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Problem with a curve near Labor Day

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Nathan Abbott
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Problem with a curve near Labor Day

Nathan Abbott
I have having a problem with evaluating a swap near Labor Day which is a holiday in the USA. I can reproduce it with the swap example by changing the settlement date, the calendar and the index. Here is the modified swap example.

#include <ql/quantlib.hpp>
#include <boost/timer.hpp>
#include <iostream>
#include <iomanip>

using namespace QuantLib;

#if defined(QL_ENABLE_SESSIONS)
namespace QuantLib {

    Integer sessionId() { return 0; }

}
#endif


int main(int, char* []) {

    try {

        boost::timer timer;
        std::cout << std::endl;

        /*********************
         ***  MARKET DATA  ***
         *********************/

        //Calendar calendar = TARGET();

        Calendar calendar = JointCalendar(UnitedStates(UnitedStates::NYSE), UnitedKingdom(UnitedKingdom::Exchange));
        // uncommenting the following line generates an error
        // calendar = Tokyo();
        //Date settlementDate(22, September, 2004);
        Date settlementDate(2, September, 2008);
        // must be a business day
        settlementDate = calendar.adjust(settlementDate);

        Integer fixingDays = 2;
        Date todaysDate = calendar.advance(settlementDate, -fixingDays, Days);
        // nothing to do with Date::todaysDate
        Settings::instance().evaluationDate() = todaysDate;


        todaysDate = Settings::instance().evaluationDate();
        std::cout << "Today: " << todaysDate.weekday()
                  << ", " << todaysDate << std::endl;

        std::cout << "Settlement date: " << settlementDate.weekday()
                  << ", " << settlementDate << std::endl;

        // deposits
        Rate d1wQuote=0.0382;
        Rate d1mQuote=0.0372;
        Rate d3mQuote=0.0363;
        Rate d6mQuote=0.0353;
        Rate d9mQuote=0.0348;
        Rate d1yQuote=0.0345;

        // swaps
        Rate s2yQuote=0.037125;
        Rate s3yQuote=0.0398;
        Rate s5yQuote=0.0443;
        Rate s10yQuote=0.05165;
        Rate s15yQuote=0.055175;


        /********************
         ***    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.

        // deposits
        boost::shared_ptr<Quote> d1wRate(new SimpleQuote(d1wQuote));
        boost::shared_ptr<Quote> d1mRate(new SimpleQuote(d1mQuote));
        boost::shared_ptr<Quote> d3mRate(new SimpleQuote(d3mQuote));
        boost::shared_ptr<Quote> d6mRate(new SimpleQuote(d6mQuote));
        boost::shared_ptr<Quote> d9mRate(new SimpleQuote(d9mQuote));
        boost::shared_ptr<Quote> d1yRate(new SimpleQuote(d1yQuote));
        // swaps
        boost::shared_ptr<Quote> s2yRate(new SimpleQuote(s2yQuote));
        boost::shared_ptr<Quote> s3yRate(new SimpleQuote(s3yQuote));
        boost::shared_ptr<Quote> s5yRate(new SimpleQuote(s5yQuote));
        boost::shared_ptr<Quote> s10yRate(new SimpleQuote(s10yQuote));
        boost::shared_ptr<Quote> s15yRate(new SimpleQuote(s15yQuote));


        /*********************
         ***  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.

        // deposits
        DayCounter depositDayCounter = Actual360();

        boost::shared_ptr<RateHelper> d1w(new DepositRateHelper(
            Handle<Quote>(d1wRate),
            1*Weeks, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));
        boost::shared_ptr<RateHelper> d1m(new DepositRateHelper(
            Handle<Quote>(d1mRate),
            1*Months, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));
        boost::shared_ptr<RateHelper> d3m(new DepositRateHelper(
            Handle<Quote>(d3mRate),
            3*Months, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));
        boost::shared_ptr<RateHelper> d6m(new DepositRateHelper(
            Handle<Quote>(d6mRate),
            6*Months, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));
        boost::shared_ptr<RateHelper> d9m(new DepositRateHelper(
            Handle<Quote>(d9mRate),
            9*Months, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));
        boost::shared_ptr<RateHelper> d1y(new DepositRateHelper(
            Handle<Quote>(d1yRate),
            1*Years, fixingDays,
            calendar, ModifiedFollowing,
            true, depositDayCounter));



        // setup swaps
        Frequency swFixedLegFrequency = Annual;
        BusinessDayConvention swFixedLegConvention = Unadjusted;
        DayCounter swFixedLegDayCounter = Thirty360(Thirty360::European);
//        boost::shared_ptr<IborIndex> swFloatingLegIndex(new Euribor6M);
         boost::shared_ptr<IborIndex> swFloatingLegIndex(new USDLibor(6*Months));

        boost::shared_ptr<RateHelper> s2y(new SwapRateHelper(
            Handle<Quote>(s2yRate), 2*Years,
            calendar, swFixedLegFrequency,
            swFixedLegConvention, swFixedLegDayCounter,
            swFloatingLegIndex));
        boost::shared_ptr<RateHelper> s3y(new SwapRateHelper(
            Handle<Quote>(s3yRate), 3*Years,
            calendar, swFixedLegFrequency,
            swFixedLegConvention, swFixedLegDayCounter,
            swFloatingLegIndex));
        boost::shared_ptr<RateHelper> s5y(new SwapRateHelper(
            Handle<Quote>(s5yRate), 5*Years,
            calendar, swFixedLegFrequency,
            swFixedLegConvention, swFixedLegDayCounter,
            swFloatingLegIndex));
        boost::shared_ptr<RateHelper> s10y(new SwapRateHelper(
            Handle<Quote>(s10yRate), 10*Years,
            calendar, swFixedLegFrequency,
            swFixedLegConvention, swFixedLegDayCounter,
            swFloatingLegIndex));
        boost::shared_ptr<RateHelper> s15y(new SwapRateHelper(
            Handle<Quote>(s15yRate), 15*Years,
            calendar, swFixedLegFrequency,
            swFixedLegConvention, swFixedLegDayCounter,
            swFloatingLegIndex));


        /*********************
         **  CURVE BUILDING **
         *********************/

        // Any DayCounter would be fine.
        // ActualActual::ISDA ensures that 30 years is 30.0
        DayCounter termStructureDayCounter =
            ActualActual(ActualActual::ISDA);


        double tolerance = 1.0e-15;

        // A depo-swap curve
        std::vector<boost::shared_ptr<RateHelper> > depoSwapInstruments;
        depoSwapInstruments.push_back(d1w);
        depoSwapInstruments.push_back(d1m);
        depoSwapInstruments.push_back(d3m);
        depoSwapInstruments.push_back(d6m);
        depoSwapInstruments.push_back(d9m);
        depoSwapInstruments.push_back(d1y);
        depoSwapInstruments.push_back(s2y);
        depoSwapInstruments.push_back(s3y);
        depoSwapInstruments.push_back(s5y);
        depoSwapInstruments.push_back(s10y);
        depoSwapInstruments.push_back(s15y);
        boost::shared_ptr<YieldTermStructure> depoSwapTermStructure(
            new PiecewiseYieldCurve<Discount,LogLinear>(
                                          settlementDate, depoSwapInstruments,
                                          termStructureDayCounter,
                                          std::vector<Handle<Quote> >(),
                                          std::vector<Date>(),
                                          tolerance));




        // Term structures that will be used for pricing:
        // the one used for discounting cash flows
        RelinkableHandle<YieldTermStructure> discountingTermStructure;
        // the one used for forward rate forecasting
        RelinkableHandle<YieldTermStructure> forecastingTermStructure;


        /*********************
        * SWAPS TO BE PRICED *
        **********************/

        // constant nominal 1,000,000 Euro
        Real nominal = 1000000.0;
        // fixed leg
        Frequency fixedLegFrequency = Annual;
        BusinessDayConvention fixedLegConvention = Unadjusted;
        BusinessDayConvention floatingLegConvention = ModifiedFollowing;
        DayCounter fixedLegDayCounter = Thirty360(Thirty360::European);
        Rate fixedRate = 0.04;
        DayCounter floatingLegDayCounter = Actual360();

        // floating leg
        Frequency floatingLegFrequency = Semiannual;
        //boost::shared_ptr<IborIndex> euriborIndex(
        //                             new Euribor6M(forecastingTermStructure));

        boost::shared_ptr<IborIndex> euriborIndex(
                                     new USDLibor(6*Months, forecastingTermStructure));
        Spread spread = 0.0;

        Integer lenghtInYears = 5;
        VanillaSwap::Type swapType = VanillaSwap::Payer;

        Date maturity = settlementDate + lenghtInYears*Years;
        Schedule fixedSchedule(settlementDate, maturity,
                               Period(fixedLegFrequency),
                               calendar, fixedLegConvention,
                               fixedLegConvention,
                               DateGeneration::Forward, false);
        Schedule floatSchedule(settlementDate, maturity,
                               Period(floatingLegFrequency),
                               calendar, floatingLegConvention,
                               floatingLegConvention,
                               DateGeneration::Forward, false);
        VanillaSwap spot5YearSwap(swapType, nominal,
            fixedSchedule, fixedRate, fixedLegDayCounter,
            floatSchedule, euriborIndex, spread,
            floatingLegDayCounter);



        // utilities for reporting
        std::vector<std::string> headers(4);
        headers[0] = "term structure";
        headers[1] = "net present value";
        headers[2] = "fair spread";
        headers[3] = "fair fixed rate";
        std::string separator = " | ";
        Size width = headers[0].size() + separator.size()
                   + headers[1].size() + separator.size()
                   + headers[2].size() + separator.size()
                   + headers[3].size() + separator.size() - 1;
        std::string rule(width, '-'), dblrule(width, '=');
        std::string tab(8, ' ');

        // calculations

        std::cout << dblrule << std::endl;
        std::cout <<  "5-year market swap-rate = "
                  << std::setprecision(2) << io::rate(s5yRate->value())
                  << std::endl;
        std::cout << dblrule << std::endl;

        std::cout << tab << "5-years swap paying "
                  << io::rate(fixedRate) << std::endl;
        std::cout << headers[0] << separator
                  << headers[1] << separator
                  << headers[2] << separator
                  << headers[3] << separator << std::endl;
        std::cout << rule << std::endl;

        Real NPV;
        Rate fairRate;
        Spread fairSpread;

        boost::shared_ptr<PricingEngine> swapEngine(
                         new DiscountingSwapEngine(discountingTermStructure));

        spot5YearSwap.setPricingEngine(swapEngine);

        // Of course, you're not forced to really use different curves
        forecastingTermStructure.linkTo(depoSwapTermStructure);
        discountingTermStructure.linkTo(depoSwapTermStructure);

        NPV = spot5YearSwap.NPV();
        fairSpread = spot5YearSwap.fairSpread();
        fairRate = spot5YearSwap.fairRate();

        std::cout << std::setw(headers[0].size())
                  << "depo-swap" << separator;
        std::cout << std::setw(headers[1].size())
                  << std::fixed << std::setprecision(2) << NPV << separator;
        std::cout << std::setw(headers[2].size())
                  << io::rate(fairSpread) << separator;
        std::cout << std::setw(headers[3].size())
                  << io::rate(fairRate) << separator;
        std::cout << std::endl;

        QL_REQUIRE(std::fabs(fairRate-s5yQuote)<1e-8,
                   "5-years swap mispriced by "
                   << io::rate(std::fabs(fairRate-s5yQuote)));

        Real seconds = timer.elapsed();
        Integer hours = int(seconds/3600);
        seconds -= hours * 3600;
        Integer minutes = int(seconds/60);
        seconds -= minutes * 60;
        std::cout << " \nRun completed in ";
        if (hours > 0)
            std::cout << hours << " h ";
        if (hours > 0 || minutes > 0)
            std::cout << minutes << " m ";
        std::cout << std::fixed << std::setprecision(0)
                  << seconds << " s\n" << std::endl;

        return 0;

    } catch (std::exception& e) {
        std::cout << e.what() << std::endl;
        return 1;
    } catch (...) {
        std::cout << "unknown error" << std::endl;
        return 1;
    }
}

The example was compiled with Boost 1.35.0 and Visual Studio 2005.

The output of the program is this:

Today: Thursday, August 28th, 2008
Settlement date: Tuesday, September 2nd, 2008
====================================================================
5-year market swap-rate = 4.43 %
====================================================================
        5-years swap paying 4.00 %
term structure | net present value | fair spread | fair fixed rate |
--------------------------------------------------------------------
1st iteration: could not bootstrap the 7th instrument, maturity September 1st, 2010: negative time (-0.00273224) given

All I did is change to settlement date to September 2nd, 2008, change the calendar to JointCalendar(UnitedStates(UnitedStates::NYSE), UnitedKingdom(UnitedKingdom::Exchange)), and change the the index from Euribor6M to USDLibor(6*Months).

The program seems to be trying to calculate the discount factor on 09/01/08 which is Labor Day in the USA.  Am I doing something wrong in setting up the curve? Any help would be appreciated. The program works correctly if the settlement date is set to September 22 2004.

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