static void Main(string[] args)
{
// boost::timer timer;
Date today = new Date(16,Month.October,2007);
Settings.setEvaluationDate(today);
Console.WriteLine();
Console.WriteLine("Pricing a callable fixed rate bond using");
Console.WriteLine("Hull White model w/ reversion parameter = 0.03");
Console.WriteLine("BAC4.65 09/15/12 ISIN: US06060WBJ36");
Console.WriteLine("roughly five year tenor, ");
Console.WriteLine("quarterly coupon and call dates");
Console.WriteLine("reference date is : " + today );
/* 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
double bbCurveRate = 0.055;
DayCounter bbDayCounter = new ActualActual(ActualActual.Convention.Bond);
InterestRate bbIR = new InterestRate(bbCurveRate,bbDayCounter,Compounding.Compounded ,Frequency.Semiannual);
Handle<YieldTermStructure> termStructure = new Handle<YieldTermStructure>(flatRate( today,
bbIR.rate(),
bbIR.dayCounter(),
bbIR.compounding(),
bbIR.frequency()));
// set up the call schedule
CallabilitySchedule callSchedule = new CallabilitySchedule();
double callPrice = 100.0;
int numberOfCallDates = 24;
Date callDate = new Date(15,Month.September,2006);
for (int i=0; i< numberOfCallDates; i++)
{
Calendar nullCalendar = new NullCalendar();
Callability.Price myPrice = new Callability.Price(callPrice, Callability.Price.Type.Clean);
callSchedule.Add( new Callability(myPrice,Callability.Type.Call, callDate ));
callDate = nullCalendar.advance(callDate, 3, TimeUnit.Months);
}
// set up the callable bond
Date dated = new Date(16,Month.September,2004);
Date issue = dated;
Date maturity = new Date(15,Month.September,2012);
int settlementDays = 3; // Bloomberg OAS1 settle is Oct 19, 2007
Calendar bondCalendar = new UnitedStates(UnitedStates.Market.GovernmentBond);
double coupon = .0465;
Frequency frequency = Frequency.Quarterly;
double redemption = 100.0;
double 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 = new ActualActual(ActualActual.Convention.Bond);
// PFC1 shows no indication dates are being adjusted
// for weekends/holidays for vanilla bonds
BusinessDayConvention accrualConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention paymentConvention = BusinessDayConvention.Unadjusted;
Schedule sch = new Schedule( dated, maturity, new Period(frequency), bondCalendar,
accrualConvention, accrualConvention,
DateGeneration.Rule.Backward, false);
int maxIterations = 1000;
double accuracy = 1e-8;
int gridIntervals = 40;
double reversionParameter = .03;
// output price/yield results for varying volatility parameter
double sigma = Const.QL_Epsilon; // core dumps if zero on Cygwin
ShortRateModel hw0 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine0 = new TreeCallableFixedRateBondEngine(hw0, gridIntervals, termStructure);
CallableFixedRateBond callableBond = new CallableFixedRateBond( settlementDays, faceAmount, sch,
new InitializedList<double>(1, coupon),
bondDayCounter, paymentConvention,
redemption, issue, callSchedule);
callableBond.setPricingEngine(engine0);
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("96.50 / 5.47");
//
sigma = .01;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw1 = new HullWhite(termStructure,reversionParameter,sigma);
IPricingEngine engine1 = new TreeCallableFixedRateBondEngine(hw1,gridIntervals,termStructure);
callableBond.setPricingEngine(engine1);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine( "{0:0.00} / {1:0.00} ", callableBond.cleanPrice() ,
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("95.68 / 5.66");
//
sigma = .03;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw2 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine2 = new TreeCallableFixedRateBondEngine(hw2, gridIntervals, termStructure);
callableBond.setPricingEngine(engine2);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("92.34 / 6.49");
//
sigma = .06;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw3 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine3 = new TreeCallableFixedRateBondEngine(hw3, gridIntervals, termStructure);
callableBond.setPricingEngine(engine3);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("87.16 / 7.83");
//
sigma = .12;
Console.WriteLine("sigma/vol (%) = {0:0.00}", (100.0 * sigma));
ShortRateModel hw4 = new HullWhite(termStructure, reversionParameter, sigma);
IPricingEngine engine4 = new TreeCallableFixedRateBondEngine(hw4, gridIntervals, termStructure);
callableBond.setPricingEngine(engine4);
Console.WriteLine("QuantLib price/yld (%) ");
Console.WriteLine("{0:0.00} / {1:0.00} ", callableBond.cleanPrice(),
100.0 * callableBond.yield(bondDayCounter,
Compounding.Compounded,
frequency,
accuracy,
maxIterations));
Console.WriteLine("Bloomberg price/yld (%) ");
Console.WriteLine("77.31 / 10.65");
}
