CPIBond to price US Treasury TIPS
Posted by ian_dfw on Oct 30, 2015; 8:07pm
URL: http://quantlib.414.s1.nabble.com/CPIBond-to-price-US-Treasury-TIPS-tp17011.html
Hi,
I am new user of Quantlib and now trying to price US Treasury TIPS with the CPIBond class, so I basically try to follow the inflationcpibond sampole C++ code with some modification of dates of settlement and bond start/end dates, also the zcii data. But after such changes, the clean price is only $8.9 when notional is $100. What am I doing wrong?
#include "stdafx.h"
#include <ql/indexes/inflation/ukrpi.hpp>
#include <ql/indexes/inflation/uscpi.hpp>
#include <ql/time/calendars/unitedkingdom.hpp>
#include <ql/time/calendars/unitedstates.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/indexes/ibor/gbplibor.hpp>
#include <ql/termstructures/inflation/inflationhelpers.hpp>
#include <ql/termstructures/inflation/piecewisezeroinflationcurve.hpp>
#include <ql/cashflows/indexedcashflow.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/instruments/zerocouponinflationswap.hpp>
#include <ql/pricingengines/bond/discountingbondengine.hpp>
#include <ql/cashflows/cpicoupon.hpp>
#include <ql/cashflows/cpicouponpricer.hpp>
#include <ql/instruments/cpiswap.hpp>
#include <ql/instruments/bonds/cpibond.hpp>
using namespace QuantLib;
using namespace std;
#include <iostream>
namespace
{
struct Datum
{
Date date;
Rate rate;
};
typedef BootstrapHelper<ZeroInflationTermStructure> Helper;
std::vector<boost::shared_ptr<Helper> > makeHelpers(Datum iiData[],
Size N,
const boost::shared_ptr<ZeroInflationIndex>& ii,
const Period& observationLag,
const Calendar& calendar,
const BusinessDayConvention& bdc,
const DayCounter& dc)
{
std::vector<boost::shared_ptr<Helper>> instruments;
for (Size i = 0; i < N; i++)
{
Date maturity = iiData[i].date;
Handle<Quote> quote(boost::shared_ptr<Quote>(new SimpleQuote(iiData[i].rate / 100.0)));
boost::shared_ptr<Helper> h(
new ZeroCouponInflationSwapHelper(quote,
observationLag,
maturity, calendar,
bdc,
dc,
ii)
);
instruments.push_back(h);
}
return instruments;
}
struct CommonVars
{
Calendar calendar;
BusinessDayConvention convention;
Date evaluationDate;
Period observationLag;
DayCounter dayCounter;
boost::shared_ptr<USCPI> ii;
RelinkableHandle<YieldTermStructure> yTS;
RelinkableHandle<ZeroInflationTermStructure> cpiTS;
// setup
CommonVars()
{
// usual setup
calendar = UnitedStates();
convention = ModifiedFollowing;
Date today(25, Oct, 2015);
evaluationDate = calendar.adjust(today);
Settings::instance().evaluationDate() = evaluationDate;
dayCounter = ActualActual();
Date from(20, Jun, 2013);
Date to(20, Oct, 2015);
Schedule rpiSchedule =
MakeSchedule().from(from).to(to)
.withTenor(1 * Months)
.withCalendar(UnitedStates())
.withConvention(ModifiedFollowing);
bool interp = false;
ii = boost::shared_ptr<USCPI>(new USCPI(interp, cpiTS));
Real fixData[] =
{
206.1, 207.3, 208.0, 208.9, 209.7, 210.9,
209.8, 211.4, 212.1, 214.0, 215.1, 216.8,
216.5, 217.2, 218.4, 217.7, 216,
212.9, 210.1, 211.4, 211.3, 211.5,
212.8, 213.4, 213.4, 213.4, 214.4
/*
237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945,
237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945,
237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945, 237.945
*/
};
for (Size i = 0; i < sizeof(fixData) / sizeof(Real); ++i)
{
ii->addFixing(rpiSchedule[i], fixData[i]);
}
yTS.linkTo(boost::shared_ptr<YieldTermStructure>(new FlatForward(evaluationDate, 0.0075, dayCounter)));
// now build the zero inflation curve
observationLag = Period(2, Months);
Datum zciisData[] =
{
{ Date(25, November, 2010), 0.010 },
{ Date(25, November, 2011), 0.020 },
{ Date(26, November, 2012), 0.030 },
{ Date(25, November, 2013), 0.040 },
{ Date(25, November, 2014), 0.050 },
{ Date(25, November, 2015), 0.500 },
{ Date(25, November, 2016), 0.800 },
{ Date(25, November, 2017), 1.100 },
{ Date(25, November, 2018), 1.500 },
{ Date(25, November, 2019), 1.800 },
{ Date(25, November, 2021), 2.033 },
{ Date(25, November, 2024), 2.133 },
{ Date(26, November, 2029), 2.300 },
{ Date(27, November, 2034), 2.467 },
{ Date(25, November, 2039), 2.633 },
{ Date(25, November, 2049), 2.967 },
{ Date(25, November, 2059), 3.000 },
};
std::vector<boost::shared_ptr<Helper> > helpers =
makeHelpers(zciisData,
sizeof(zciisData) / sizeof(Datum),
ii,
observationLag,
calendar,
convention,
dayCounter);
Rate baseZeroRate = zciisData[0].rate / 100.0;
cpiTS.linkTo(
boost::shared_ptr<ZeroInflationTermStructure>(
new PiecewiseZeroInflationCurve<Linear>(evaluationDate,
calendar,
dayCounter,
observationLag,
ii->frequency(),
ii->interpolated(),
baseZeroRate,
Handle<YieldTermStructure>(yTS),
helpers)
)
);
}
// teardown
~CommonVars()
{
// break circular references and allow curves to be destroyed
cpiTS.linkTo(boost::shared_ptr<ZeroInflationTermStructure>());
}
};
}
void testInflationCleanPrice()
{
CommonVars common;
Real notional = 100.0;
std::vector<Rate> fixedRates(1, 0.02375);
DayCounter fixedDayCount = Actual365Fixed();
BusinessDayConvention fixedPaymentConvention = ModifiedFollowing;
Calendar fixedPaymentCalendar = UnitedStates();
boost::shared_ptr<ZeroInflationIndex> fixedIndex = common.ii;
Period contractObservationLag = Period(1, Months);
CPI::InterpolationType observationInterpolation = CPI::Flat;
Natural settlementDays = 1;
bool growthOnly = true;
Real baseCPI = 206.1;
// set the schedules
Date startDate(15, Jan, 2007);
Date endDate(15, Jan, 2017);
Schedule fixedSchedule =
MakeSchedule().from(startDate).to(endDate)
.withTenor(Period(6, Months))
.withCalendar(UnitedStates())
.withConvention(ModifiedFollowing)
.backwards();
CPIBond bond(settlementDays,
notional,
growthOnly,
baseCPI,
contractObservationLag,
fixedIndex,
observationInterpolation,
fixedSchedule,
fixedRates,
fixedDayCount,
fixedPaymentConvention);
boost::shared_ptr<DiscountingBondEngine> engine(new DiscountingBondEngine(common.yTS));
bond.setPricingEngine(engine);
Real calculated = bond.cleanPrice();
Real tolerance = 1.0e-8;
cout << "NPV: " << bond.NPV() << endl;
cout << "Clean price: " << calculated << endl;
cout << "Dirty price: " << bond.dirtyPrice() << endl;
}