QuantLib: CallableBonds.cpp

A free/open-source library for quantitative finance Reference manual - version 1.12

CallableBonds.cpp

This examples prices a number of callable bonds and compares the results to known good data. It uses the experimental CallableBond class.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/* This example sets up a callable fixed rate bond with a Hull White pricing
engine and compares to Bloomberg's Hull White price/yield calculations.
*/
#include <ql/qldefines.hpp>
#ifdef BOOST_MSVC
# include <ql/auto_link.hpp>
#endif
#include <ql/experimental/callablebonds/callablebond.hpp>
#include <ql/experimental/callablebonds/treecallablebondengine.hpp>
#include <ql/models/shortrate/onefactormodels/hullwhite.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/unitedstates.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <vector>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <boost/timer.hpp>
using namespace std;
using namespace QuantLib;
#if defined(QL_ENABLE_SESSIONS)
namespace QuantLib {
Integer sessionId() { return 0; }
}
#endif
boost::shared_ptr<YieldTermStructure>
flatRate(const Date& today,
const boost::shared_ptr<Quote>& forward,
const DayCounter& dc,
const Compounding& compounding,
const Frequency& frequency) {
return boost::shared_ptr<YieldTermStructure>(
new FlatForward(today,
Handle<Quote>(forward),
dc,
compounding,
frequency));
}
boost::shared_ptr<YieldTermStructure>
flatRate(const Date& today,
Rate forward,
const DayCounter& dc,
const Compounding &compounding,
const Frequency &frequency) {
return flatRate(today,
boost::shared_ptr<Quote>(new SimpleQuote(forward)),
dc,
compounding,
frequency);
}
int main(int, char* [])
{
try {
boost::timer timer;
Date today = Date(16,October,2007);
Settings::instance().evaluationDate() = today;
cout << endl;
cout << "Pricing a callable fixed rate bond using" << endl;
cout << "Hull White model w/ reversion parameter = 0.03" << endl;
cout << "BAC4.65 09/15/12 ISIN: US06060WBJ36" << endl;
cout << "roughly five year tenor, ";
cout << "quarterly coupon and call dates" << endl;
cout << "reference date is : " << today << endl << endl;
/* Bloomberg OAS1: "N" model (Hull White)
varying volatility parameter
The curve entered into Bloomberg OAS1 is a flat curve,
at constant yield = 5.5%, semiannual compounding.
Assume here OAS1 curve uses an ACT/ACT day counter,
as documented in PFC1 as a "default" in the latter case.
*/
// set up a flat curve corresponding to Bloomberg flat curve
Rate bbCurveRate = 0.055;
DayCounter bbDayCounter = ActualActual(ActualActual::Bond);
InterestRate bbIR(bbCurveRate,bbDayCounter,Compounded, Semiannual);
Handle<YieldTermStructure> termStructure(flatRate(today,
bbIR.rate(),
bbIR.dayCounter(),
bbIR.compounding(),
bbIR.frequency()));
// set up the call schedule
CallabilitySchedule callSchedule;
Real callPrice = 100.;
Size numberOfCallDates = 24;
Date callDate = Date(15,September,2006);
for (Size i=0; i< numberOfCallDates; i++) {
Calendar nullCalendar = NullCalendar();
Callability::Price myPrice(callPrice,
Callability::Price::Clean);
callSchedule.push_back(
boost::shared_ptr<Callability>(
new Callability(myPrice,
Callability::Call,
callDate )));
callDate = nullCalendar. advance(callDate, 3, Months);
}
// set up the callable bond
Date dated = Date(16,September,2004);
Date issue = dated;
Date maturity = Date(15,September,2012);
Natural settlementDays = 3; // Bloomberg OAS1 settle is Oct 19, 2007
Calendar bondCalendar = UnitedStates(UnitedStates::GovernmentBond);
Real coupon = .0465;
Frequency frequency = Quarterly;
Real redemption = 100.0;
Real faceAmount = 100.0;
/* The 30/360 day counter Bloomberg uses for this bond cannot
reproduce the US Bond/ISMA (constant) cashflows used in PFC1.
Therefore use ActAct(Bond)
*/
DayCounter bondDayCounter = ActualActual(ActualActual::Bond);
// PFC1 shows no indication dates are being adjusted
// for weekends/holidays for vanilla bonds
BusinessDayConvention accrualConvention = Unadjusted;
BusinessDayConvention paymentConvention = Unadjusted;
Schedule sch(dated, maturity, Period(frequency), bondCalendar,
accrualConvention, accrualConvention,
DateGeneration::Backward, false);
Size maxIterations = 1000;
Real accuracy = 1e-8;
Integer gridIntervals = 40;
Real reversionParameter = .03;
// output price/yield results for varying volatility parameter
Real sigma = QL_EPSILON; // core dumps if zero on Cygwin
boost::shared_ptr<ShortRateModel> hw0(
new HullWhite(termStructure,reversionParameter,sigma));
boost::shared_ptr<PricingEngine> engine0(
new TreeCallableFixedRateBondEngine(hw0,gridIntervals));
CallableFixedRateBond callableBond(settlementDays, faceAmount, sch,
vector<Rate>(1, coupon),
bondDayCounter, paymentConvention,
redemption, issue, callSchedule);
callableBond.setPricingEngine(engine0);
cout << setprecision(2)
<< showpoint
<< fixed
<< "sigma/vol (%) = "
<< 100.*sigma
<< endl;
cout << "QuantLib price/yld (%) ";
cout << callableBond.cleanPrice() << " / "
<< 100. * callableBond.yield(bondDayCounter,
Compounded,
frequency,
accuracy,
maxIterations)
<< endl;
cout << "Bloomberg price/yld (%) ";
cout << "96.50 / 5.47"
<< endl
<< endl;
sigma = .01;
cout << "sigma/vol (%) = " << 100.*sigma << endl;
boost::shared_ptr<ShortRateModel> hw1(
new HullWhite(termStructure,reversionParameter,sigma));
boost::shared_ptr<PricingEngine> engine1(
new TreeCallableFixedRateBondEngine(hw1,gridIntervals));
callableBond.setPricingEngine(engine1);
cout << "QuantLib price/yld (%) ";
cout << callableBond.cleanPrice() << " / "
<< 100.* callableBond.yield(bondDayCounter,
Compounded,
frequency,
accuracy,
maxIterations)
<< endl;
cout << "Bloomberg price/yld (%) ";
cout << "95.68 / 5.66"
<< endl
<< endl;
sigma = .03;
boost::shared_ptr<ShortRateModel> hw2(
new HullWhite(termStructure, reversionParameter, sigma));
boost::shared_ptr<PricingEngine> engine2(
new TreeCallableFixedRateBondEngine(hw2,gridIntervals));
callableBond.setPricingEngine(engine2);
cout << "sigma/vol (%) = "
<< 100.*sigma
<< endl;
cout << "QuantLib price/yld (%) ";
cout << callableBond.cleanPrice() << " / "
<< 100. * callableBond.yield(bondDayCounter,
Compounded,
frequency,
accuracy,
maxIterations)
<< endl;
cout << "Bloomberg price/yld (%) ";
cout << "92.34 / 6.49"
<< endl
<< endl;
sigma = .06;
boost::shared_ptr<ShortRateModel> hw3(
new HullWhite(termStructure, reversionParameter, sigma));
boost::shared_ptr<PricingEngine> engine3(
new TreeCallableFixedRateBondEngine(hw3,gridIntervals));
callableBond.setPricingEngine(engine3);
cout << "sigma/vol (%) = "
<< 100.*sigma
<< endl;
cout << "QuantLib price/yld (%) ";
cout << callableBond.cleanPrice() << " / "
<< 100. * callableBond.yield(bondDayCounter,
Compounded,
frequency,
accuracy,
maxIterations)
<< endl;
cout << "Bloomberg price/yld (%) ";
cout << "87.16 / 7.83"
<< endl
<< endl;
sigma = .12;
boost::shared_ptr<ShortRateModel> hw4(
new HullWhite(termStructure, reversionParameter, sigma));
boost::shared_ptr<PricingEngine> engine4(
new TreeCallableFixedRateBondEngine(hw4,gridIntervals));
callableBond.setPricingEngine(engine4);
cout << "sigma/vol (%) = "
<< 100.*sigma
<< endl;
cout << "QuantLib price/yld (%) ";
cout << callableBond.cleanPrice() << " / "
<< 100.* callableBond.yield(bondDayCounter,
Compounded,
frequency,
accuracy,
maxIterations)
<< endl;
cout << "Bloomberg price/yld (%) ";
cout << "77.31 / 10.65"
<< endl
<< endl;
double seconds = timer.elapsed();
Integer hours = int(seconds/3600);
seconds -= hours * 3600;
Integer minutes = int(seconds/60);
seconds -= minutes * 60;
cout << " \nRun completed in ";
if (hours > 0)
cout << hours << " h ";
if (hours > 0 || minutes > 0)
cout << minutes << " m ";
cout << fixed << setprecision(0)
<< seconds << " s\n" << endl;
return 0;
} catch (std::exception& e) {
std::cerr << e.what() << std::endl;
return 1;
} catch (...) {
std::cerr << "unknown error" << std::endl;
return 1;
}
}