public override void calculate()
{
if (arguments_.exercise.type() != Exercise.Type.European)
{
throw new ApplicationException("not an European option");
}
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
if (payoff == null)
{
throw new ApplicationException("non-striked payoff given");
}
double variance = process_.blackVolatility().link.blackVariance(arguments_.exercise.lastDate(), payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(arguments_.exercise.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(arguments_.exercise.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);
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);
try {
results_.theta = black.theta(spot, t);
results_.thetaPerDay = black.thetaPerDay(spot, t);
} catch {
results_.theta = null;
results_.thetaPerDay = null;
}
results_.strikeSensitivity = black.strikeSensitivity();
results_.itmCashProbability = black.itmCashProbability();
}
private double vanillaEquivalent()
{
// Call KI equates to vanilla - callKO
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double forwardPrice = underlying() * dividendDiscount() / riskFreeDiscount();
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, stdDeviation(), riskFreeDiscount());
double vanilla = black.value();
if (vanilla < 0.0)
{
vanilla = 0.0;
}
return(vanilla);
}
public override void calculate() {
if(arguments_.exercise.type() != Exercise.Type.European)
throw new ApplicationException("not an European option");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
if (payoff == null)
throw new ApplicationException("non-striked payoff given");
double variance = process_.blackVolatility().link.blackVariance(arguments_.exercise.lastDate(), payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(arguments_.exercise.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(arguments_.exercise.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);
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);
try {
results_.theta = black.theta(spot, t);
results_.thetaPerDay = black.thetaPerDay(spot, t);
} catch {
results_.theta = null;
results_.thetaPerDay = null;
}
results_.strikeSensitivity = black.strikeSensitivity();
results_.itmCashProbability = black.itmCashProbability();
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European Option");
EuropeanExercise exercise = arguments_.exercise as EuropeanExercise;
Utils.QL_REQUIRE(exercise != null, () => "not an European Option");
SpreadBasketPayoff spreadPayoff = arguments_.payoff as SpreadBasketPayoff;
Utils.QL_REQUIRE(spreadPayoff != null, () => " spread payoff expected");
PlainVanillaPayoff payoff = spreadPayoff.basePayoff() as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
double strike = payoff.strike();
double f1 = process1_.stateVariable().link.value();
double f2 = process2_.stateVariable().link.value();
// use atm vols
double variance1 = process1_.blackVolatility().link.blackVariance(exercise.lastDate(), f1);
double variance2 = process2_.blackVolatility().link.blackVariance(exercise.lastDate(), f2);
double riskFreeDiscount = process1_.riskFreeRate().link.discount(exercise.lastDate());
Func <double, double> Square = x => x * x;
double f = f1 / (f2 + strike);
double v = Math.Sqrt(variance1
+ variance2 * Square(f2 / (f2 + strike))
- 2 * rho_ * Math.Sqrt(variance1 * variance2)
* (f2 / (f2 + strike)));
BlackCalculator black = new BlackCalculator(new PlainVanillaPayoff(payoff.optionType(), 1.0), f, v, riskFreeDiscount);
results_.value = (f2 + strike) * black.value();
}
public Calculator(BlackCalculator black) {
black_ = black;
}
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");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "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();
Utils.QL_REQUIRE(spot > 0.0, () => "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 = 0;
switch (payoff.optionType())
{
case Option.Type.Call:
phi = 1;
break;
case Option.Type.Put:
phi = -1;
break;
default:
Utils.QL_FAIL("invalid option type");
break;
}
//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(IPricingEngineResults r)
{
OneAssetOption.Results results = r as OneAssetOption.Results;
setGridLimits();
initializeInitialCondition();
initializeOperator();
initializeBoundaryConditions();
initializeStepCondition();
List <IOperator> operatorSet = new List <IOperator>();
List <Vector> arraySet = new List <Vector>();
BoundaryConditionSet bcSet = new BoundaryConditionSet();
StepConditionSet <Vector> conditionSet = new StepConditionSet <Vector>();
prices_ = (SampledCurve)intrinsicValues_.Clone();
controlPrices_ = (SampledCurve)intrinsicValues_.Clone();
controlOperator_ = (TridiagonalOperator)finiteDifferenceOperator_.Clone();
controlBCs_[0] = BCs_[0];
controlBCs_[1] = BCs_[1];
operatorSet.Add(finiteDifferenceOperator_);
operatorSet.Add(controlOperator_);
arraySet.Add(prices_.values());
arraySet.Add(controlPrices_.values());
bcSet.Add(BCs_);
bcSet.Add(controlBCs_);
conditionSet.Add(stepCondition_);
conditionSet.Add(new NullCondition <Vector>());
var model = new FiniteDifferenceModel <ParallelEvolver <CrankNicolson <TridiagonalOperator> > >(operatorSet, bcSet);
object temp = arraySet;
model.rollback(ref temp, getResidualTime(), 0.0, timeSteps_, conditionSet);
arraySet = (List <Vector>)temp;
prices_.setValues(arraySet[0]);
controlPrices_.setValues(arraySet[1]);
StrikedTypePayoff striked_payoff = payoff_ as StrikedTypePayoff;
Utils.QL_REQUIRE(striked_payoff != null, () => "non-striked payoff given");
double variance = process_.blackVolatility().link.blackVariance(exerciseDate_, striked_payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(exerciseDate_);
double riskFreeDiscount = process_.riskFreeRate().link.discount(exerciseDate_);
double spot = process_.stateVariable().link.value();
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(striked_payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results.value = prices_.valueAtCenter()
- controlPrices_.valueAtCenter()
+ black.value();
results.delta = prices_.firstDerivativeAtCenter()
- controlPrices_.firstDerivativeAtCenter()
+ black.delta(spot);
results.gamma = prices_.secondDerivativeAtCenter()
- controlPrices_.secondDerivativeAtCenter()
+ black.gamma(spot);
results.additionalResults["priceCurve"] = prices_;
}
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"
}
public override void calculate(IPricingEngineResults r)
{
OneAssetOption.Results results = r as OneAssetOption.Results;
setGridLimits();
initializeInitialCondition();
initializeOperator();
initializeBoundaryConditions();
initializeStepCondition();
// typedef StandardSystemFiniteDifferenceModel model_type;
List<IOperator> operatorSet = new List<IOperator>();
List<Vector> arraySet = new List<Vector>();
BoundaryConditionSet bcSet = new BoundaryConditionSet();
StepConditionSet<Vector> conditionSet = new StepConditionSet<Vector>();
prices_ = (SampledCurve)intrinsicValues_.Clone();
controlPrices_ = (SampledCurve)intrinsicValues_.Clone();
controlOperator_ = (TridiagonalOperator)finiteDifferenceOperator_.Clone();
controlBCs_[0] = BCs_[0];
controlBCs_[1] = BCs_[1];
operatorSet.Add(finiteDifferenceOperator_);
operatorSet.Add(controlOperator_);
arraySet.Add(prices_.values());
arraySet.Add(controlPrices_.values());
bcSet.Add(BCs_);
bcSet.Add(controlBCs_);
conditionSet.Add(stepCondition_);
conditionSet.Add(new NullCondition<Vector>());
var model = new FiniteDifferenceModel<ParallelEvolver<CrankNicolson<TridiagonalOperator>>>(operatorSet, bcSet);
object temp = arraySet;
model.rollback(ref temp, getResidualTime(), 0.0, timeSteps_, conditionSet);
arraySet = (List<Vector>)temp;
prices_.setValues(arraySet[0]);
controlPrices_.setValues(arraySet[1]);
StrikedTypePayoff striked_payoff = payoff_ as StrikedTypePayoff;
if (striked_payoff == null)
throw new ApplicationException("non-striked payoff given");
double variance = process_.blackVolatility().link.blackVariance(exerciseDate_, striked_payoff.strike());
double dividendDiscount = process_.dividendYield().link.discount(exerciseDate_);
double riskFreeDiscount = process_.riskFreeRate().link.discount(exerciseDate_);
double spot = process_.stateVariable().link.value();
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(striked_payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results.value = prices_.valueAtCenter()
- controlPrices_.valueAtCenter()
+ black.value();
results.delta = prices_.firstDerivativeAtCenter()
- controlPrices_.firstDerivativeAtCenter()
+ black.delta(spot);
results.gamma = prices_.secondDerivativeAtCenter()
- controlPrices_.secondDerivativeAtCenter()
+ black.gamma(spot);
results.additionalResults.Add("priceCurve", prices_);
}
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"
}
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");
}
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
if (payoff == null)
{
throw new ApplicationException("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();
if (!(spot > 0.0))
{
throw new ApplicationException("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 override void calculate()
{
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European option");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
Date settlementDate = process_.riskFreeRate().link.referenceDate();
double riskless = 0.0;
int i;
for (i = 0; i < arguments_.cashFlow.Count; i++)
{
if (arguments_.cashFlow[i].date() >= settlementDate)
{
riskless += arguments_.cashFlow[i].amount() *
process_.riskFreeRate().link.discount(arguments_.cashFlow[i].date());
}
}
double spot = process_.stateVariable().link.value() - riskless;
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying after subtracting dividends");
double dividendDiscount = process_.dividendYield().link.discount(arguments_.exercise.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(arguments_.exercise.lastDate());
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
double variance = process_.blackVolatility().link.blackVariance(arguments_.exercise.lastDate(),
payoff.strike());
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results_.value = black.value();
results_.delta = black.delta(spot);
results_.gamma = black.gamma(spot);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double t = voldc.yearFraction(process_.blackVolatility().link.referenceDate(), arguments_.exercise.lastDate());
results_.vega = black.vega(t);
double delta_theta = 0.0, delta_rho = 0.0;
for (i = 0; i < arguments_.cashFlow.Count; i++)
{
Date d = arguments_.cashFlow[i].date();
if (d >= settlementDate)
{
delta_theta -= arguments_.cashFlow[i].amount() *
process_.riskFreeRate().link.zeroRate(d, rfdc, Compounding.Continuous, Frequency.Annual).value() *
process_.riskFreeRate().link.discount(d);
double t1 = process_.time(d);
delta_rho += arguments_.cashFlow[i].amount() * t1 *
process_.riskFreeRate().link.discount(t1);
}
}
t = process_.time(arguments_.exercise.lastDate());
try
{
results_.theta = black.theta(spot, t) +
delta_theta * black.delta(spot);
}
catch (Exception)
{
results_.theta = null;
}
results_.rho = black.rho(t) + delta_rho * black.delta(spot);
}
public override void calculate()
{
/* this engine cannot really check for the averageType==Geometric
since it can be used as control variate for the Arithmetic version
QL_REQUIRE(arguments_.averageType == Average::Geometric,
"not a geometric average option");
*/
if(!(arguments_.exercise.type() == Exercise.Type.European))
throw new ApplicationException("not an European Option");
double runningLog;
int pastFixings;
if (arguments_.averageType == Average.Type.Geometric) {
if(!(arguments_.runningAccumulator>0.0))
throw new ApplicationException("positive running product required: "
+ arguments_.runningAccumulator + " not allowed");
runningLog =
Math.Log(arguments_.runningAccumulator.GetValueOrDefault());
pastFixings = arguments_.pastFixings.GetValueOrDefault();
} else { // it is being used as control variate
runningLog = 1.0;
pastFixings = 0;
}
PlainVanillaPayoff payoff = (PlainVanillaPayoff)(arguments_.payoff);
if (payoff == null)
throw new ApplicationException("non-plain payoff given");
Date referenceDate = process_.riskFreeRate().link.referenceDate();
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
List<double> fixingTimes = new InitializedList<double>(arguments_.fixingDates.Count());
int i;
for (i=0; i<arguments_.fixingDates.Count(); i++) {
if (arguments_.fixingDates[i]>=referenceDate) {
double t = voldc.yearFraction(referenceDate,
arguments_.fixingDates[i]);
fixingTimes.Add(t);
}
}
int remainingFixings = fixingTimes.Count();
int numberOfFixings = pastFixings + remainingFixings;
double N = numberOfFixings;
double pastWeight = pastFixings/N;
double futureWeight = 1.0-pastWeight;
/*double timeSum = std::accumulate(fixingTimes.begin(),
fixingTimes.end(), 0.0);*/
double timeSum = 0;
fixingTimes.ForEach((ii, vv) => timeSum += fixingTimes[ii]);
double vola = process_.blackVolatility().link.blackVol(
arguments_.exercise.lastDate(),
payoff.strike());
double temp = 0.0;
for (i=pastFixings+1; i<numberOfFixings; i++)
temp += fixingTimes[i-pastFixings-1]*(N-i);
double variance = vola*vola /N/N * (timeSum+ 2.0*temp);
double dsigG_dsig = Math.Sqrt((timeSum + 2.0*temp))/N;
double sigG = vola * dsigG_dsig;
double dmuG_dsig = -(vola * timeSum)/N;
Date exDate = arguments_.exercise.lastDate();
double dividendRate = process_.dividendYield().link.
zeroRate(exDate, divdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double riskFreeRate = process_.riskFreeRate().link.
zeroRate(exDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double nu = riskFreeRate - dividendRate - 0.5*vola*vola;
double s = process_.stateVariable().link.value();
if(!(s > 0.0))
throw new ApplicationException("positive underlying value required");
int M = (pastFixings == 0 ? 1 : pastFixings);
double muG = pastWeight * runningLog/M +
futureWeight * Math.Log(s) + nu*timeSum/N;
double forwardPrice = Math.Exp(muG + variance / 2.0);
double riskFreeDiscount = process_.riskFreeRate().link.discount(
arguments_.exercise.lastDate());
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance),
riskFreeDiscount);
results_.value = black.value();
results_.delta = futureWeight*black.delta(forwardPrice)*forwardPrice/s;
results_.gamma = forwardPrice*futureWeight/(s*s)
*( black.gamma(forwardPrice)*futureWeight*forwardPrice
- pastWeight*black.delta(forwardPrice) );
double Nx_1, nx_1;
CumulativeNormalDistribution CND = new CumulativeNormalDistribution();
NormalDistribution ND = new NormalDistribution();
if (sigG > Const.QL_Epsilon) {
double x_1 = (muG-Math.Log(payoff.strike())+variance)/sigG;
Nx_1 = CND.value(x_1);
nx_1 = ND.value( x_1);
} else {
Nx_1 = (muG > Math.Log(payoff.strike()) ? 1.0 : 0.0);
nx_1 = 0.0;
}
results_.vega = forwardPrice * riskFreeDiscount *
( (dmuG_dsig + sigG * dsigG_dsig)*Nx_1 + nx_1*dsigG_dsig );
if (payoff.optionType() == Option.Type.Put)
results_.vega -= riskFreeDiscount * forwardPrice *
(dmuG_dsig + sigG * dsigG_dsig);
double tRho = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(),
arguments_.exercise.lastDate());
results_.rho = black.rho(tRho)*timeSum/(N*tRho)
- (tRho-timeSum/N)*results_.value;
double tDiv = divdc.yearFraction(
process_.dividendYield().link.referenceDate(),
arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(tDiv)*timeSum /(N*tDiv);
results_.strikeSensitivity = black.strikeSensitivity();
results_.theta = Utils.blackScholesTheta(process_,
results_.value.GetValueOrDefault(),
results_.delta.GetValueOrDefault(),
results_.gamma.GetValueOrDefault());
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.accruedCoupon == null &&
arguments_.lastFixing == null, () =>
"this engine cannot price options already started");
Utils.QL_REQUIRE(arguments_.localCap == null &&
arguments_.localFloor == null &&
arguments_.globalCap == null &&
arguments_.globalFloor == null, () =>
"this engine cannot price capped/floored options");
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European option");
PercentageStrikePayoff moneyness = arguments_.payoff as PercentageStrikePayoff;
Utils.QL_REQUIRE(moneyness != null, () => "wrong payoff given");
List <Date> resetDates = arguments_.resetDates;
resetDates.Add(arguments_.exercise.lastDate());
double underlying = process_.stateVariable().link.value();
Utils.QL_REQUIRE(underlying > 0.0, () => "negative or null underlying");
StrikedTypePayoff payoff = new PlainVanillaPayoff(moneyness.optionType(), 1.0);
results_.value = 0.0;
results_.delta = results_.gamma = 0.0;
results_.theta = 0.0;
results_.rho = results_.dividendRho = 0.0;
results_.vega = 0.0;
for (int i = 1; i < resetDates.Count; i++)
{
double discount = process_.riskFreeRate().link.discount(resetDates[i - 1]);
double rDiscount = process_.riskFreeRate().link.discount(resetDates[i]) /
process_.riskFreeRate().link.discount(resetDates[i - 1]);
double qDiscount = process_.dividendYield().link.discount(resetDates[i]) /
process_.dividendYield().link.discount(resetDates[i - 1]);
double forward = (1.0 / moneyness.strike()) * qDiscount / rDiscount;
double variance = process_.blackVolatility().link.blackForwardVariance(
resetDates[i - 1], resetDates[i],
underlying * moneyness.strike());
BlackCalculator black = new BlackCalculator(payoff, forward, Math.Sqrt(variance), rDiscount);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
results_.value += discount * moneyness.strike() * black.value();
results_.delta += 0.0;
results_.gamma += 0.0;
results_.theta += process_.riskFreeRate().link.forwardRate(
resetDates[i - 1], resetDates[i], rfdc, Compounding.Continuous, Frequency.NoFrequency).value() *
discount * moneyness.strike() * black.value();
double dt = rfdc.yearFraction(resetDates[i - 1], resetDates[i]);
double t = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(), resetDates[i - 1]);
results_.rho += discount * moneyness.strike() * (black.rho(dt) - t * black.value());
dt = divdc.yearFraction(resetDates[i - 1], resetDates[i]);
results_.dividendRho += discount * moneyness.strike() * black.dividendRho(dt);
dt = voldc.yearFraction(resetDates[i - 1], resetDates[i]);
results_.vega += discount * moneyness.strike() * black.vega(dt);
}
}
public override void calculate()
{
Utils.QL_REQUIRE( arguments_.exercise.type() == Exercise.Type.European, () => "not an European option" );
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE( payoff != null, () => "non-striked payoff given" );
Date settlementDate = process_.riskFreeRate().link.referenceDate();
double riskless = 0.0;
int i;
for (i=0; i<arguments_.cashFlow.Count; i++)
if (arguments_.cashFlow[i].date() >= settlementDate)
riskless += arguments_.cashFlow[i].amount() *
process_.riskFreeRate().link.discount(arguments_.cashFlow[i].date());
double spot = process_.stateVariable().link.value() - riskless;
Utils.QL_REQUIRE( spot > 0.0, () => "negative or null underlying after subtracting dividends" );
double dividendDiscount = process_.dividendYield().link.discount(arguments_.exercise.lastDate());
double riskFreeDiscount = process_.riskFreeRate().link.discount(arguments_.exercise.lastDate());
double forwardPrice = spot * dividendDiscount / riskFreeDiscount;
double variance = process_.blackVolatility().link.blackVariance( arguments_.exercise.lastDate(),
payoff.strike());
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results_.value = black.value();
results_.delta = black.delta(spot);
results_.gamma = black.gamma(spot);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double t = voldc.yearFraction( process_.blackVolatility().link.referenceDate(),arguments_.exercise.lastDate());
results_.vega = black.vega(t);
double delta_theta = 0.0, delta_rho = 0.0;
for (i = 0; i < arguments_.cashFlow.Count; i++)
{
Date d = arguments_.cashFlow[i].date();
if (d >= settlementDate)
{
delta_theta -= arguments_.cashFlow[i].amount() *
process_.riskFreeRate().link.zeroRate(d,rfdc,Compounding.Continuous,Frequency.Annual).value() *
process_.riskFreeRate().link.discount(d);
double t1 = process_.time(d);
delta_rho += arguments_.cashFlow[i].amount() * t1 *
process_.riskFreeRate().link.discount(t1);
}
}
t = process_.time(arguments_.exercise.lastDate());
try
{
results_.theta = black.theta(spot, t) +
delta_theta * black.delta(spot);
}
catch (Exception)
{
results_.theta = null;
}
results_.rho = black.rho(t) + delta_rho * black.delta(spot);
}
public override void calculate()
{
if (arguments_.averageType != Average.Type.Geometric)
{
throw new ApplicationException("not a geometric average option");
}
if (arguments_.exercise.type() != Exercise.Type.European)
{
throw new ApplicationException("not an European Option");
}
Date exercise = arguments_.exercise.lastDate();
PlainVanillaPayoff payoff = (PlainVanillaPayoff)(arguments_.payoff);
if (payoff == null)
{
throw new ApplicationException("non-plain payoff given");
}
double volatility =
process_.blackVolatility().link.blackVol(exercise, payoff.strike());
double variance =
process_.blackVolatility().link.blackVariance(exercise,
payoff.strike());
double riskFreeDiscount =
process_.riskFreeRate().link.discount(exercise);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double dividendYield = 0.5 * (
process_.riskFreeRate().link.zeroRate(exercise, rfdc,
Compounding.Continuous,
Frequency.NoFrequency).rate() +
process_.dividendYield().link.zeroRate(exercise, divdc,
Compounding.Continuous,
Frequency.NoFrequency).rate() +
volatility * volatility / 6.0);
double t_q = divdc.yearFraction(
process_.dividendYield().link.referenceDate(), exercise);
double dividendDiscount = Math.Exp(-dividendYield * t_q);
double spot = process_.stateVariable().link.value();
if (!(spot > 0.0))
{
throw new ApplicationException("negative or null underlying");
}
double forward = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(payoff,
forward,
Math.Sqrt(variance / 3.0),
riskFreeDiscount);
results_.value = black.value();
results_.delta = black.delta(spot);
results_.gamma = black.gamma(spot);
results_.dividendRho = black.dividendRho(t_q) / 2.0;
double t_r = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(),
arguments_.exercise.lastDate());
results_.rho = black.rho(t_r) + 0.5 * black.dividendRho(t_q);
double t_v = voldc.yearFraction(
process_.blackVolatility().link.referenceDate(),
arguments_.exercise.lastDate());
results_.vega = black.vega(t_v) / Math.Sqrt(3.0) +
black.dividendRho(t_q) * volatility / 6.0;
try{
results_.theta = black.theta(spot, t_v);
}
catch (System.Exception /*Error*/) {
results_.theta = double.NaN; //Null<Real>();
}
}
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();
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()
{
/* this engine cannot really check for the averageType==Geometric
* since it can be used as control variate for the Arithmetic version
* QL_REQUIRE(arguments_.averageType == Average::Geometric,"not a geometric average option")
*/
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European Option");
double runningLog;
int pastFixings;
if (arguments_.averageType == Average.Type.Geometric)
{
Utils.QL_REQUIRE(arguments_.runningAccumulator > 0.0, () =>
"positive running product required: " + arguments_.runningAccumulator + " not allowed");
runningLog = Math.Log(arguments_.runningAccumulator.GetValueOrDefault());
pastFixings = arguments_.pastFixings.GetValueOrDefault();
}
else
{ // it is being used as control variate
runningLog = 1.0;
pastFixings = 0;
}
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
Date referenceDate = process_.riskFreeRate().link.referenceDate();
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
List <double> fixingTimes = new List <double>();
int i;
for (i = 0; i < arguments_.fixingDates.Count; i++)
{
if (arguments_.fixingDates[i] >= referenceDate)
{
double t = voldc.yearFraction(referenceDate, arguments_.fixingDates[i]);
fixingTimes.Add(t);
}
}
int remainingFixings = fixingTimes.Count;
int numberOfFixings = pastFixings + remainingFixings;
double N = numberOfFixings;
double pastWeight = pastFixings / N;
double futureWeight = 1.0 - pastWeight;
double timeSum = 0;
fixingTimes.ForEach((ii, vv) => timeSum += fixingTimes[ii]);
double vola = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), payoff.strike());
double temp = 0.0;
for (i = pastFixings + 1; i < numberOfFixings; i++)
{
temp += fixingTimes[i - pastFixings - 1] * (N - i);
}
double variance = vola * vola / N / N * (timeSum + 2.0 * temp);
double dsigG_dsig = Math.Sqrt((timeSum + 2.0 * temp)) / N;
double sigG = vola * dsigG_dsig;
double dmuG_dsig = -(vola * timeSum) / N;
Date exDate = arguments_.exercise.lastDate();
double dividendRate = process_.dividendYield().link.
zeroRate(exDate, divdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double riskFreeRate = process_.riskFreeRate().link.
zeroRate(exDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double nu = riskFreeRate - dividendRate - 0.5 * vola * vola;
double s = process_.stateVariable().link.value();
Utils.QL_REQUIRE(s > 0.0, () => "positive underlying value required");
int M = (pastFixings == 0 ? 1 : pastFixings);
double muG = pastWeight * runningLog / M + futureWeight * Math.Log(s) + nu * timeSum / N;
double forwardPrice = Math.Exp(muG + variance / 2.0);
double riskFreeDiscount = process_.riskFreeRate().link.discount(arguments_.exercise.lastDate());
BlackCalculator black = new BlackCalculator(payoff, forwardPrice, Math.Sqrt(variance), riskFreeDiscount);
results_.value = black.value();
results_.delta = futureWeight * black.delta(forwardPrice) * forwardPrice / s;
results_.gamma = forwardPrice * futureWeight / (s * s)
* (black.gamma(forwardPrice) * futureWeight * forwardPrice
- pastWeight * black.delta(forwardPrice));
double Nx_1, nx_1;
CumulativeNormalDistribution CND = new CumulativeNormalDistribution();
NormalDistribution ND = new NormalDistribution();
if (sigG > Const.QL_EPSILON)
{
double x_1 = (muG - Math.Log(payoff.strike()) + variance) / sigG;
Nx_1 = CND.value(x_1);
nx_1 = ND.value(x_1);
}
else
{
Nx_1 = (muG > Math.Log(payoff.strike()) ? 1.0 : 0.0);
nx_1 = 0.0;
}
results_.vega = forwardPrice * riskFreeDiscount *
((dmuG_dsig + sigG * dsigG_dsig) * Nx_1 + nx_1 * dsigG_dsig);
if (payoff.optionType() == Option.Type.Put)
{
results_.vega -= riskFreeDiscount * forwardPrice *
(dmuG_dsig + sigG * dsigG_dsig);
}
double tRho = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(),
arguments_.exercise.lastDate());
results_.rho = black.rho(tRho) * timeSum / (N * tRho)
- (tRho - timeSum / N) * results_.value;
double tDiv = divdc.yearFraction(
process_.dividendYield().link.referenceDate(),
arguments_.exercise.lastDate());
results_.dividendRho = black.dividendRho(tDiv) * timeSum / (N * tDiv);
results_.strikeSensitivity = black.strikeSensitivity();
results_.theta = Utils.blackScholesTheta(process_,
results_.value.GetValueOrDefault(),
results_.delta.GetValueOrDefault(),
results_.gamma.GetValueOrDefault());
}
public override void calculate()
{
if (arguments_.averageType != Average.Type.Geometric)
throw new ApplicationException("not a geometric average option");
if (arguments_.exercise.type() != Exercise.Type.European)
throw new ApplicationException("not an European Option");
Date exercise = arguments_.exercise.lastDate();
PlainVanillaPayoff payoff = (PlainVanillaPayoff)(arguments_.payoff);
if (payoff == null)
throw new ApplicationException("non-plain payoff given");
double volatility =
process_.blackVolatility().link.blackVol(exercise, payoff.strike());
double variance =
process_.blackVolatility().link.blackVariance(exercise,
payoff.strike());
double riskFreeDiscount =
process_.riskFreeRate().link.discount(exercise);
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
double dividendYield = 0.5 * (
process_.riskFreeRate().link.zeroRate(exercise, rfdc,
Compounding.Continuous,
Frequency.NoFrequency).rate() +
process_.dividendYield().link.zeroRate(exercise, divdc,
Compounding.Continuous,
Frequency.NoFrequency).rate() +
volatility * volatility / 6.0);
double t_q = divdc.yearFraction(
process_.dividendYield().link.referenceDate(), exercise);
double dividendDiscount = Math.Exp(-dividendYield * t_q);
double spot = process_.stateVariable().link.value();
if (!(spot > 0.0))
throw new ApplicationException("negative or null underlying");
double forward = spot * dividendDiscount / riskFreeDiscount;
BlackCalculator black = new BlackCalculator(payoff,
forward,
Math.Sqrt(variance / 3.0),
riskFreeDiscount);
results_.value = black.value();
results_.delta = black.delta(spot);
results_.gamma = black.gamma(spot);
results_.dividendRho = black.dividendRho(t_q) / 2.0;
double t_r = rfdc.yearFraction(process_.riskFreeRate().link.referenceDate(),
arguments_.exercise.lastDate());
results_.rho = black.rho(t_r) + 0.5 * black.dividendRho(t_q);
double t_v = voldc.yearFraction(
process_.blackVolatility().link.referenceDate(),
arguments_.exercise.lastDate());
results_.vega = black.vega(t_v) / Math.Sqrt(3.0) +
black.dividendRho(t_q) * volatility / 6.0;
try{
results_.theta = black.theta(spot, t_v);
}
catch (System.Exception /*Error*/){
results_.theta = double.NaN; //Null<Real>();
}
}
public Calculator(BlackCalculator black)
{
black_ = black;
}
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");
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
if(payoff == null) throw new ApplicationException("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();
if (!(spot > 0.0)) throw new ApplicationException("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);
}
}
