ConvertibleBonds.cpp

For a given set of option parameters, this example computes the value of a convertible bond with an embedded put option for two different equity options types (with european and american exercise features) using the Tsiveriotis-Fernandes method with different implied tree algorithms. The tree types are Jarrow-Rudd, Cox-Ross-Rubinstein, Additive equiprobabilities, Trigeorgis, Tian and Leisen-Reimer.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
#include <ql/qldefines.hpp>
#if !defined(BOOST_ALL_NO_LIB) && defined(BOOST_MSVC)
#  include <ql/auto_link.hpp>
#endif
#include <ql/instruments/bonds/convertiblebonds.hpp>
#include <ql/pricingengines/bond/binomialconvertibleengine.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/utilities/dataformatters.hpp>
 
#include <iostream>
#include <iomanip>
 
#define LENGTH(a) (sizeof(a)/sizeof(a[0]))
 
using namespace QuantLib;
 
int main(int, char* []) {
 
    try {
 
        std::cout << std::endl;
 
        Option::Type type(Option::Put);
        Real underlying = 36.0;
        Real spreadRate = 0.005;
 
        Spread dividendYield = 0.02;
        Rate riskFreeRate = 0.06;
        Volatility volatility = 0.20;
 
        Integer settlementDays = 3;
        Integer length = 5;
        Real redemption = 100.0;
        Real conversionRatio = redemption/underlying; // at the money
 
        // set up dates/schedules
        Calendar calendar = TARGET();
        Date today = calendar.adjust(Date::todaysDate());
 
        Settings::instance().evaluationDate() = today;
        Date settlementDate = calendar.advance(today, settlementDays, Days);
        Date exerciseDate = calendar.advance(settlementDate, length, Years);
        Date issueDate = calendar.advance(exerciseDate, -length, Years);
 
        BusinessDayConvention convention = ModifiedFollowing;
 
        Frequency frequency = Annual;
 
        Schedule schedule(issueDate, exerciseDate,
                          Period(frequency), calendar,
                          convention, convention,
                          DateGeneration::Backward, false);
 
        DividendSchedule dividends;
        CallabilitySchedule callability;
 
        std::vector<Real> coupons(1, 0.05);
 
        DayCounter bondDayCount = Thirty360(Thirty360::BondBasis);
 
        Integer callLength[] = { 2, 4 };  // Call dates, years 2, 4.
        Integer putLength[] = { 3 }; // Put dates year 3
 
        Real callPrices[] = { 101.5, 100.85 };
        Real putPrices[]= { 105.0 };
 
        // Load call schedules
        for (Size i=0; i<LENGTH(callLength); i++) {
            callability.push_back(
                   ext::make_shared<SoftCallability>(Bond::Price(callPrices[i],
                                                                 Bond::Price::Clean),
                                                     schedule.date(callLength[i]),
                                                     1.20));
        }
 
        for (Size j=0; j<LENGTH(putLength); j++) {
            callability.push_back(
                   ext::make_shared<Callability>(Bond::Price(putPrices[j],
                                                             Bond::Price::Clean),
                                                 Callability::Put,
                                                 schedule.date(putLength[j])));
        }
 
        // Assume dividends are paid every 6 months.
        for (Date d = today + 6*Months; d < exerciseDate; d += 6*Months) {
            dividends.push_back(ext::make_shared<FixedDividend>(1.0, d));
        }
 
        DayCounter dayCounter = Actual365Fixed();
        Time maturity = dayCounter.yearFraction(settlementDate,
                                                exerciseDate);
 
        std::cout << "option type = "  << type << std::endl;
        std::cout << "Time to maturity = "        << maturity
                  << std::endl;
        std::cout << "Underlying price = "        << underlying
                  << std::endl;
        std::cout << "Risk-free interest rate = " << io::rate(riskFreeRate)
                  << std::endl;
        std::cout << "Dividend yield = " << io::rate(dividendYield)
                  << std::endl;
        std::cout << "Volatility = " << io::volatility(volatility)
                  << std::endl;
        std::cout << std::endl;
 
        std::string method;
        std::cout << std::endl ;
 
        // write column headings
        Size widths[] = { 35, 14, 14 };
        Size totalWidth = widths[0] + widths[1] + widths[2];
        std::string rule(totalWidth, '-'), dblrule(totalWidth, '=');
 
        std::cout << dblrule << std::endl;
        std::cout << "Tsiveriotis-Fernandes method" << std::endl;
        std::cout << dblrule << std::endl;
        std::cout << std::setw(widths[0]) << std::left << "Tree type"
                  << std::setw(widths[1]) << std::left << "European"
                  << std::setw(widths[1]) << std::left << "American"
                  << std::endl;
        std::cout << rule << std::endl;
 
        auto exercise = ext::make_shared<EuropeanExercise>(exerciseDate);
        auto amExercise = ext::make_shared<AmericanExercise>(settlementDate, exerciseDate);
 
        Handle<Quote> underlyingH(ext::make_shared<SimpleQuote>(underlying));
 
        Handle<YieldTermStructure> flatTermStructure(
            ext::make_shared<FlatForward>(settlementDate, riskFreeRate, dayCounter));
 
        Handle<YieldTermStructure> flatDividendTS(
            ext::make_shared<FlatForward>(settlementDate, dividendYield, dayCounter));
 
        Handle<BlackVolTermStructure> flatVolTS(
            ext::make_shared<BlackConstantVol>(settlementDate, calendar, volatility, dayCounter));
 
        auto stochasticProcess = ext::make_shared<BlackScholesMertonProcess>(
            underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
 
        Size timeSteps = 801;
 
        Handle<Quote> creditSpread(ext::make_shared<SimpleQuote>(spreadRate));
 
        auto rate = ext::make_shared<SimpleQuote>(riskFreeRate);
 
        Handle<YieldTermStructure> discountCurve(
                ext::make_shared<FlatForward>(today, Handle<Quote>(rate), dayCounter));
 
        ConvertibleFixedCouponBond europeanBond(
                            exercise, conversionRatio, callability,
                            issueDate, settlementDays,
                            coupons, bondDayCount, schedule, redemption);
 
        ConvertibleFixedCouponBond americanBond(
                          amExercise, conversionRatio, callability,
                          issueDate, settlementDays,
                          coupons, bondDayCount, schedule, redemption);
 
        method = "Jarrow-Rudd";
        auto jrEngine = ext::make_shared<BinomialConvertibleEngine<JarrowRudd>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(jrEngine);
        americanBond.setPricingEngine(jrEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Cox-Ross-Rubinstein";
        auto crrEngine = ext::make_shared<BinomialConvertibleEngine<CoxRossRubinstein>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(crrEngine);
        americanBond.setPricingEngine(crrEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Additive equiprobabilities";
        auto aeqpEngine = ext::make_shared<BinomialConvertibleEngine<AdditiveEQPBinomialTree>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(aeqpEngine);
        americanBond.setPricingEngine(aeqpEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Trigeorgis";
        auto trEngine = ext::make_shared<BinomialConvertibleEngine<Trigeorgis>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(trEngine);
        americanBond.setPricingEngine(trEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Tian";
        auto tianEngine = ext::make_shared<BinomialConvertibleEngine<Tian>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(tianEngine);
        americanBond.setPricingEngine(tianEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Leisen-Reimer";
        auto lrEngine = ext::make_shared<BinomialConvertibleEngine<LeisenReimer>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(lrEngine);
        americanBond.setPricingEngine(lrEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        method = "Joshi";
        auto joshiEngine = ext::make_shared<BinomialConvertibleEngine<Joshi4>>(stochasticProcess, timeSteps, creditSpread, dividends);
        europeanBond.setPricingEngine(joshiEngine);
        americanBond.setPricingEngine(joshiEngine);
        std::cout << std::setw(widths[0]) << std::left << method
                  << std::fixed
                  << std::setw(widths[1]) << std::left << europeanBond.NPV()
                  << std::setw(widths[2]) << std::left << americanBond.NPV()
                  << std::endl;
 
        std::cout << dblrule << std::endl;
 
        return 0;
    } catch (std::exception& e) {
        std::cerr << e.what() << std::endl;
        return 1;
    } catch (...) {
        std::cerr << "unknown error" << std::endl;
        return 1;
    }
 
}