FittedBondCurve.cpp

For a given set of coupons and terms to maturity, this example computes the value of a bond by fitting the yields to a curve using different methods. The fitting methods are exponential splines, simple polynomials, Nelson-Siegel, and cubic B-splines. It then shifts the evaluation date into the future to compute implied forward par rates. It also computes yields after small price shifts.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/* This example shows how to fit a term structure to a set of bonds
using four different fitting methodologies. Though fitting is most
useful for large numbers of bonds with non-smooth yield tenor
structures, for comparison purposes, relatively smooth bond yields
are fit here and compared to known solutions (par coupons), or
results generated from the bootstrap fitting method.
*/
#include <ql/qldefines.hpp>
#ifdef BOOST_MSVC
# include <ql/auto_link.hpp>
#endif
#include <ql/termstructures/yield/fittedbonddiscountcurve.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/bondhelpers.hpp>
#include <ql/termstructures/yield/nonlinearfittingmethods.hpp>
#include <ql/pricingengines/bond/bondfunctions.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
#include <iostream>
#include <iomanip>
#define LENGTH(a) (sizeof(a)/sizeof(a[0]))
using namespace std;
using namespace QuantLib;
#if defined(QL_ENABLE_SESSIONS)
namespace QuantLib {
ThreadKey sessionId() { return 0; }
}
#endif
// par-rate approximation
Rate parRate(const YieldTermStructure& yts,
const std::vector<Date>& dates,
const DayCounter& resultDayCounter) {
QL_REQUIRE(dates.size() >= 2, "at least two dates are required");
Real sum = 0.0;
Time dt;
for (Size i=1; i<dates.size(); ++i) {
dt = resultDayCounter.yearFraction(dates[i-1], dates[i]);
QL_REQUIRE(dt>=0.0, "unsorted dates");
sum += yts.discount(dates[i]) * dt;
}
Real result = yts.discount(dates.front()) - yts.discount(dates.back());
return result/sum;
}
void printOutput(const std::string& tag,
const ext::shared_ptr<FittedBondDiscountCurve>& curve) {
cout << tag << endl;
cout << "reference date : "
<< curve->referenceDate()
<< endl;
cout << "number of iterations : "
<< curve->fitResults().numberOfIterations()
<< endl
<< endl;
}
int main(int, char* []) {
try {
const Size numberOfBonds = 15;
Real cleanPrice[numberOfBonds];
for (Size i=0; i<numberOfBonds; i++) {
cleanPrice[i]=100.0;
}
std::vector< ext::shared_ptr<SimpleQuote> > quote;
for (Size i=0; i<numberOfBonds; i++) {
ext::shared_ptr<SimpleQuote> cp(new SimpleQuote(cleanPrice[i]));
quote.push_back(cp);
}
RelinkableHandle<Quote> quoteHandle[numberOfBonds];
for (Size i=0; i<numberOfBonds; i++) {
quoteHandle[i].linkTo(quote[i]);
}
Integer lengths[] = { 2, 4, 6, 8, 10, 12, 14, 16,
18, 20, 22, 24, 26, 28, 30 };
Real coupons[] = { 0.0200, 0.0225, 0.0250, 0.0275, 0.0300,
0.0325, 0.0350, 0.0375, 0.0400, 0.0425,
0.0450, 0.0475, 0.0500, 0.0525, 0.0550 };
Frequency frequency = Annual;
DayCounter dc = SimpleDayCounter();
BusinessDayConvention accrualConvention = ModifiedFollowing;
BusinessDayConvention convention = ModifiedFollowing;
Real redemption = 100.0;
Calendar calendar = TARGET();
Date today = calendar.adjust(Date::todaysDate());
Date origToday = today;
Settings::instance().evaluationDate() = today;
// changing bondSettlementDays=3 increases calculation
// time of exponentialsplines fitting method
Natural bondSettlementDays = 0;
Natural curveSettlementDays = 0;
Date bondSettlementDate = calendar.advance(today, bondSettlementDays*Days);
cout << endl;
cout << "Today's date: " << today << endl;
cout << "Bonds' settlement date: " << bondSettlementDate << endl;
cout << "Calculating fit for 15 bonds....." << endl << endl;
std::vector<ext::shared_ptr<BondHelper> > instrumentsA;
std::vector<ext::shared_ptr<RateHelper> > instrumentsB;
for (Size j=0; j<LENGTH(lengths); j++) {
Date maturity = calendar.advance(bondSettlementDate, lengths[j]*Years);
Schedule schedule(bondSettlementDate, maturity, Period(frequency),
calendar, accrualConvention, accrualConvention,
DateGeneration::Backward, false);
ext::shared_ptr<BondHelper> helperA(
new FixedRateBondHelper(quoteHandle[j],
bondSettlementDays,
100.0,
schedule,
std::vector<Rate>(1,coupons[j]),
dc,
convention,
redemption));
ext::shared_ptr<RateHelper> helperB(
new FixedRateBondHelper(quoteHandle[j],
bondSettlementDays,
100.0,
schedule,
std::vector<Rate>(1, coupons[j]),
dc,
convention,
redemption));
instrumentsA.push_back(helperA);
instrumentsB.push_back(helperB);
}
bool constrainAtZero = true;
Real tolerance = 1.0e-10;
Size max = 5000;
ext::shared_ptr<YieldTermStructure> ts0 (
new PiecewiseYieldCurve<Discount,LogLinear>(curveSettlementDays,
calendar,
instrumentsB,
dc));
ExponentialSplinesFitting exponentialSplines(constrainAtZero);
ext::shared_ptr<FittedBondDiscountCurve> ts1 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
exponentialSplines,
tolerance,
max));
printOutput("(a) exponential splines", ts1);
SimplePolynomialFitting simplePolynomial(3, constrainAtZero);
ext::shared_ptr<FittedBondDiscountCurve> ts2 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
simplePolynomial,
tolerance,
max));
printOutput("(b) simple polynomial", ts2);
NelsonSiegelFitting nelsonSiegel;
ext::shared_ptr<FittedBondDiscountCurve> ts3 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
nelsonSiegel,
tolerance,
max));
printOutput("(c) Nelson-Siegel", ts3);
// a cubic bspline curve with 11 knot points, implies
// n=6 (constrained problem) basis functions
Time knots[] = { -30.0, -20.0, 0.0, 5.0, 10.0, 15.0,
20.0, 25.0, 30.0, 40.0, 50.0 };
std::vector<Time> knotVector;
for (Size i=0; i< LENGTH(knots); i++) {
knotVector.push_back(knots[i]);
}
CubicBSplinesFitting cubicBSplines(knotVector, constrainAtZero);
ext::shared_ptr<FittedBondDiscountCurve> ts4 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
cubicBSplines,
tolerance,
max));
printOutput("(d) cubic B-splines", ts4);
SvenssonFitting svensson;
ext::shared_ptr<FittedBondDiscountCurve> ts5 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
svensson,
tolerance,
max));
printOutput("(e) Svensson", ts5);
Handle<YieldTermStructure> discountCurve(
ext::make_shared<FlatForward>(
curveSettlementDays, calendar, 0.01, dc));
SpreadFittingMethod nelsonSiegelSpread(
ext::make_shared<NelsonSiegelFitting>(),
discountCurve);
ext::shared_ptr<FittedBondDiscountCurve> ts6 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
nelsonSiegelSpread,
tolerance,
max));
printOutput("(f) Nelson-Siegel spreaded", ts6);
cout << "Output par rates for each curve. In this case, "
<< endl
<< "par rates should equal coupons for these par bonds."
<< endl
<< endl;
cout << setw(6) << "tenor" << " | "
<< setw(6) << "coupon" << " | "
<< setw(6) << "bstrap" << " | "
<< setw(6) << "(a)" << " | "
<< setw(6) << "(b)" << " | "
<< setw(6) << "(c)" << " | "
<< setw(6) << "(d)" << " | "
<< setw(6) << "(e)" << " | "
<< setw(6) << "(f)" << endl;
for (Size i=0; i<instrumentsA.size(); i++) {
std::vector<ext::shared_ptr<CashFlow> > cfs =
instrumentsA[i]->bond()->cashflows();
Size cfSize = instrumentsA[i]->bond()->cashflows().size();
std::vector<Date> keyDates;
keyDates.push_back(bondSettlementDate);
for (Size j=0; j<cfSize-1; j++) {
if (!cfs[j]->hasOccurred(bondSettlementDate, false)) {
Date myDate = cfs[j]->date();
keyDates.push_back(myDate);
}
}
Real tenor = dc.yearFraction(today, cfs[cfSize-1]->date());
cout << setw(6) << fixed << setprecision(3) << tenor << " | "
<< setw(6) << fixed << setprecision(3)
<< 100.*coupons[i] << " | "
// piecewise bootstrap
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts0,keyDates,dc) << " | "
// exponential splines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts1,keyDates,dc) << " | "
// simple polynomial
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts2,keyDates,dc) << " | "
// Nelson-Siegel
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts3,keyDates,dc) << " | "
// cubic bsplines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts4,keyDates,dc) << " | "
// Svensson
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts5,keyDates,dc) << " | "
// Nelson-Siegel Spreaded
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts6,keyDates,dc) << endl;
}
cout << endl << endl << endl;
cout << "Now add 23 months to today. Par rates should be " << endl
<< "automatically recalculated because today's date " << endl
<< "changes. Par rates will NOT equal coupons (YTM " << endl
<< "will, with the correct compounding), but the " << endl
<< "piecewise yield curve par rates can be used as " << endl
<< "a benchmark for correct par rates."
<< endl
<< endl;
today = calendar.advance(origToday,23,Months,convention);
Settings::instance().evaluationDate() = today;
bondSettlementDate = calendar.advance(today, bondSettlementDays*Days);
printOutput("(a) exponential splines", ts1);
printOutput("(b) simple polynomial", ts2);
printOutput("(c) Nelson-Siegel", ts3);
printOutput("(d) cubic B-splines", ts4);
printOutput("(e) Svensson", ts5);
printOutput("(f) Nelson-Siegel spreaded", ts6);
cout << endl
<< endl;
cout << setw(6) << "tenor" << " | "
<< setw(6) << "coupon" << " | "
<< setw(6) << "bstrap" << " | "
<< setw(6) << "(a)" << " | "
<< setw(6) << "(b)" << " | "
<< setw(6) << "(c)" << " | "
<< setw(6) << "(d)" << " | "
<< setw(6) << "(e)" << " | "
<< setw(6) << "(f)" << endl;
for (Size i=0; i<instrumentsA.size(); i++) {
std::vector<ext::shared_ptr<CashFlow> > cfs =
instrumentsA[i]->bond()->cashflows();
Size cfSize = instrumentsA[i]->bond()->cashflows().size();
std::vector<Date> keyDates;
keyDates.push_back(bondSettlementDate);
for (Size j=0; j<cfSize-1; j++) {
if (!cfs[j]->hasOccurred(bondSettlementDate, false)) {
Date myDate = cfs[j]->date();
keyDates.push_back(myDate);
}
}
Real tenor = dc.yearFraction(today, cfs[cfSize-1]->date());
cout << setw(6) << fixed << setprecision(3) << tenor << " | "
<< setw(6) << fixed << setprecision(3)
<< 100.*coupons[i] << " | "
// piecewise bootstrap
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts0,keyDates,dc) << " | "
// exponential splines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts1,keyDates,dc) << " | "
// simple polynomial
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts2,keyDates,dc) << " | "
// Nelson-Siegel
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts3,keyDates,dc) << " | "
// cubic bsplines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts4,keyDates,dc) << " | "
// Svensson
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts5,keyDates,dc) << " | "
// Nelson-Siegel Spreaded
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts6,keyDates,dc) << endl;
}
cout << endl << endl << endl;
cout << "Now add one more month, for a total of two years " << endl
<< "from the original date. The first instrument is " << endl
<< "now expired and par rates should again equal " << endl
<< "coupon values, since clean prices did not change."
<< endl
<< endl;
instrumentsA.erase(instrumentsA.begin(),
instrumentsA.begin()+1);
instrumentsB.erase(instrumentsB.begin(),
instrumentsB.begin()+1);
today = calendar.advance(origToday,24,Months,convention);
Settings::instance().evaluationDate() = today;
bondSettlementDate = calendar.advance(today, bondSettlementDays*Days);
ext::shared_ptr<YieldTermStructure> ts00 (
new PiecewiseYieldCurve<Discount,LogLinear>(curveSettlementDays,
calendar,
instrumentsB,
dc));
ext::shared_ptr<FittedBondDiscountCurve> ts11 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
exponentialSplines,
tolerance,
max));
printOutput("(a) exponential splines", ts11);
ext::shared_ptr<FittedBondDiscountCurve> ts22 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
simplePolynomial,
tolerance,
max));
printOutput("(b) simple polynomial", ts22);
ext::shared_ptr<FittedBondDiscountCurve> ts33 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
nelsonSiegel,
tolerance,
max));
printOutput("(c) Nelson-Siegel", ts33);
ext::shared_ptr<FittedBondDiscountCurve> ts44 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
cubicBSplines,
tolerance,
max));
printOutput("(d) cubic B-splines", ts44);
ext::shared_ptr<FittedBondDiscountCurve> ts55 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
svensson,
tolerance,
max));
printOutput("(e) Svensson", ts55);
ext::shared_ptr<FittedBondDiscountCurve> ts66 (
new FittedBondDiscountCurve(curveSettlementDays,
calendar,
instrumentsA,
dc,
nelsonSiegelSpread,
tolerance,
max));
printOutput("(f) Nelson-Siegel spreaded", ts66);
cout << setw(6) << "tenor" << " | "
<< setw(6) << "coupon" << " | "
<< setw(6) << "bstrap" << " | "
<< setw(6) << "(a)" << " | "
<< setw(6) << "(b)" << " | "
<< setw(6) << "(c)" << " | "
<< setw(6) << "(d)" << " | "
<< setw(6) << "(e)" << " | "
<< setw(6) << "(f)" << endl;
for (Size i=0; i<instrumentsA.size(); i++) {
std::vector<ext::shared_ptr<CashFlow> > cfs =
instrumentsA[i]->bond()->cashflows();
Size cfSize = instrumentsA[i]->bond()->cashflows().size();
std::vector<Date> keyDates;
keyDates.push_back(bondSettlementDate);
for (Size j=0; j<cfSize-1; j++) {
if (!cfs[j]->hasOccurred(bondSettlementDate, false)) {
Date myDate = cfs[j]->date();
keyDates.push_back(myDate);
}
}
Real tenor = dc.yearFraction(today, cfs[cfSize-1]->date());
cout << setw(6) << fixed << setprecision(3) << tenor << " | "
<< setw(6) << fixed << setprecision(3)
<< 100.*coupons[i+1] << " | "
// piecewise bootstrap
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts00,keyDates,dc) << " | "
// exponential splines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts11,keyDates,dc) << " | "
// simple polynomial
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts22,keyDates,dc) << " | "
// Nelson-Siegel
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts33,keyDates,dc) << " | "
// cubic bsplines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts44,keyDates,dc) << " | "
// Svensson
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts55,keyDates,dc) << " | "
// Nelson-Siegel Spreaded
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts66,keyDates,dc) << endl;
}
cout << endl << endl << endl;
cout << "Now decrease prices by a small amount, corresponding" << endl
<< "to a theoretical five basis point parallel + shift of" << endl
<< "the yield curve. Because bond quotes change, the new " << endl
<< "par rates should be recalculated automatically."
<< endl
<< endl;
for (Size k=0; k<LENGTH(lengths)-1; k++) {
Real P = instrumentsA[k]->quote()->value();
const Bond& b = *instrumentsA[k]->bond();
Rate ytm = BondFunctions::yield(b, P,
dc, Compounded, frequency,
today);
Time dur = BondFunctions::duration(b, ytm,
dc, Compounded, frequency,
Duration::Modified,
today);
const Real bpsChange = 5.;
// dP = -dur * P * dY
Real deltaP = -dur * P * (bpsChange/10000.);
quote[k+1]->setValue(P + deltaP);
}
cout << setw(6) << "tenor" << " | "
<< setw(6) << "coupon" << " | "
<< setw(6) << "bstrap" << " | "
<< setw(6) << "(a)" << " | "
<< setw(6) << "(b)" << " | "
<< setw(6) << "(c)" << " | "
<< setw(6) << "(d)" << " | "
<< setw(6) << "(e)" << " | "
<< setw(6) << "(f)" << endl;
for (Size i=0; i<instrumentsA.size(); i++) {
std::vector<ext::shared_ptr<CashFlow> > cfs =
instrumentsA[i]->bond()->cashflows();
Size cfSize = instrumentsA[i]->bond()->cashflows().size();
std::vector<Date> keyDates;
keyDates.push_back(bondSettlementDate);
for (Size j=0; j<cfSize-1; j++) {
if (!cfs[j]->hasOccurred(bondSettlementDate, false)) {
Date myDate = cfs[j]->date();
keyDates.push_back(myDate);
}
}
Real tenor = dc.yearFraction(today, cfs[cfSize-1]->date());
cout << setw(6) << fixed << setprecision(3) << tenor << " | "
<< setw(6) << fixed << setprecision(3)
<< 100.*coupons[i+1] << " | "
// piecewise bootstrap
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts00,keyDates,dc) << " | "
// exponential splines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts11,keyDates,dc) << " | "
// simple polynomial
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts22,keyDates,dc) << " | "
// Nelson-Siegel
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts33,keyDates,dc) << " | "
// cubic bsplines
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts44,keyDates,dc) << " | "
// Svensson
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts55,keyDates,dc) << " | "
// Nelson-Siegel Spreaded
<< setw(6) << fixed << setprecision(3)
<< 100.*parRate(*ts66,keyDates,dc) << endl;
}
return 0;
} catch (std::exception& e) {
cerr << e.what() << endl;
return 1;
} catch (...) {
cerr << "unknown error" << endl;
return 1;
}
}