public static Greeks GetOptionOnFutureGreeks(double underlyingPrice, double strike, double riskFreeRate,
DateTime expirationDate, DateTime calculationDate, string optionType, string exerciseType,
double optionPrice = double.NaN, double impliedVol = 0.15, string engineName = "baw")
{
QLNet.Date ExpirationDateObj = new QLNet.Date(expirationDate.Day, expirationDate.Month, expirationDate.Year);
QLNet.Date CalculationDateObj = new QLNet.Date(calculationDate.Day, calculationDate.Month, calculationDate.Year);
QLNet.DayCounter DayCountObj = new QLNet.Actual365Fixed();
QLNet.Calendar CalendarObj = new QLNet.UnitedStates();
Greeks GreeksOutput = new Greeks();
QLNet.Option.Type OptionTypeObj;
QLNet.Exercise ExerciseObj;
double ImpliedVol;
double OptionPrice;
int CalDte = DayCountObj.dayCount(CalculationDateObj, ExpirationDateObj);
GreeksOutput.CalDte = CalDte;
if (!double.IsNaN(optionPrice))
{
if (optionType.ToUpper() == "C")
{
if (optionPrice + strike - underlyingPrice <= 1.0e-12)
{
GreeksOutput.Delta = 1;
return(GreeksOutput);
}
}
else if (optionType.ToUpper() == "P")
{
if (optionPrice - strike + underlyingPrice <= 1.0e-12)
{
GreeksOutput.Delta = -1;
return(GreeksOutput);
}
}
}
if (CalDte == 0)
{
if (optionType.ToUpper() == "C")
{
if (strike <= underlyingPrice)
{
GreeksOutput.Delta = 1;
}
else
{
GreeksOutput.Delta = 0;
}
}
else if (optionType.ToUpper() == "P")
{
if (strike >= underlyingPrice)
{
GreeksOutput.Delta = -1;
}
else
{
GreeksOutput.Delta = 0;
}
}
return(GreeksOutput);
}
if (optionType.ToUpper() == "C")
{
OptionTypeObj = QLNet.Option.Type.Call;
}
else if (optionType.ToUpper() == "P")
{
OptionTypeObj = QLNet.Option.Type.Put;
}
else
{
return(GreeksOutput);
}
if (exerciseType.ToUpper() == "E")
{
ExerciseObj = new QLNet.EuropeanExercise(ExpirationDateObj);
}
else if (exerciseType.ToUpper() == "A")
{
ExerciseObj = new QLNet.AmericanExercise(CalculationDateObj, ExpirationDateObj);
}
else
{
return(GreeksOutput);
}
QLNet.Settings.setEvaluationDate(CalculationDateObj);
QLNet.Handle <Quote> UnderlyingObj = new QLNet.Handle <Quote>(new QLNet.SimpleQuote(underlyingPrice));
QLNet.Handle <YieldTermStructure> FlatRateObj = new QLNet.Handle <YieldTermStructure>(new QLNet.FlatForward(CalculationDateObj, riskFreeRate, DayCountObj));
QLNet.Handle <BlackVolTermStructure> FlatVolTsObj = new QLNet.Handle <BlackVolTermStructure>(new QLNet.BlackConstantVol(CalculationDateObj, CalendarObj, impliedVol, DayCountObj));
QLNet.BlackProcess BlackProc = new QLNet.BlackProcess(UnderlyingObj, FlatRateObj, FlatVolTsObj);
QLNet.PlainVanillaPayoff PayoffObj = new QLNet.PlainVanillaPayoff(OptionTypeObj, strike);
QLNet.VanillaOption OptionObj = new QLNet.VanillaOption(PayoffObj, ExerciseObj);
if (engineName == "baw")
{
OptionObj.setPricingEngine(new QLNet.BaroneAdesiWhaleyApproximationEngine(BlackProc));
}
else if (engineName == "fda")
{
OptionObj.setPricingEngine(new QLNet.FDAmericanEngine(BlackProc, 100, 100));
}
else
{
return(GreeksOutput);
}
if (!double.IsNaN(optionPrice))
{
try
{
ImpliedVol = OptionObj.impliedVolatility(targetValue: optionPrice, process: BlackProc, accuracy: 1e-5);
}
catch
{
return(GreeksOutput);
}
FlatVolTsObj = new QLNet.Handle <BlackVolTermStructure>(new QLNet.BlackConstantVol(CalculationDateObj, CalendarObj, ImpliedVol, DayCountObj));
BlackProc = new QLNet.BlackProcess(UnderlyingObj, FlatRateObj, FlatVolTsObj);
if (engineName == "baw")
{
OptionObj.setPricingEngine(new QLNet.BaroneAdesiWhaleyApproximationEngine(BlackProc));
}
else if (engineName == "fda")
{
OptionObj.setPricingEngine(new QLNet.FDAmericanEngine(BlackProc, 100, 100));
}
OptionPrice = optionPrice;
}
else
{
OptionPrice = OptionObj.NPV();
ImpliedVol = impliedVol;
}
OptionObj = new QLNet.VanillaOption(PayoffObj, new QLNet.EuropeanExercise(ExpirationDateObj));
OptionObj.setPricingEngine(new QLNet.AnalyticEuropeanEngine(BlackProc));
GreeksOutput.Delta = OptionObj.delta();
GreeksOutput.Vega = OptionObj.vega();
GreeksOutput.Theta = OptionObj.thetaPerDay();
GreeksOutput.Gamma = OptionObj.gamma();
GreeksOutput.OptionPrice = OptionPrice;
GreeksOutput.ImpliedVol = ImpliedVol;
return(GreeksOutput);
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.American, () => "not an American Option");
AmericanExercise ex = arguments_.exercise as AmericanExercise;
Utils.QL_REQUIRE(ex != null, () => "non-American exercise given");
Utils.QL_REQUIRE(!ex.payoffAtExpiry(), () => "payoff at expiry not handled");
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
double variance = process_.blackVolatility().link.blackVariance(ex.lastDate(), payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(ex.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(ex.lastDate());
double spot = process_.stateVariable().link.value();
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying given");
double strike = payoff.strike();
if (payoff.optionType() == Option.Type.Put)
{
// use put-call simmetry
Utils.swap <double>(ref spot, ref strike);
Utils.swap <double>(ref riskFreeDiscount, ref dividendDiscount);
payoff = new PlainVanillaPayoff(Option.Type.Call, strike);
}
if (dividendDiscount >= 1.0)
{
// early exercise is never optimal - use Black formula
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results_.value = black.value();
results_.delta = black.delta(spot);
results_.deltaForward = black.deltaForward();
results_.elasticity = black.elasticity(spot);
results_.gamma = black.gamma(spot);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double t = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(), arguments_.exercise.lastDate());
results_.rho = black.rho(t);
t = divdc.yearFraction(process_.dividendYield().link.referenceDate(), arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(t);
t = voldc.yearFraction(process_.blackVolatility().link.referenceDate(), arguments_.exercise.lastDate());
results_.vega = black.vega(t);
results_.theta = black.theta(spot, t);
results_.thetaPerDay = black.thetaPerDay(spot, t);
results_.strikeSensitivity = black.strikeSensitivity();
results_.itmCashProbability = black.itmCashProbability();
}
else
{
// early exercise can be optimal - use approximation
results_.value = americanCallApproximation(spot, strike, riskFreeDiscount, dividendDiscount, variance);
}
}
public static Greeks GetOptionOnFutureGreeks(double underlyingPrice,double strike,double riskFreeRate,
DateTime expirationDate, DateTime calculationDate, string optionType, string exerciseType,
double optionPrice=double.NaN,double impliedVol=0.15,string engineName="baw")
{
QLNet.Date ExpirationDateObj = new QLNet.Date(expirationDate.Day, expirationDate.Month, expirationDate.Year);
QLNet.Date CalculationDateObj = new QLNet.Date(calculationDate.Day, calculationDate.Month, calculationDate.Year);
QLNet.DayCounter DayCountObj = new QLNet.Actual365Fixed();
QLNet.Calendar CalendarObj = new QLNet.UnitedStates();
Greeks GreeksOutput = new Greeks();
QLNet.Option.Type OptionTypeObj;
QLNet.Exercise ExerciseObj;
double ImpliedVol;
double OptionPrice;
int CalDte = DayCountObj.dayCount(CalculationDateObj, ExpirationDateObj);
GreeksOutput.CalDte = CalDte;
if (!double.IsNaN(optionPrice))
{
if (optionType.ToUpper() == "C")
{
if (optionPrice + strike - underlyingPrice <= 1.0e-12)
{
GreeksOutput.Delta = 1;
return GreeksOutput;
}
}
else if (optionType.ToUpper() == "P")
{
if (optionPrice - strike + underlyingPrice <= 1.0e-12)
{
GreeksOutput.Delta = -1;
return GreeksOutput;
}
}
}
if (CalDte == 0)
{
if (optionType.ToUpper() == "C")
{
if (strike <= underlyingPrice)
{
GreeksOutput.Delta = 1;
}
else
{
GreeksOutput.Delta = 0;
}
}
else if (optionType.ToUpper() == "P")
{
if (strike >= underlyingPrice)
{
GreeksOutput.Delta = -1;
}
else
{
GreeksOutput.Delta = 0;
}
}
return GreeksOutput;
}
if (optionType.ToUpper() == "C")
{
OptionTypeObj = QLNet.Option.Type.Call;
}
else if (optionType.ToUpper() == "P")
{
OptionTypeObj = QLNet.Option.Type.Put;
}
else
{
return GreeksOutput;
}
if (exerciseType.ToUpper() == "E")
{
ExerciseObj = new QLNet.EuropeanExercise(ExpirationDateObj);
}
else if (exerciseType.ToUpper() == "A")
{
ExerciseObj = new QLNet.AmericanExercise(CalculationDateObj, ExpirationDateObj);
}
else
{
return GreeksOutput;
}
QLNet.Settings.setEvaluationDate(CalculationDateObj);
QLNet.Handle<Quote> UnderlyingObj = new QLNet.Handle<Quote>(new QLNet.SimpleQuote(underlyingPrice));
QLNet.Handle<YieldTermStructure> FlatRateObj = new QLNet.Handle<YieldTermStructure>(new QLNet.FlatForward(CalculationDateObj, riskFreeRate, DayCountObj));
QLNet.Handle<BlackVolTermStructure> FlatVolTsObj = new QLNet.Handle<BlackVolTermStructure>(new QLNet.BlackConstantVol(CalculationDateObj, CalendarObj, impliedVol, DayCountObj));
QLNet.BlackProcess BlackProc = new QLNet.BlackProcess(UnderlyingObj, FlatRateObj, FlatVolTsObj);
QLNet.PlainVanillaPayoff PayoffObj = new QLNet.PlainVanillaPayoff(OptionTypeObj, strike);
QLNet.VanillaOption OptionObj = new QLNet.VanillaOption(PayoffObj, ExerciseObj);
if (engineName == "baw")
{
OptionObj.setPricingEngine(new QLNet.BaroneAdesiWhaleyApproximationEngine(BlackProc));
}
else if (engineName == "fda")
{
OptionObj.setPricingEngine(new QLNet.FDAmericanEngine(BlackProc, 100, 100));
}
else
{
return GreeksOutput;
}
if (!double.IsNaN(optionPrice))
{
try
{
ImpliedVol = OptionObj.impliedVolatility(targetValue:optionPrice, process:BlackProc,accuracy:1e-5);
}
catch
{
return GreeksOutput;
}
FlatVolTsObj = new QLNet.Handle<BlackVolTermStructure>(new QLNet.BlackConstantVol(CalculationDateObj, CalendarObj, ImpliedVol, DayCountObj));
BlackProc = new QLNet.BlackProcess(UnderlyingObj, FlatRateObj, FlatVolTsObj);
if (engineName == "baw")
{
OptionObj.setPricingEngine(new QLNet.BaroneAdesiWhaleyApproximationEngine(BlackProc));
}
else if (engineName == "fda")
{
OptionObj.setPricingEngine(new QLNet.FDAmericanEngine(BlackProc, 100, 100));
}
OptionPrice = optionPrice;
}
else
{
OptionPrice = OptionObj.NPV();
ImpliedVol = impliedVol;
}
OptionObj = new QLNet.VanillaOption(PayoffObj, new QLNet.EuropeanExercise(ExpirationDateObj));
OptionObj.setPricingEngine(new QLNet.AnalyticEuropeanEngine(BlackProc));
GreeksOutput.Delta = OptionObj.delta();
GreeksOutput.Vega = OptionObj.vega();
GreeksOutput.Theta = OptionObj.thetaPerDay();
GreeksOutput.Gamma = OptionObj.gamma();
GreeksOutput.OptionPrice = OptionPrice;
GreeksOutput.ImpliedVol = ImpliedVol;
return GreeksOutput;
}
public override void calculate()
{
if (arguments_.barrierType == DoubleBarrier.Type.KIKO ||
arguments_.barrierType == DoubleBarrier.Type.KOKI)
{
AmericanExercise ex = arguments_.exercise as AmericanExercise;
Utils.QL_REQUIRE(ex != null, () => "KIKO/KOKI options must have American exercise");
Utils.QL_REQUIRE(ex.dates()[0] <=
process_.blackVolatility().currentLink().referenceDate(),
() => "American option with window exercise not handled yet");
}
else
{
EuropeanExercise ex = arguments_.exercise as EuropeanExercise;
Utils.QL_REQUIRE(ex != null, () => "non-European exercise given");
}
CashOrNothingPayoff payoff = arguments_.payoff as CashOrNothingPayoff;
Utils.QL_REQUIRE(payoff != null, () => "a cash-or-nothing payoff must be given");
double spot = process_.stateVariable().currentLink().value();
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying given");
double variance =
process_.blackVolatility().currentLink().blackVariance(
arguments_.exercise.lastDate(),
payoff.strike());
double barrier_lo = arguments_.barrier_lo.Value;
double barrier_hi = arguments_.barrier_hi.Value;
DoubleBarrier.Type barrierType = arguments_.barrierType;
Utils.QL_REQUIRE(barrier_lo > 0.0,
() => "positive low barrier value required");
Utils.QL_REQUIRE(barrier_hi > 0.0,
() => "positive high barrier value required");
Utils.QL_REQUIRE(barrier_lo < barrier_hi,
() => "barrier_lo must be < barrier_hi");
Utils.QL_REQUIRE(barrierType == DoubleBarrier.Type.KnockIn ||
barrierType == DoubleBarrier.Type.KnockOut ||
barrierType == DoubleBarrier.Type.KIKO ||
barrierType == DoubleBarrier.Type.KOKI,
() => "Unsupported barrier type");
// degenerate cases
switch (barrierType)
{
case DoubleBarrier.Type.KnockOut:
if (spot <= barrier_lo || spot >= barrier_hi)
{
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier.Type.KnockIn:
if (spot <= barrier_lo || spot >= barrier_hi)
{
// knocked in - pays
results_.value = payoff.cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier.Type.KIKO:
if (spot >= barrier_hi)
{
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
else if (spot <= barrier_lo)
{
// knocked in, pays
results_.value = payoff.cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
case DoubleBarrier.Type.KOKI:
if (spot <= barrier_lo)
{
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
else if (spot >= barrier_hi)
{
// knocked in, pays
results_.value = payoff.cashPayoff();
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.rho = 0;
return;
}
break;
}
AnalyticDoubleBarrierBinaryEngineHelper helper = new AnalyticDoubleBarrierBinaryEngineHelper(process_,
payoff, arguments_);
switch (barrierType)
{
case DoubleBarrier.Type.KnockOut:
case DoubleBarrier.Type.KnockIn:
results_.value = helper.payoffAtExpiry(spot, variance, barrierType);
break;
case DoubleBarrier.Type.KIKO:
case DoubleBarrier.Type.KOKI:
results_.value = helper.payoffKIKO(spot, variance, barrierType);
break;
default:
results_.value = null;
break;
}
}
public override void calculate()
{
if (!(arguments_.exercise.type() == Exercise.Type.American))
{
throw new Exception("not an American Option");
}
AmericanExercise ex = arguments_.exercise as AmericanExercise;
if (ex == null)
{
throw new Exception("non-American exercise given");
}
if (ex.payoffAtExpiry())
{
throw new Exception("payoff at expiry not handled");
}
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
if (payoff == null)
{
throw new Exception("non-striked payoff given");
}
double variance = process_.blackVolatility().link.blackVariance(ex.lastDate(), payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(ex.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(ex.lastDate());
double spot = process_.stateVariable().link.value();
if (!(spot > 0.0))
{
throw new Exception("negative or null underlying given");
}
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
if (dividendDiscount >= 1.0 && payoff.optionType() == Option.Type.Call)
{
// early exercise never optimal
results_.value = black.value();
results_.delta = black.delta(spot);
results_.deltaForward = black.deltaForward();
results_.elasticity = black.elasticity(spot);
results_.gamma = black.gamma(spot);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double t = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(), arguments_.exercise.lastDate());
results_.rho = black.rho(t);
t = divdc.yearFraction(process_.dividendYield().link.referenceDate(), arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(t);
t = voldc.yearFraction(process_.blackVolatility().link.referenceDate(), arguments_.exercise.lastDate());
results_.vega = black.vega(t);
results_.theta = black.theta(spot, t);
results_.thetaPerDay = black.thetaPerDay(spot, t);
results_.strikeSensitivity = black.strikeSensitivity();
results_.itmCashProbability = black.itmCashProbability();
}
else
{
// early exercise can be optimal
CumulativeNormalDistribution cumNormalDist = new CumulativeNormalDistribution();
NormalDistribution normalDist = new NormalDistribution();
double tolerance = 1e-6;
double Sk = BaroneAdesiWhaleyApproximationEngine.criticalPrice(payoff, riskFreeDiscount, dividendDiscount, variance, tolerance);
double forwardSk = Sk * dividendDiscount / riskFreeDiscount;
double alpha = -2.0 * Math.Log(riskFreeDiscount) / (variance);
double beta = 2.0 * Math.Log(dividendDiscount / riskFreeDiscount) / (variance);
double h = 1 - riskFreeDiscount;
double phi;
switch (payoff.optionType())
{
case Option.Type.Call:
phi = 1;
break;
case Option.Type.Put:
phi = -1;
break;
default:
throw new ArgumentException("invalid option type");
}
//it can throw: to be fixed
// FLOATING_POINT_EXCEPTION
double temp_root = Math.Sqrt((beta - 1) * (beta - 1) + (4 * alpha) / h);
double lambda = (-(beta - 1) + phi * temp_root) / 2;
double lambda_prime = -phi * alpha / (h * h * temp_root);
double black_Sk = Utils.blackFormula(payoff.optionType(), payoff.strike(), forwardSk, Math.Sqrt(variance)) * riskFreeDiscount;
double hA = phi * (Sk - payoff.strike()) - black_Sk;
double d1_Sk = (Math.Log(forwardSk / payoff.strike()) + 0.5 * variance) / Math.Sqrt(variance);
double d2_Sk = d1_Sk - Math.Sqrt(variance);
double part1 = forwardSk * normalDist.value(d1_Sk) / (alpha * Math.Sqrt(variance));
double part2 = -phi *forwardSk *cumNormalDist.value(phi *d1_Sk) * Math.Log(dividendDiscount) / Math.Log(riskFreeDiscount);
double part3 = +phi *payoff.strike() * cumNormalDist.value(phi * d2_Sk);
double V_E_h = part1 + part2 + part3;
double b = (1 - h) * alpha * lambda_prime / (2 * (2 * lambda + beta - 1));
double c = -((1 - h) * alpha / (2 * lambda + beta - 1)) * (V_E_h / (hA) + 1 / h + lambda_prime / (2 * lambda + beta - 1));
double temp_spot_ratio = Math.Log(spot / Sk);
double chi = temp_spot_ratio * (b * temp_spot_ratio + c);
if (phi * (Sk - spot) > 0)
{
results_.value = black.value() + hA * Math.Pow((spot / Sk), lambda) / (1 - chi);
}
else
{
results_.value = phi * (spot - payoff.strike());
}
double temp_chi_prime = (2 * b / spot) * Math.Log(spot / Sk);
double chi_prime = temp_chi_prime + c / spot;
double chi_double_prime = 2 * b / (spot * spot) - temp_chi_prime / spot - c / (spot * spot);
results_.delta = phi * dividendDiscount * cumNormalDist.value(phi * d1_Sk) + (lambda / (spot * (1 - chi)) + chi_prime / ((1 - chi) * (1 - chi))) * (phi * (Sk - payoff.strike()) - black_Sk) * Math.Pow((spot / Sk), lambda);
results_.gamma = phi * dividendDiscount * normalDist.value(phi * d1_Sk) / (spot * Math.Sqrt(variance)) + (2 * lambda * chi_prime / (spot * (1 - chi) * (1 - chi)) + 2 * chi_prime * chi_prime / ((1 - chi) * (1 - chi) * (1 - chi)) + chi_double_prime / ((1 - chi) * (1 - chi)) + lambda * (1 - lambda) / (spot * spot * (1 - chi))) * (phi * (Sk - payoff.strike()) - black_Sk) * Math.Pow((spot / Sk), lambda);
} // end of "early exercise can be optimal"
}
public override void calculate()
{
AmericanExercise ex = arguments_.exercise as AmericanExercise;
Utils.QL_REQUIRE(ex != null, () => "non-American exercise given");
Utils.QL_REQUIRE(ex.payoffAtExpiry(), () => "payoff must be at expiry");
Utils.QL_REQUIRE(ex.dates()[0] <= process_.blackVolatility().link.referenceDate(), () =>
"American option with window exercise not handled yet");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double spot = process_.stateVariable().link.value();
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying given");
double variance = process_.blackVolatility().link.blackVariance(ex.lastDate(), payoff.strike());
double?barrier = arguments_.barrier;
Utils.QL_REQUIRE(barrier > 0.0, () => "positive barrier value required");
Barrier.Type barrierType = arguments_.barrierType;
// KO degenerate cases
if ((barrierType == Barrier.Type.DownOut && spot <= barrier) ||
(barrierType == Barrier.Type.UpOut && spot >= barrier))
{
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.theta = 0;
results_.rho = 0;
results_.dividendRho = 0;
return;
}
// KI degenerate cases
if ((barrierType == Barrier.Type.DownIn && spot <= barrier) ||
(barrierType == Barrier.Type.UpIn && spot >= barrier))
{
// knocked in - is a digital european
Exercise exercise = new EuropeanExercise(arguments_.exercise.lastDate());
IPricingEngine engine = new AnalyticEuropeanEngine(process_);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
results_.value = opt.NPV();
results_.delta = opt.delta();
results_.gamma = opt.gamma();
results_.vega = opt.vega();
results_.theta = opt.theta();
results_.rho = opt.rho();
results_.dividendRho = opt.dividendRho();
return;
}
double riskFreeDiscount = process_.riskFreeRate().link.discount(ex.lastDate());
AnalyticBinaryBarrierEngine_helper helper = new AnalyticBinaryBarrierEngine_helper(
process_, payoff, ex, arguments_);
results_.value = helper.payoffAtExpiry(spot, variance, riskFreeDiscount);
}
public override void calculate()
{
if (!(arguments_.exercise.type() == Exercise.Type.American))
{
throw new ApplicationException("not an American Option");
}
AmericanExercise ex = arguments_.exercise as AmericanExercise;
if (ex == null)
{
throw new ApplicationException("non-American exercise given");
}
if (ex.payoffAtExpiry())
{
throw new ApplicationException("payoff at expiry not handled");
}
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
if (payoff == null)
{
throw new ApplicationException("non-striked payoff given");
}
double variance = process_.blackVolatility().link.blackVariance(ex.lastDate(), payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(ex.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(ex.lastDate());
double spot = process_.stateVariable().link.value();
if (!(spot > 0.0))
{
throw new ApplicationException("negative or null underlying given");
}
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
if (dividendDiscount >= 1.0 && payoff.optionType() == Option.Type.Call)
{
// early exercise never optimal
results_.value = black.value();
results_.delta = black.delta(spot);
results_.deltaForward = black.deltaForward();
results_.elasticity = black.elasticity(spot);
results_.gamma = black.gamma(spot);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double t = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(), arguments_.exercise.lastDate());
results_.rho = black.rho(t);
t = divdc.yearFraction(process_.dividendYield().link.referenceDate(), arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(t);
t = voldc.yearFraction(process_.blackVolatility().link.referenceDate(), arguments_.exercise.lastDate());
results_.vega = black.vega(t);
results_.theta = black.theta(spot, t);
results_.thetaPerDay = black.thetaPerDay(spot, t);
results_.strikeSensitivity = black.strikeSensitivity();
results_.itmCashProbability = black.itmCashProbability();
}
else
{
// early exercise can be optimal
CumulativeNormalDistribution cumNormalDist = new CumulativeNormalDistribution();
double tolerance = 1e-6;
double Sk = criticalPrice(payoff, riskFreeDiscount,
dividendDiscount, variance, tolerance);
double forwardSk = Sk * dividendDiscount / riskFreeDiscount;
double d1 = (Math.Log(forwardSk / payoff.strike()) + 0.5 * variance)
/ Math.Sqrt(variance);
double n = 2.0 * Math.Log(dividendDiscount / riskFreeDiscount) / variance;
double K = -2.0 * Math.Log(riskFreeDiscount) /
(variance * (1.0 - riskFreeDiscount));
double Q, a;
switch (payoff.optionType())
{
case Option.Type.Call:
Q = (-(n - 1.0) + Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4.0 * K)) / 2.0;
a = (Sk / Q) * (1.0 - dividendDiscount * cumNormalDist.value(d1));
if (spot < Sk)
{
results_.value = black.value() +
a * Math.Pow((spot / Sk), Q);
}
else
{
results_.value = spot - payoff.strike();
}
break;
case Option.Type.Put:
Q = (-(n - 1.0) - Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4.0 * K)) / 2.0;
a = -(Sk / Q) *
(1.0 - dividendDiscount * cumNormalDist.value(-d1));
if (spot > Sk)
{
results_.value = black.value() +
a * Math.Pow((spot / Sk), Q);
}
else
{
results_.value = payoff.strike() - spot;
}
break;
default:
throw new ApplicationException("unknown option type");
}
} // end of "early exercise can be optimal"
}
//static void Main(string[] args)
//{
// List<double> xGrid = Enumerable.Range(0, 100).Select(x => x / 10.0).ToList();
// List<double> yGrid = Enumerable.Range(0, 100).Select(x => x / 10.0).ToList();
// //List<double> xGrid = Enumerable.Range(0, 100);
// CubicInterpolation cubic = new CubicInterpolation(xGrid, xGrid.Count, yGrid,
// CubicInterpolation.DerivativeApprox.Kruger, true,
// CubicInterpolation.BoundaryCondition.SecondDerivative , 0.0,
// CubicInterpolation.BoundaryCondition.SecondDerivative , 0.0);
//}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
// set up dates
Calendar calendar = new TARGET();
Date todaysDate = new Date(15, Month.May, 1998);
Date settlementDate = new Date(17, Month.May, 1998);
Settings.setEvaluationDate(todaysDate);
// our options
Option.Type type = Option.Type.Put;
double underlying = 36;
double strike = 40;
double dividendYield = 0.00;
double riskFreeRate = 0.06;
double volatility = 0.20;
Date maturity = new Date(17, Month.May, 1999);
DayCounter dayCounter = new Actual365Fixed();
Console.WriteLine("Option type = " + type);
Console.WriteLine("Maturity = " + maturity);
Console.WriteLine("Underlying price = " + underlying);
Console.WriteLine("Strike = " + strike);
Console.WriteLine("Risk-free interest rate = {0:0.000000%}", riskFreeRate);
Console.WriteLine("Dividend yield = {0:0.000000%}", dividendYield);
Console.WriteLine("Volatility = {0:0.000000%}", volatility);
Console.Write("\n");
string method;
Console.Write("\n");
// write column headings
int[] widths = new int[] { 35, 14, 14, 14 };
Console.Write("{0,-" + widths[0] + "}", "Method");
Console.Write("{0,-" + widths[1] + "}", "European");
Console.Write("{0,-" + widths[2] + "}", "Bermudan");
Console.WriteLine("{0,-" + widths[3] + "}", "American");
List<Date> exerciseDates = new List<Date>(); ;
for (int i = 1; i <= 4; i++)
exerciseDates.Add(settlementDate + new Period(3 * i, TimeUnit.Months));
Exercise europeanExercise = new EuropeanExercise(maturity);
Exercise bermudanExercise = new BermudanExercise(exerciseDates);
Exercise americanExercise = new AmericanExercise(settlementDate, maturity);
Handle<Quote> underlyingH = new Handle<Quote>(new SimpleQuote(underlying));
// bootstrap the yield/dividend/vol curves
var flatTermStructure = new Handle<YieldTermStructure>(new FlatForward(settlementDate, riskFreeRate, dayCounter));
var flatDividendTS = new Handle<YieldTermStructure>(new FlatForward(settlementDate, dividendYield, dayCounter));
var flatVolTS = new Handle<BlackVolTermStructure>(new BlackConstantVol(settlementDate, calendar, volatility, dayCounter));
StrikedTypePayoff payoff = new PlainVanillaPayoff(type, strike);
var bsmProcess = new BlackScholesMertonProcess(underlyingH, flatDividendTS, flatTermStructure, flatVolTS);
// options
VanillaOption europeanOption = new VanillaOption(payoff, europeanExercise);
VanillaOption bermudanOption = new VanillaOption(payoff, bermudanExercise);
VanillaOption americanOption = new VanillaOption(payoff, americanExercise);
// Analytic formulas:
// Black-Scholes for European
method = "Black-Scholes";
europeanOption.setPricingEngine(new AnalyticEuropeanEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
europeanOption.theta();
// Barone-Adesi and Whaley approximation for American
method = "Barone-Adesi/Whaley";
americanOption.setPricingEngine(new BaroneAdesiWhaleyApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Bjerksund and Stensland approximation for American
method = "Bjerksund/Stensland";
americanOption.setPricingEngine(new BjerksundStenslandApproximationEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + "}", "N/A");
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Integral
method = "Integral";
europeanOption.setPricingEngine(new IntegralEngine(bsmProcess));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + "}", "N/A");
Console.WriteLine("{0,-" + widths[3] + "}", "N/A");
// Finite differences
int timeSteps = 801;
method = "Finite differences";
europeanOption.setPricingEngine(new FDEuropeanEngine(bsmProcess, timeSteps, timeSteps - 1));
bermudanOption.setPricingEngine(new FDBermudanEngine(bsmProcess, timeSteps, timeSteps - 1));
americanOption.setPricingEngine(new FDAmericanEngine(bsmProcess, timeSteps, timeSteps - 1));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Jarrow-Rudd
method = "Binomial Jarrow-Rudd";
europeanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<JarrowRudd>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
method = "Binomial Cox-Ross-Rubinstein";
europeanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<CoxRossRubinstein>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Additive equiprobabilities
method = "Additive equiprobabilities";
europeanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<AdditiveEQPBinomialTree>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Trigeorgis
method = "Binomial Trigeorgis";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Trigeorgis>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Tian
method = "Binomial Tian";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Tian>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Leisen-Reimer
method = "Binomial Leisen-Reimer";
europeanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<LeisenReimer>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Binomial method: Binomial Joshi
method = "Binomial Joshi";
europeanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps));
bermudanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps));
americanOption.setPricingEngine(new BinomialVanillaEngine<Joshi4>(bsmProcess, timeSteps));
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", bermudanOption.NPV());
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// Monte Carlo Method: MC (crude)
timeSteps = 1;
method = "MC (crude)";
ulong mcSeed = 42;
IPricingEngine mcengine1 = new MakeMCEuropeanEngine<PseudoRandom>(bsmProcess)
.withSteps(timeSteps)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
europeanOption.setPricingEngine(mcengine1);
// Real errorEstimate = europeanOption.errorEstimate();
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: QMC (Sobol)
method = "QMC (Sobol)";
int nSamples = 32768; // 2^15
IPricingEngine mcengine2 = new MakeMCEuropeanEngine<LowDiscrepancy>(bsmProcess)
.withSteps(timeSteps)
.withSamples(nSamples)
.value();
europeanOption.setPricingEngine(mcengine2);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", europeanOption.NPV());
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", "N/A");
// Monte Carlo Method: MC (Longstaff Schwartz)
method = "MC (Longstaff Schwartz)";
IPricingEngine mcengine3 = new MakeMCAmericanEngine<PseudoRandom>(bsmProcess)
.withSteps(100)
.withAntitheticVariate()
.withCalibrationSamples(4096)
.withAbsoluteTolerance(0.02)
.withSeed(mcSeed)
.value();
americanOption.setPricingEngine(mcengine3);
Console.Write("{0,-" + widths[0] + "}", method);
Console.Write("{0,-" + widths[1] + ":0.000000}", "N/A");
Console.Write("{0,-" + widths[2] + ":0.000000}", "N/A");
Console.WriteLine("{0,-" + widths[3] + ":0.000000}", americanOption.NPV());
// End test
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}