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.
#if !defined(BOOST_ALL_NO_LIB) && defined(BOOST_MSVC)
#endif
#include <iostream>
#include <iomanip>
#define LENGTH(a) (sizeof(a)/sizeof(a[0]))
int main(int, char* []) {
try {
std::cout << std::endl;
Rate riskFreeRate = 0.06;
Real conversionRatio = redemption/underlying;
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);
Schedule schedule(issueDate, exerciseDate,
convention, convention,
DateGeneration::Backward, false);
std::vector<Real> coupons(1, 0.05);
Real callPrices[] = { 101.5, 100.85 };
Real putPrices[]= { 105.0 };
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])));
}
for (
Date d = today + 6*Months;
d < exerciseDate;
d += 6*Months) {
dividends.push_back(ext::make_shared<FixedDividend>(1.0,
d));
}
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 ;
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);
auto underlyingH = makeQuoteHandle(underlying);
ext::make_shared<FlatForward>(settlementDate, riskFreeRate, dayCounter));
ext::make_shared<FlatForward>(settlementDate, dividendYield, dayCounter));
ext::make_shared<BlackConstantVol>(settlementDate, calendar, volatility, dayCounter));
auto stochasticProcess = ext::make_shared<BlackScholesMertonProcess>(
underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
auto creditSpread = makeQuoteHandle(spreadRate);
auto rate = ext::make_shared<SimpleQuote>(riskFreeRate);
ext::make_shared<FlatForward>(today,
Handle<Quote>(rate), dayCounter));
exercise, conversionRatio, callability,
issueDate, settlementDays,
coupons, bondDayCount, schedule, redemption);
amExercise, conversionRatio, callability,
issueDate, settlementDays,
coupons, bondDayCount, schedule, redemption);
method = "Jarrow-Rudd";
auto jrEngine = ext::make_shared<BinomialConvertibleEngine<JarrowRudd>>(stochasticProcess, timeSteps, creditSpread, dividends);
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);
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);
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);
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);
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);
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);
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;
}
}
binomial engine for convertible bonds
Actual/365 (Fixed) day count convention.
Date adjust(const Date &, BusinessDayConvention convention=Following) const
Date advance(const Date &, Integer n, TimeUnit unit, BusinessDayConvention convention=Following, bool endOfMonth=false) const
convertible fixed-coupon bond
Time yearFraction(const Date &, const Date &, const Date &refPeriodStart=Date(), const Date &refPeriodEnd=Date()) const
Returns the period between two dates as a fraction of year.
Shared handle to an observable.
Real NPV() const
returns the net present value of the instrument.
void setPricingEngine(const ext::shared_ptr< PricingEngine > &)
set the pricing engine to be used.
const Date & date(Size i) const
30/360 day count convention
Frequency
Frequency of events.
BusinessDayConvention
Business Day conventions.
Real Time
continuous quantity with 1-year units
Real Volatility
volatility
QL_INTEGER Integer
integer number
Real Spread
spreads on interest rates
std::size_t Size
size of a container
std::vector< ext::shared_ptr< Dividend > > DividendSchedule
std::vector< ext::shared_ptr< Callability > > CallabilitySchedule
Global definitions and compiler switches.