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);
}
}
}
}
}
}
// Test inflation cap/floor parity, i.e. that cap-floor = swap, note that this
// is different from nominal because in nominal world standard cap/floors do
// not have the first optionlet. This is because they set in advance so
// there is no point. However, yoy inflation generally sets in arrears,
// (actually in arrears with a lag of a few months) thus the first optionlet
// is relevant. Hence we can do a parity test without a special definition
// of the YoY cap/floor instrument.
void InflationCapFloorTest::testParity() {
BOOST_TEST_MESSAGE("Testing yoy inflation cap/floor parity...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
Rate strikes[] = { 0., 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 };
// cap-floor-swap parity is model-independent
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]);
ext::shared_ptr<Instrument> cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,
leg, strikes[j], vols[k], whichPricer);
ext::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
strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
0.0, //spread on index
vars.dc,
UnitedKingdom());
Handle<YieldTermStructure> hTS(vars.nominalTS);
ext::shared_ptr<PricingEngine> sppe(new DiscountingSwapEngine(hTS));
swap.setPricingEngine(sppe);
// N.B. nominals are 10e6
if (std::fabs((cap->NPV()-floor->NPV()) - swap.NPV()) > 1.0e-6) {
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());
}
}
}
}
}
// remove circular refernce
vars.hy.linkTo(ext::shared_ptr<YoYInflationTermStructure>());
}
void InflationCapFloorTest::testCachedValue() {
BOOST_TEST_MESSAGE("Testing Black yoy inflation cap/floor price"
" against cached values...");
CommonVars vars;
Size whichPricer = 0; // black
Real K = 0.0295; // one centi-point is fair rate error i.e. < 1 cp
Size j = 2;
Leg leg = vars.makeYoYLeg(vars.evaluationDate,j);
ext::shared_ptr<Instrument> cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
ext::shared_ptr<Instrument> floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVblack = 219.452;
Real cachedFloorNPVblack = 314.641;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVblack)<0.02,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVblack<<" Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVblack)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVblack)<0.02,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVblack<<" Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVblack)));
whichPricer = 1; // dd
cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVdd = 9114.61;
Real cachedFloorNPVdd = 9209.8;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVdd)<0.22,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVdd<<" dd Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVdd)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVdd)<0.22,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVdd<<" dd Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVdd)));
whichPricer = 2; // bachelier
cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVbac = 8852.4;
Real cachedFloorNPVbac = 8947.59;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVbac)<0.22,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVbac<<" bac Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVbac)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVbac)<0.22,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVbac<<" bac Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVbac)));
// remove circular refernce
vars.hy.linkTo(ext::shared_ptr<YoYInflationTermStructure>());
}
void InflationCapFloorTest::testConsistency() {
BOOST_TEST_MESSAGE("Testing consistency between yoy inflation cap,"
" floor and collar...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate cap_rates[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
Rate floor_rates[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
Volatility vols[] = { 0.001, 0.005, 0.010, 0.015, 0.020 };
for (Size whichPricer = 0; whichPricer < 3; whichPricer++) {
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.makeYoYLeg(vars.evaluationDate,lengths[i]);
ext::shared_ptr<YoYInflationCapFloor> cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,
leg, cap_rates[j], vols[l], whichPricer);
ext::shared_ptr<YoYInflationCapFloor> floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,
leg, floor_rates[k], vols[l], whichPricer);
YoYInflationCollar collar(leg,std::vector<Rate>(1,cap_rates[j]),
std::vector<Rate>(1,floor_rates[k]));
collar.setPricingEngine(vars.makeEngine(vols[l], whichPricer));
if (std::fabs((cap->NPV()-floor->NPV())-collar.NPV()) > 1e-6) {
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. ONE per year
Real capletsNPV = 0.0;
std::vector<ext::shared_ptr<YoYInflationCapFloor> > caplets;
for (Integer m=0; m<lengths[i]*1; m++) {
caplets.push_back(cap->optionlet(m));
caplets[m]->setPricingEngine(vars.makeEngine(vols[l], whichPricer));
capletsNPV += caplets[m]->NPV();
}
if (std::fabs(cap->NPV() - capletsNPV) > 1e-6) {
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<ext::shared_ptr<YoYInflationCapFloor> > floorlets;
for (Integer m=0; m<lengths[i]*1; m++) {
floorlets.push_back(floor->optionlet(m));
floorlets[m]->setPricingEngine(vars.makeEngine(vols[l], whichPricer));
floorletsNPV += floorlets[m]->NPV();
}
if (std::fabs(floor->NPV() - floorletsNPV) > 1e-6) {
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<ext::shared_ptr<YoYInflationCapFloor> > collarlets;
for (Integer m=0; m<lengths[i]*1; m++) {
collarlets.push_back(collar.optionlet(m));
collarlets[m]->setPricingEngine(vars.makeEngine(vols[l], whichPricer));
collarletsNPV += collarlets[m]->NPV();
}
if (std::fabs(collar.NPV() - collarletsNPV) > 1e-6) {
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"
);
}
}
}
}
}
}
} // pricer loop
// remove circular refernce
vars.hy.linkTo(ext::shared_ptr<YoYInflationTermStructure>());
}