public GFunctionExactYield(CmsCoupon coupon)
{
SwapIndex swapIndex = coupon.swapIndex();
VanillaSwap swap = swapIndex.underlyingSwap(coupon.fixingDate());
Schedule schedule = swap.fixedSchedule();
Handle <YieldTermStructure> rateCurve = swapIndex.forwardingTermStructure();
DayCounter dc = swapIndex.dayCounter();
double swapStartTime = dc.yearFraction(rateCurve.link.referenceDate(), schedule.startDate());
double swapFirstPaymentTime = dc.yearFraction(rateCurve.link.referenceDate(), schedule.date(1));
double paymentTime = dc.yearFraction(rateCurve.link.referenceDate(), coupon.date());
delta_ = (paymentTime - swapStartTime) / (swapFirstPaymentTime - swapStartTime);
List <CashFlow> fixedLeg = new List <CashFlow>(swap.fixedLeg());
int n = fixedLeg.Count;
accruals_ = new List <double>();
for (int i = 0; i < n; ++i)
{
Coupon coupon1 = fixedLeg[i] as Coupon;
accruals_.Add(coupon1.accrualPeriod());
}
}
//===========================================================================//
// GFunctionWithShifts //
//===========================================================================//
public GFunctionWithShifts(CmsCoupon coupon, Handle <Quote> meanReversion)
{
meanReversion_ = meanReversion;
calibratedShift_ = 0.03;
tmpRs_ = 10000000.0;
accuracy_ = 1.0e-14;
SwapIndex swapIndex = coupon.swapIndex();
VanillaSwap swap = swapIndex.underlyingSwap(coupon.fixingDate());
swapRateValue_ = swap.fairRate();
objectiveFunction_ = new ObjectiveFunction(this, swapRateValue_);
Schedule schedule = swap.fixedSchedule();
Handle <YieldTermStructure> rateCurve = swapIndex.forwardingTermStructure();
DayCounter dc = swapIndex.dayCounter();
swapStartTime_ = dc.yearFraction(rateCurve.link.referenceDate(), schedule.startDate());
discountAtStart_ = rateCurve.link.discount(schedule.startDate());
double paymentTime = dc.yearFraction(rateCurve.link.referenceDate(), coupon.date());
shapedPaymentTime_ = shapeOfShift(paymentTime);
List <CashFlow> fixedLeg = new List <CashFlow>(swap.fixedLeg());
int n = fixedLeg.Count;
shapedSwapPaymentTimes_ = new List <double>();
swapPaymentDiscounts_ = new List <double>();
accruals_ = new List <double>();
for (int i = 0; i < n; ++i)
{
Coupon coupon1 = fixedLeg[i] as Coupon;
accruals_.Add(coupon1.accrualPeriod());
Date paymentDate = new Date(coupon1.date().serialNumber());
double swapPaymentTime = dc.yearFraction(rateCurve.link.referenceDate(), paymentDate);
shapedSwapPaymentTimes_.Add(shapeOfShift(swapPaymentTime));
swapPaymentDiscounts_.Add(rateCurve.link.discount(paymentDate));
}
discountRatio_ = swapPaymentDiscounts_.Last() / discountAtStart_;
}
public override void calculate()
{
double basisPoint = 1.0e-4;
Date exerciseDate = arguments_.exercise.date(0);
// the part of the swap preceding exerciseDate should be truncated
// to avoid taking into account unwanted cashflows
// for the moment we add a check avoiding this situation
VanillaSwap swap = arguments_.swap;
double strike = swap.fixedRate;
List <CashFlow> fixedLeg = swap.fixedLeg();
FixedRateCoupon firstCoupon = fixedLeg[0] as FixedRateCoupon;
Utils.QL_REQUIRE(firstCoupon != null, () => "wrong coupon type");
Utils.QL_REQUIRE(firstCoupon.accrualStartDate() >= exerciseDate,
() => "swap start (" + firstCoupon.accrualStartDate() + ") before exercise date ("
+ exerciseDate + ") not supported in Black swaption engine");
// using the forecasting curve
swap.setPricingEngine(new DiscountingSwapEngine(swap.iborIndex().forwardingTermStructure()));
double atmForward = swap.fairRate();
// Volatilities are quoted for zero-spreaded swaps.
// Therefore, any spread on the floating leg must be removed
// with a corresponding correction on the fixed leg.
if (swap.spread.IsNotEqual(0.0))
{
double correction = swap.spread * Math.Abs(swap.floatingLegBPS() / swap.fixedLegBPS());
strike -= correction;
atmForward -= correction;
results_.additionalResults["spreadCorrection"] = correction;
}
else
{
results_.additionalResults["spreadCorrection"] = 0.0;
}
results_.additionalResults["strike"] = strike;
results_.additionalResults["atmForward"] = atmForward;
// using the discounting curve
swap.setPricingEngine(new DiscountingSwapEngine(discountCurve_, false));
double annuity = 0;
switch (arguments_.settlementType)
{
case Settlement.Type.Physical:
{
annuity = Math.Abs(swap.fixedLegBPS()) / basisPoint;
break;
}
case Settlement.Type.Cash:
{
DayCounter dayCount = firstCoupon.dayCounter();
// we assume that the cash settlement date is equal
// to the swap start date
Date discountDate = model_ == CashAnnuityModel.DiscountCurve
? firstCoupon.accrualStartDate()
: discountCurve_.link.referenceDate();
double fixedLegCashBPS =
CashFlows.bps(fixedLeg,
new InterestRate(atmForward, dayCount, Compounding.Compounded, Frequency.Annual), false,
discountDate);
annuity = Math.Abs(fixedLegCashBPS / basisPoint) * discountCurve_.link.discount(discountDate);
break;
}
default:
Utils.QL_FAIL("unknown settlement type");
break;
}
results_.additionalResults["annuity"] = annuity;
double swapLength = vol_.link.swapLength(swap.floatingSchedule().dates().First(),
swap.floatingSchedule().dates().Last());
results_.additionalResults["swapLength"] = swapLength;
double variance = vol_.link.blackVariance(exerciseDate,
swapLength,
strike);
double displacement = displacement_ == null
? vol_.link.shift(exerciseDate, swapLength)
: Convert.ToDouble(displacement_);
double stdDev = Math.Sqrt(variance);
results_.additionalResults["stdDev"] = stdDev;
Option.Type w = (arguments_.type == VanillaSwap.Type.Payer) ? Option.Type.Call : Option.Type.Put;
results_.value = new Spec().value(w, strike, atmForward, stdDev, annuity, displacement);
double exerciseTime = vol_.link.timeFromReference(exerciseDate);
results_.additionalResults["vega"] =
new Spec().vega(strike, atmForward, stdDev, exerciseTime, annuity, displacement);
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
Date todaysDate = new Date(15, 2, 2002);
Calendar calendar = new TARGET();
Date settlementDate = new Date(19, 2, 2002);
Settings.setEvaluationDate(todaysDate);
// flat yield term structure impling 1x5 swap at 5%
Quote flatRate = new SimpleQuote(0.04875825);
Handle<YieldTermStructure> rhTermStructure = new Handle<YieldTermStructure>(
new FlatForward(settlementDate, new Handle<Quote>(flatRate),
new Actual365Fixed()));
// Define the ATM/OTM/ITM swaps
Frequency fixedLegFrequency = Frequency.Annual;
BusinessDayConvention fixedLegConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention floatingLegConvention = BusinessDayConvention.ModifiedFollowing;
DayCounter fixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
Frequency floatingLegFrequency = Frequency.Semiannual;
VanillaSwap.Type type = VanillaSwap.Type.Payer;
double dummyFixedRate = 0.03;
IborIndex indexSixMonths = new Euribor6M(rhTermStructure);
Date startDate = calendar.advance(settlementDate, 1, TimeUnit.Years,
floatingLegConvention);
Date maturity = calendar.advance(startDate, 5, TimeUnit.Years,
floatingLegConvention);
Schedule fixedSchedule = new Schedule(startDate, maturity, new Period(fixedLegFrequency),
calendar, fixedLegConvention, fixedLegConvention,
DateGeneration.Rule.Forward, false);
Schedule floatSchedule = new Schedule(startDate, maturity, new Period(floatingLegFrequency),
calendar, floatingLegConvention, floatingLegConvention,
DateGeneration.Rule.Forward, false);
VanillaSwap swap = new VanillaSwap(
type, 1000.0,
fixedSchedule, dummyFixedRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
swap.setPricingEngine(new DiscountingSwapEngine(rhTermStructure));
double fixedAtmRate = swap.fairRate();
double fixedOtmRate = fixedAtmRate * 1.2;
double fixedItmRate = fixedAtmRate * 0.8;
VanillaSwap atmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedAtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap otmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedOtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap itmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedItmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
// defining the swaptions to be used in model calibration
List<Period> swaptionMaturities = new List<Period>(5);
swaptionMaturities.Add(new Period(1, TimeUnit.Years));
swaptionMaturities.Add(new Period(2, TimeUnit.Years));
swaptionMaturities.Add(new Period(3, TimeUnit.Years));
swaptionMaturities.Add(new Period(4, TimeUnit.Years));
swaptionMaturities.Add(new Period(5, TimeUnit.Years));
List<CalibrationHelper> swaptions = new List<CalibrationHelper>();
// List of times that have to be included in the timegrid
List<double> times = new List<double>();
for (int i = 0; i < NumRows; i++)
{
int j = NumCols - i - 1; // 1x5, 2x4, 3x3, 4x2, 5x1
int k = i * NumCols + j;
Quote vol = new SimpleQuote(SwaptionVols[k]);
swaptions.Add(new SwaptionHelper(swaptionMaturities[i],
new Period(SwapLenghts[j], TimeUnit.Years),
new Handle<Quote>(vol),
indexSixMonths,
indexSixMonths.tenor(),
indexSixMonths.dayCounter(),
indexSixMonths.dayCounter(),
rhTermStructure, false));
swaptions.Last().addTimesTo(times);
}
// Building time-grid
TimeGrid grid = new TimeGrid(times, 30);
// defining the models
G2 modelG2 = new G2(rhTermStructure);
HullWhite modelHw = new HullWhite(rhTermStructure);
HullWhite modelHw2 = new HullWhite(rhTermStructure);
BlackKarasinski modelBk = new BlackKarasinski(rhTermStructure);
// model calibrations
Console.WriteLine("G2 (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new G2SwaptionEngine(modelG2, 6.0, 16));
CalibrateModel(modelG2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n" +
"b = {2:0.000000}, " +
"eta = {3:0.0000000}\n" +
"rho = {4:0.00000}\n",
modelG2.parameters()[0],
modelG2.parameters()[1],
modelG2.parameters()[2],
modelG2.parameters()[3],
modelG2.parameters()[4]);
Console.WriteLine("Hull-White (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new JamshidianSwaptionEngine(modelHw));
CalibrateModel(modelHw, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw.parameters()[0],
modelHw.parameters()[1]);
Console.WriteLine("Hull-White (numerical) calibration");
for (int i = 0; i < swaptions.Count(); i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelHw2, grid));
CalibrateModel(modelHw2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw2.parameters()[0],
modelHw2.parameters()[1]);
Console.WriteLine("Black-Karasinski (numerical) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelBk, grid));
CalibrateModel(modelBk, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.00000}\n",
modelBk.parameters()[0],
modelBk.parameters()[1]);
// ATM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ATM)",
fixedAtmRate);
List<Date> bermudanDates = new List<Date>();
List<CashFlow> leg = swap.fixedLeg();
for (int i = 0; i < leg.Count; i++)
{
Coupon coupon = (Coupon)leg[i];
bermudanDates.Add(coupon.accrualStartDate());
}
Exercise bermudanExercise = new BermudanExercise(bermudanDates);
Swaption bermudanSwaption = new Swaption(atmSwap, bermudanExercise);
// Do the pricing for each model
// G2 price the European swaption here, it should switch to bermudan
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.00}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", bermudanSwaption.NPV());
// OTM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (OTM)",
fixedOtmRate);
Swaption otmBermudanSwaption = new Swaption(otmSwap, bermudanExercise);
// Do the pricing for each model
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.0000}", otmBermudanSwaption.NPV());
// ITM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ITM)",
fixedItmRate);
Swaption itmBermudanSwaption = new Swaption(itmSwap, bermudanExercise);
// Do the pricing for each model
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", itmBermudanSwaption.NPV());
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public override void calculate()
{
double basisPoint = 1.0e-4;
Date exerciseDate = arguments_.exercise.date(0);
// the part of the swap preceding exerciseDate should be truncated
// to avoid taking into account unwanted cashflows
VanillaSwap swap = arguments_.swap;
double strike = swap.fixedRate;
// using the forecasting curve
swap.setPricingEngine(new DiscountingSwapEngine(swap.iborIndex().forwardingTermStructure()));
double atmForward = swap.fairRate();
// Volatilities are quoted for zero-spreaded swaps.
// Therefore, any spread on the floating leg must be removed
// with a corresponding correction on the fixed leg.
if (swap.spread != 0.0)
{
double correction = swap.spread * Math.Abs(swap.floatingLegBPS() / swap.fixedLegBPS());
strike -= correction;
atmForward -= correction;
results_.additionalResults["spreadCorrection"] = correction;
}
else
{
results_.additionalResults["spreadCorrection"] = 0.0;
}
results_.additionalResults["strike"] = strike;
results_.additionalResults["atmForward"] = atmForward;
// using the discounting curve
swap.setPricingEngine(new DiscountingSwapEngine(termStructure_));
double annuity;
switch (arguments_.settlementType)
{
case Settlement.Type.Physical: {
annuity = Math.Abs(swap.fixedLegBPS()) / basisPoint;
break;
}
case Settlement.Type.Cash: {
List <CashFlow> fixedLeg = swap.fixedLeg();
FixedRateCoupon firstCoupon = (FixedRateCoupon)fixedLeg[0];
DayCounter dayCount = firstCoupon.dayCounter();
double fixedLegCashBPS =
CashFlows.bps(fixedLeg,
new InterestRate(atmForward, dayCount, QLNet.Compounding.Compounded, Frequency.Annual), false,
termStructure_.link.referenceDate());
annuity = Math.Abs(fixedLegCashBPS / basisPoint);
break;
}
default:
throw new ApplicationException("unknown settlement type");
}
results_.additionalResults["annuity"] = annuity;
// the swap length calculation might be improved using the value date
// of the exercise date
double swapLength = volatility_.link.swapLength(exerciseDate,
arguments_.floatingPayDates.Last());
results_.additionalResults["swapLength"] = swapLength;
double variance = volatility_.link.blackVariance(exerciseDate,
swapLength,
strike);
double stdDev = Math.Sqrt(variance);
results_.additionalResults["stdDev"] = stdDev;
Option.Type w = (arguments_.type == VanillaSwap.Type.Payer) ?
Option.Type.Call : Option.Type.Put;
results_.value = Utils.blackFormula(w, strike, atmForward, stdDev, annuity);
double exerciseTime = volatility_.link.timeFromReference(exerciseDate);
results_.additionalResults["vega"] = Math.Sqrt(exerciseTime) *
Utils.blackFormulaStdDevDerivative(strike, atmForward, stdDev, annuity);
}
