =
// = Nom * [rate + Min(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
// = VanillaFloatingLeg - Call
//
Size whichPricer = 0;
// Case gearing = 1 and spread = 0
Leg cappedLeg =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors0,vars.volatility);
Swap capLeg(fixedLeg,cappedLeg);
capLeg.setPricingEngine(engine);
YoYInflationCap cap(floatLeg, std::vector<Rate>(1, capstrike));
cap.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped Leg: gearing=1, spread=0%, strike=" << capstrike*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - npvCap << "\n" <<
" Diff: " << error );
}
// gearing = 1 and spread = 0
// FLOORED coupon - Decomposition of payoff
// Payoff = Nom * Max(rate,strike) * accrualperiod =
// = Nom * [rate + Max(0,strike-rate)] * accrualperiod =
// = Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
// = VanillaFloatingLeg + Put
//
Leg flooredLeg =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps0,floors,vars.volatility);
Swap floorLeg(fixedLeg,flooredLeg);
floorLeg.setPricingEngine(engine);
YoYInflationFloor floor(floatLeg, std::vector<Rate>(1, floorstrike));
floor.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = std::abs(npvFlooredLeg-(npvVanilla + npvFloor));
if (error>tolerance) {
BOOST_ERROR("YoY Floored Leg: gearing=1, spread=0%, strike=" << floorstrike *100 <<
"%\n" <<
" Floored Floating Leg NPV: " << npvFlooredLeg << "\n" <<
" Floating Leg NPV + Floor NPV: " << npvVanilla + npvFloor << "\n" <<
" Diff: " << error );
}
// gearing = 1 and spread = 0
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
// = VanillaFloatingLeg - Collar
//
Leg collaredLeg =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors,vars.volatility);
Swap collarLeg(fixedLeg,collaredLeg);
collarLeg.setPricingEngine(engine);
YoYInflationCollar collar(floatLeg,
std::vector<Rate>(1, capstrike),
std::vector<Rate>(1, floorstrike));
collar.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = std::abs(npvCollaredLeg -(npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nYoY Collared Leg: gearing=1, spread=0%, strike=" <<
floorstrike*100 << "% and " << capstrike*100 << "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg << "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - npvCollar << "\n" <<
" Diff: " << error );
}
// gearing = a and spread = b
// CAPPED coupon - Decomposition of payoff
// Payoff
// = Nom * Min(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg + Put(|a|*rate+b,strike)
//
// Positive gearing
Leg cappedLeg_p =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_p,spread_p);
Swap capLeg_p(fixedLeg,cappedLeg_p);
capLeg_p.setPricingEngine(engine);
YoYInflationCap cap_p(floatLeg_p,std::vector<Rate>(1,capstrike));
cap_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped Leg: gearing=" << gearing_p << ", " <<
"spread= " << spread_p *100 <<
"%, strike=" << capstrike*100 << "%, " <<
"effective strike= " << (capstrike-spread_p)/gearing_p*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" Vanilla Leg NPV: " << npvVanilla << "\n" <<
" Cap NPV: " << npvCap << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - npvCap << "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg cappedLeg_n =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_n,spread_n);
Swap capLeg_n(fixedLeg,cappedLeg_n);
capLeg_n.setPricingEngine(engine);
YoYInflationFloor floor_n(floatLeg,std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
floor_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = std::abs(npvCappedLeg - (npvVanilla+ gearing_n*npvFloor));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped Leg: gearing=" << gearing_n << ", " <<
"spread= " << spread_n *100 <<
"%, strike=" << capstrike*100 << "%, " <<
"effective strike= " << (capstrike-spread_n)/gearing_n*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" npv Vanilla: " << npvVanilla << "\n" <<
" npvFloor: " << npvFloor << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla + gearing_n*npvFloor << "\n" <<
" Diff: " << error );
}
// gearing = a and spread = b
// FLOORED coupon - Decomposition of payoff
// Payoff
// = Nom * Max(a*rate+b,strike) * accrualperiod =
// = Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
// = Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
// = VanillaFloatingLeg - Call(|a|*rate+b,strike)
//
// Positive gearing
Leg flooredLeg_p1 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_p,spread_p);
Swap floorLeg_p1(fixedLeg,flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
YoYInflationFloor floor_p1(floatLeg_p,std::vector<Rate>(1,floorstrike));
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = std::abs(npvFlooredLeg - (npvVanilla+npvFloor));
if (error>tolerance) {
BOOST_ERROR("\nYoY Floored Leg: gearing=" << gearing_p << ", "
<< "spread= " << spread_p *100<< "%, strike=" << floorstrike *100 << "%, "
<< "effective strike= " << (floorstrike-spread_p)/gearing_p*100
<< "%\n" <<
" Floored Floating Leg NPV: " << npvFlooredLeg
<< "\n" <<
" Floating Leg NPV + Floor NPV: " << npvVanilla + npvFloor
<< "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg flooredLeg_n =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_n,spread_n);
Swap floorLeg_n(fixedLeg,flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
YoYInflationCap cap_n(floatLeg,std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n));
cap_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = std::abs(npvFlooredLeg - (npvVanilla - gearing_n*npvCap));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped Leg: gearing=" << gearing_n << ", " <<
"spread= " << spread_n *100 <<
"%, strike=" << floorstrike*100 << "%, " <<
"effective strike= " << (floorstrike-spread_n)/gearing_n*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvFlooredLeg << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - gearing_n*npvCap << "\n" <<
" Diff: " << error );
}
// gearing = a and spread = b
// COLLARED coupon - Decomposition of payoff
// Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
// --> If a>0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
// --> If a<0 (assuming positive effective strike):
// Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
//
// Positive gearing
Leg collaredLeg_p =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_p,spread_p);
Swap collarLeg_p1(fixedLeg,collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
YoYInflationCollar collar_p(floatLeg_p,
std::vector<Rate>(1,capstrike),
std::vector<Rate>(1,floorstrike));
collar_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = std::abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nYoY Collared Leg: gearing=" << gearing_p << ", "
<< "spread= " << spread_p*100 << "%, strike="
<< floorstrike*100 << "% and " << capstrike*100
<< "%, "
<< "effective strike=" << (floorstrike-spread_p)/gearing_p*100
<< "% and " << (capstrike-spread_p)/gearing_p*100
<< "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg
<< "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - npvCollar
<< "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg collaredLeg_n =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_n,spread_n);
Swap collarLeg_n1(fixedLeg,collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
YoYInflationCollar collar_n(floatLeg,
std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n),
std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
collar_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = std::abs(npvCollaredLeg - (npvVanilla - gearing_n*npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nYoY Collared Leg: gearing=" << gearing_n << ", "
<< "spread= " << spread_n*100 << "%, strike="
<< floorstrike*100 << "% and " << capstrike*100
<< "%, "
<< "effective strike=" << (floorstrike-spread_n)/gearing_n*100
<< "% and " << (capstrike-spread_n)/gearing_n*100
<< "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg
<< "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - gearing_n*npvCollar
<< "\n" <<
" Diff: " << error );
}
}
void SwaptionTest::testSpreadTreatment() {
BOOST_MESSAGE("Testing swaption treatment of spread...");
CommonVars vars;
Spread spreads[] = { -0.002, -0.001, 0.0, 0.001, 0.002 };
for (Size i=0; i<LENGTH(exercises); i++) {
for (Size j=0; j<LENGTH(lengths); j++) {
for (Size k=0; k<LENGTH(type); k++) {
Date exerciseDate = vars.calendar.advance(vars.today,
exercises[i]);
Date startDate =
vars.calendar.advance(exerciseDate,
vars.settlementDays,Days);
for (Size l=0; l<LENGTH(spreads); l++) {
boost::shared_ptr<VanillaSwap> swap =
MakeVanillaSwap(lengths[j], vars.index, 0.06)
.withEffectiveDate(startDate)
.withFloatingLegSpread(spreads[l])
.withType(type[k]);
// FLOATING_POINT_EXCEPTION
Spread correction = spreads[l] *
swap->floatingLegBPS() /
swap->fixedLegBPS();
boost::shared_ptr<VanillaSwap> equivalentSwap =
MakeVanillaSwap(lengths[j], vars.index, 0.06+correction)
.withEffectiveDate(startDate)
.withFloatingLegSpread(0.0)
.withType(type[k]);
boost::shared_ptr<Swaption> swaption1 =
vars.makeSwaption(swap,exerciseDate,0.20);
boost::shared_ptr<Swaption> swaption2 =
vars.makeSwaption(equivalentSwap,exerciseDate,0.20);
boost::shared_ptr<Swaption> swaption1_cash =
vars.makeSwaption(swap,exerciseDate,0.20,
Settlement::Cash);
boost::shared_ptr<Swaption> swaption2_cash =
vars.makeSwaption(equivalentSwap,exerciseDate,0.20,
Settlement::Cash);
if (std::fabs(swaption1->NPV()-swaption2->NPV()) > 1.0e-6)
BOOST_ERROR("wrong spread treatment:" <<
"\nexercise: " << exerciseDate <<
"\nlength: " << lengths[j] <<
"\ntype " << type[k] <<
"\nspread: " << io::rate(spreads[l]) <<
"\noriginal swaption value: " << swaption1->NPV() <<
"\nequivalent swaption value: " << swaption2->NPV());
if (std::fabs(swaption1_cash->NPV()-swaption2_cash->NPV()) > 1.0e-6)
BOOST_ERROR("wrong spread treatment:" <<
"\nexercise date: " << exerciseDate <<
"\nlength: " << lengths[j] <<
"\npay " << (type[k] ? "fixed" : "floating") <<
"\nspread: " << io::rate(spreads[l]) <<
"\nvalue of original swaption: " << swaption1_cash->NPV() <<
"\nvalue of equivalent swaption: " << swaption2_cash->NPV());
}
}
}
}
}