FRA.cpp

This example values a forward-rate agreement (FRA) at different forward dates under two yield curve assumptions. It thereby illustrates how set up a term structure, and to use it to price a simple forward-rate agreement.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/* This example shows how to set up a term structure and price a simple
forward-rate agreement.
*/
#include <ql/qldefines.hpp>
#ifdef BOOST_MSVC
# include <ql/auto_link.hpp>
#endif
#include <ql/instruments/forwardrateagreement.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/termstructures/yield/ratehelpers.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <iostream>
#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
int main(int, char* []) {
try {
std::cout << std::endl;
/*********************
*** MARKET DATA ***
*********************/
RelinkableHandle<YieldTermStructure> euriborTermStructure;
ext::shared_ptr<IborIndex> euribor3m(
new Euribor3M(euriborTermStructure));
Date todaysDate = Date(23, May, 2006);
Settings::instance().evaluationDate() = todaysDate;
Calendar calendar = euribor3m->fixingCalendar();
Integer fixingDays = euribor3m->fixingDays();
Date settlementDate = calendar.advance(todaysDate, fixingDays, Days);
std::cout << "Today: " << todaysDate.weekday()
<< ", " << todaysDate << std::endl;
std::cout << "Settlement date: " << settlementDate.weekday()
<< ", " << settlementDate << std::endl;
// 3 month term FRA quotes (index refers to monthsToStart)
Rate threeMonthFraQuote[10];
threeMonthFraQuote[1]=0.030;
threeMonthFraQuote[2]=0.031;
threeMonthFraQuote[3]=0.032;
threeMonthFraQuote[6]=0.033;
threeMonthFraQuote[9]=0.034;
/********************
*** QUOTES ***
********************/
// SimpleQuote stores a value which can be manually changed;
// other Quote subclasses could read the value from a database
// or some kind of data feed.
// FRAs
ext::shared_ptr<SimpleQuote> fra1x4Rate(
new SimpleQuote(threeMonthFraQuote[1]));
ext::shared_ptr<SimpleQuote> fra2x5Rate(
new SimpleQuote(threeMonthFraQuote[2]));
ext::shared_ptr<SimpleQuote> fra3x6Rate(
new SimpleQuote(threeMonthFraQuote[3]));
ext::shared_ptr<SimpleQuote> fra6x9Rate(
new SimpleQuote(threeMonthFraQuote[6]));
ext::shared_ptr<SimpleQuote> fra9x12Rate(
new SimpleQuote(threeMonthFraQuote[9]));
RelinkableHandle<Quote> h1x4; h1x4.linkTo(fra1x4Rate);
RelinkableHandle<Quote> h2x5; h2x5.linkTo(fra2x5Rate);
RelinkableHandle<Quote> h3x6; h3x6.linkTo(fra3x6Rate);
RelinkableHandle<Quote> h6x9; h6x9.linkTo(fra6x9Rate);
RelinkableHandle<Quote> h9x12; h9x12.linkTo(fra9x12Rate);
/*********************
*** RATE HELPERS ***
*********************/
// RateHelpers are built from the above quotes together with
// other instrument dependant infos. Quotes are passed in
// relinkable handles which could be relinked to some other
// data source later.
DayCounter fraDayCounter = euribor3m->dayCounter();
BusinessDayConvention convention = euribor3m->businessDayConvention();
bool endOfMonth = euribor3m->endOfMonth();
ext::shared_ptr<RateHelper> fra1x4(
new FraRateHelper(h1x4, 1, 4,
fixingDays, calendar, convention,
endOfMonth, fraDayCounter));
ext::shared_ptr<RateHelper> fra2x5(
new FraRateHelper(h2x5, 2, 5,
fixingDays, calendar, convention,
endOfMonth, fraDayCounter));
ext::shared_ptr<RateHelper> fra3x6(
new FraRateHelper(h3x6, 3, 6,
fixingDays, calendar, convention,
endOfMonth, fraDayCounter));
ext::shared_ptr<RateHelper> fra6x9(
new FraRateHelper(h6x9, 6, 9,
fixingDays, calendar, convention,
endOfMonth, fraDayCounter));
ext::shared_ptr<RateHelper> fra9x12(
new FraRateHelper(h9x12, 9, 12,
fixingDays, calendar, convention,
endOfMonth, fraDayCounter));
/*********************
** CURVE BUILDING **
*********************/
// Any DayCounter would be fine.
// ActualActual::ISDA ensures that 30 years is 30.0
DayCounter termStructureDayCounter =
ActualActual(ActualActual::ISDA);
// A FRA curve
std::vector<ext::shared_ptr<RateHelper> > fraInstruments;
fraInstruments.push_back(fra1x4);
fraInstruments.push_back(fra2x5);
fraInstruments.push_back(fra3x6);
fraInstruments.push_back(fra6x9);
fraInstruments.push_back(fra9x12);
ext::shared_ptr<YieldTermStructure> fraTermStructure(
new PiecewiseYieldCurve<Discount,LogLinear>(
settlementDate, fraInstruments,
termStructureDayCounter));
// Term structures used for pricing/discounting
RelinkableHandle<YieldTermStructure> discountingTermStructure;
discountingTermStructure.linkTo(fraTermStructure);
/***********************
*** construct FRA's ***
***********************/
Calendar fraCalendar = euribor3m->fixingCalendar();
BusinessDayConvention fraBusinessDayConvention =
euribor3m->businessDayConvention();
Position::Type fraFwdType = Position::Long;
Real fraNotional = 100.0;
const Integer FraTermMonths = 3;
Integer monthsToStart[] = { 1, 2, 3, 6, 9 };
euriborTermStructure.linkTo(fraTermStructure);
cout << endl;
cout << "Test FRA construction, NPV calculation, and FRA purchase"
<< endl
<< endl;
Size i;
for (i=0; i<LENGTH(monthsToStart); i++) {
Date fraValueDate = fraCalendar.advance(
settlementDate,monthsToStart[i],Months,
fraBusinessDayConvention);
Date fraMaturityDate = fraCalendar.advance(
fraValueDate,FraTermMonths,Months,
fraBusinessDayConvention);
Rate fraStrikeRate = threeMonthFraQuote[monthsToStart[i]];
ForwardRateAgreement myFRA(fraValueDate, fraMaturityDate,
fraFwdType,fraStrikeRate,
fraNotional, euribor3m,
discountingTermStructure);
cout << "3m Term FRA, Months to Start: "
<< monthsToStart[i]
<< endl;
cout << "strike FRA rate: "
<< io::rate(fraStrikeRate)
<< endl;
cout << "FRA 3m forward rate: "
<< myFRA.forwardRate()
<< endl;
cout << "FRA market quote: "
<< io::rate(threeMonthFraQuote[monthsToStart[i]])
<< endl;
cout << "FRA spot value: "
<< myFRA.spotValue()
<< endl;
cout << "FRA forward value: "
<< myFRA.forwardValue()
<< endl;
cout << "FRA implied Yield: "
<< myFRA.impliedYield(myFRA.spotValue(),
myFRA.forwardValue(),
settlementDate,
Simple,
fraDayCounter)
<< endl;
cout << "market Zero Rate: "
<< discountingTermStructure->zeroRate(fraMaturityDate,
fraDayCounter,
Simple)
<< endl;
cout << "FRA NPV [should be zero]: "
<< myFRA.NPV()
<< endl
<< endl;
}
cout << endl << endl;
cout << "Now take a 100 basis-point upward shift in FRA quotes "
<< "and examine NPV"
<< endl
<< endl;
const Real BpsShift = 0.01;
threeMonthFraQuote[1]=0.030+BpsShift;
threeMonthFraQuote[2]=0.031+BpsShift;
threeMonthFraQuote[3]=0.032+BpsShift;
threeMonthFraQuote[6]=0.033+BpsShift;
threeMonthFraQuote[9]=0.034+BpsShift;
fra1x4Rate->setValue(threeMonthFraQuote[1]);
fra2x5Rate->setValue(threeMonthFraQuote[2]);
fra3x6Rate->setValue(threeMonthFraQuote[3]);
fra6x9Rate->setValue(threeMonthFraQuote[6]);
fra9x12Rate->setValue(threeMonthFraQuote[9]);
for (i=0; i<LENGTH(monthsToStart); i++) {
Date fraValueDate = fraCalendar.advance(
settlementDate,monthsToStart[i],Months,
fraBusinessDayConvention);
Date fraMaturityDate = fraCalendar.advance(
fraValueDate,FraTermMonths,Months,
fraBusinessDayConvention);
Rate fraStrikeRate =
threeMonthFraQuote[monthsToStart[i]] - BpsShift;
ForwardRateAgreement myFRA(fraValueDate, fraMaturityDate,
fraFwdType, fraStrikeRate,
fraNotional, euribor3m,
discountingTermStructure);
cout << "3m Term FRA, 100 notional, Months to Start = "
<< monthsToStart[i]
<< endl;
cout << "strike FRA rate: "
<< io::rate(fraStrikeRate)
<< endl;
cout << "FRA 3m forward rate: "
<< myFRA.forwardRate()
<< endl;
cout << "FRA market quote: "
<< io::rate(threeMonthFraQuote[monthsToStart[i]])
<< endl;
cout << "FRA spot value: "
<< myFRA.spotValue()
<< endl;
cout << "FRA forward value: "
<< myFRA.forwardValue()
<< endl;
cout << "FRA implied Yield: "
<< myFRA.impliedYield(myFRA.spotValue(),
myFRA.forwardValue(),
settlementDate,
Simple,
fraDayCounter)
<< endl;
cout << "market Zero Rate: "
<< discountingTermStructure->zeroRate(fraMaturityDate,
fraDayCounter,
Simple)
<< endl;
cout << "FRA NPV [should be positive]: "
<< myFRA.NPV()
<< endl
<< endl;
}
return 0;
} catch (exception& e) {
cerr << e.what() << endl;
return 1;
} catch (...) {
cerr << "unknown error" << endl;
return 1;
}
}