public override void calculate()
{
double sigmaShift_vega = 0.001;
double sigmaShift_volga = 0.0001;
double spotShift_delta = 0.0001 * spotFX_.link.value();
double sigmaShift_vanna = 0.0001;
Utils.QL_REQUIRE(arguments_.barrierType == DoubleBarrier.Type.KnockIn ||
arguments_.barrierType == DoubleBarrier.Type.KnockOut, () =>
"Only same type barrier supported");
Handle <Quote> x0Quote = new Handle <Quote>(new SimpleQuote(spotFX_.link.value()));
Handle <Quote> atmVolQuote = new Handle <Quote>(new SimpleQuote(atmVol_.link.value()));
BlackVolTermStructure blackVolTS = new BlackConstantVol(Settings.evaluationDate(),
new NullCalendar(), atmVolQuote, new Actual365Fixed());
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(x0Quote, foreignTS_, domesticTS_,
new Handle <BlackVolTermStructure>(blackVolTS));
IPricingEngine engineBS = getOriginalEngine_(stochProcess, series_);
BlackDeltaCalculator blackDeltaCalculatorAtm = new BlackDeltaCalculator(
Option.Type.Call, atmVol_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_));
double atmStrike = blackDeltaCalculatorAtm.atmStrike(atmVol_.link.atmType());
double call25Vol = vol25Call_.link.value();
double put25Vol = vol25Put_.link.value();
BlackDeltaCalculator blackDeltaCalculatorPut25 = new BlackDeltaCalculator(
Option.Type.Put, vol25Put_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
put25Vol * Math.Sqrt(T_));
double put25Strike = blackDeltaCalculatorPut25.strikeFromDelta(-0.25);
BlackDeltaCalculator blackDeltaCalculatorCall25 = new BlackDeltaCalculator(
Option.Type.Call, vol25Call_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
call25Vol * Math.Sqrt(T_));
double call25Strike = blackDeltaCalculatorCall25.strikeFromDelta(0.25);
//here use vanna volga interpolated smile to price vanilla
List <double> strikes = new List <double>();
List <double> vols = new List <double>();
strikes.Add(put25Strike);
vols.Add(put25Vol);
strikes.Add(atmStrike);
vols.Add(atmVol_.link.value());
strikes.Add(call25Strike);
vols.Add(call25Vol);
VannaVolga vannaVolga = new VannaVolga(x0Quote.link.value(), foreignTS_.link.discount(T_),
foreignTS_.link.discount(T_), T_);
Interpolation interpolation = vannaVolga.interpolate(strikes, strikes.Count, vols);
interpolation.enableExtrapolation();
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "invalid payoff");
double strikeVol = interpolation.value(payoff.strike());
//vannila option price
double vanillaOption = Utils.blackFormula(payoff.optionType(), payoff.strike(),
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
strikeVol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//already out
if ((x0Quote.link.value() > arguments_.barrier_hi || x0Quote.link.value() < arguments_.barrier_lo) &&
arguments_.barrierType == DoubleBarrier.Type.KnockOut)
{
results_.value = 0.0;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
//already in
else if ((x0Quote.link.value() > arguments_.barrier_hi || x0Quote.link.value() < arguments_.barrier_lo) &&
arguments_.barrierType == DoubleBarrier.Type.KnockIn)
{
results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
else
{
//set up BS barrier option pricing
//only calculate out barrier option price
// in barrier price = vanilla - out barrier
//StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
DoubleBarrierOption doubleBarrierOption = new DoubleBarrierOption(
arguments_.barrierType,
arguments_.barrier_lo.GetValueOrDefault(),
arguments_.barrier_hi.GetValueOrDefault(),
arguments_.rebate.GetValueOrDefault(),
payoff,
arguments_.exercise);
doubleBarrierOption.setPricingEngine(engineBS);
//BS price
double priceBS = doubleBarrierOption.NPV();
double priceAtmCallBS = Utils.blackFormula(Option.Type.Call, atmStrike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25CallBS = Utils.blackFormula(Option.Type.Call, call25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25PutBS = Utils.blackFormula(Option.Type.Put, put25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//market price
double priceAtmCallMkt = Utils.blackFormula(Option.Type.Call, atmStrike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25CallMkt = Utils.blackFormula(Option.Type.Call, call25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
call25Vol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25PutMkt = Utils.blackFormula(Option.Type.Put, put25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
put25Vol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//Analytical Black Scholes formula
NormalDistribution norm = new NormalDistribution();
double d1atm = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_) / atmStrike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) / (atmVolQuote.link.value() * Math.Sqrt(T_));
double vegaAtm_Analytical = x0Quote.link.value() * norm.value(d1atm) * Math.Sqrt(T_) * foreignTS_.link.discount(T_);
double vannaAtm_Analytical = vegaAtm_Analytical / x0Quote.link.value() * (1.0 - d1atm / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volgaAtm_Analytical = vegaAtm_Analytical * d1atm * (d1atm - atmVolQuote.link.value() * Math.Sqrt(T_)) / atmVolQuote.link.value();
double d125call = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_) / call25Strike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) / (atmVolQuote.link.value() * Math.Sqrt(T_));
double vega25Call_Analytical = x0Quote.link.value() * norm.value(d125call) * Math.Sqrt(T_) * foreignTS_.link.discount(T_);
double vanna25Call_Analytical = vega25Call_Analytical / x0Quote.link.value() * (1.0 - d125call / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volga25Call_Analytical = vega25Call_Analytical * d125call * (d125call - atmVolQuote.link.value() * Math.Sqrt(T_)) / atmVolQuote.link.value();
double d125Put = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_) / put25Strike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) / (atmVolQuote.link.value() * Math.Sqrt(T_));
double vega25Put_Analytical = x0Quote.link.value() * norm.value(d125Put) * Math.Sqrt(T_) * foreignTS_.link.discount(T_);
double vanna25Put_Analytical = vega25Put_Analytical / x0Quote.link.value() * (1.0 - d125Put / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volga25Put_Analytical = vega25Put_Analytical * d125Put * (d125Put - atmVolQuote.link.value() * Math.Sqrt(T_)) / atmVolQuote.link.value();
//BS vega
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vega);
doubleBarrierOption.recalculate();
double vegaBarBS = (doubleBarrierOption.NPV() - priceBS) / sigmaShift_vega;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() - sigmaShift_vega);//setback
//BS volga
//vegaBar2
//base NPV
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_volga);
doubleBarrierOption.recalculate();
double priceBS2 = doubleBarrierOption.NPV();
//shifted npv
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vega);
doubleBarrierOption.recalculate();
double vegaBarBS2 = (doubleBarrierOption.NPV() - priceBS2) / sigmaShift_vega;
double volgaBarBS = (vegaBarBS2 - vegaBarBS) / sigmaShift_volga;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value()
- sigmaShift_volga
- sigmaShift_vega); //setback
//BS Delta
//base delta
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//shift forth
doubleBarrierOption.recalculate();
double priceBS_delta1 = doubleBarrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() - 2 * spotShift_delta);//shift back
doubleBarrierOption.recalculate();
double priceBS_delta2 = doubleBarrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//set back
double deltaBar1 = (priceBS_delta1 - priceBS_delta2) / (2.0 * spotShift_delta);
//shifted vanna
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vanna); //shift sigma
//shifted delta
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta); //shift forth
doubleBarrierOption.recalculate();
priceBS_delta1 = doubleBarrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() - 2 * spotShift_delta);//shift back
doubleBarrierOption.recalculate();
priceBS_delta2 = doubleBarrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//set back
double deltaBar2 = (priceBS_delta1 - priceBS_delta2) / (2.0 * spotShift_delta);
double vannaBarBS = (deltaBar2 - deltaBar1) / sigmaShift_vanna;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() - sigmaShift_vanna);//set back
//Matrix
Matrix A = new Matrix(3, 3, 0.0);
//analytical
A[0, 0] = vegaAtm_Analytical;
A[0, 1] = vega25Call_Analytical;
A[0, 2] = vega25Put_Analytical;
A[1, 0] = vannaAtm_Analytical;
A[1, 1] = vanna25Call_Analytical;
A[1, 2] = vanna25Put_Analytical;
A[2, 0] = volgaAtm_Analytical;
A[2, 1] = volga25Call_Analytical;
A[2, 2] = volga25Put_Analytical;
Vector b = new Vector(3, 0.0);
b[0] = vegaBarBS;
b[1] = vannaBarBS;
b[2] = volgaBarBS;
Vector q = Matrix.inverse(A) * b;
double H = arguments_.barrier_hi.GetValueOrDefault();
double L = arguments_.barrier_lo.GetValueOrDefault();
double theta_tilt_minus = ((domesticTS_.link.zeroRate(T_, Compounding.Continuous).value() -
foreignTS_.link.zeroRate(T_, Compounding.Continuous).value()) /
atmVol_.link.value() - atmVol_.link.value() / 2.0) * Math.Sqrt(T_);
double h = 1.0 / atmVol_.link.value() * Math.Log(H / x0Quote.link.value()) / Math.Sqrt(T_);
double l = 1.0 / atmVol_.link.value() * Math.Log(L / x0Quote.link.value()) / Math.Sqrt(T_);
CumulativeNormalDistribution cnd = new CumulativeNormalDistribution();
double doubleNoTouch = 0.0;
for (int j = -series_; j < series_; j++)
{
double e_minus = 2 * j * (h - l) - theta_tilt_minus;
doubleNoTouch += Math.Exp(-2.0 * j * theta_tilt_minus * (h - l)) * (cnd.value(h + e_minus) - cnd.value(l + e_minus))
- Math.Exp(-2.0 * j * theta_tilt_minus * (h - l) + 2.0 * theta_tilt_minus * h) *
(cnd.value(h - 2.0 * h + e_minus) - cnd.value(l - 2.0 * h + e_minus));
}
double p_survival = doubleNoTouch;
double lambda = p_survival;
double adjust = q[0] * (priceAtmCallMkt - priceAtmCallBS)
+ q[1] * (price25CallMkt - price25CallBS)
+ q[2] * (price25PutMkt - price25PutBS);
double outPrice = priceBS + lambda * adjust;//
double inPrice;
//adapt Vanilla delta
if (adaptVanDelta_ == true)
{
outPrice += lambda * (bsPriceWithSmile_ - vanillaOption);
//capfloored by (0, vanilla)
outPrice = Math.Max(0.0, Math.Min(bsPriceWithSmile_, outPrice));
inPrice = bsPriceWithSmile_ - outPrice;
}
else
{
//capfloored by (0, vanilla)
outPrice = Math.Max(0.0, Math.Min(vanillaOption, outPrice));
inPrice = vanillaOption - outPrice;
}
if (arguments_.barrierType == DoubleBarrier.Type.KnockOut)
{
results_.value = outPrice;
}
else
{
results_.value = inPrice;
}
results_.additionalResults["VanillaPrice"] = vanillaOption;
results_.additionalResults["BarrierInPrice"] = inPrice;
results_.additionalResults["BarrierOutPrice"] = outPrice;
results_.additionalResults["lambda"] = lambda;
}
}
public override void calculate()
{
double sigmaShift_vega = 0.0001;
double sigmaShift_volga = 0.0001;
double spotShift_delta = 0.0001 * spotFX_.link.value();
double sigmaShift_vanna = 0.0001;
Handle <Quote> x0Quote = new Handle <Quote>(new SimpleQuote(spotFX_.link.value())); //used for shift
Handle <Quote> atmVolQuote = new Handle <Quote>(new SimpleQuote(atmVol_.link.value())); //used for shift
BlackVolTermStructure blackVolTS = new BlackConstantVol(Settings.evaluationDate(),
new NullCalendar(), atmVolQuote, new Actual365Fixed());
BlackScholesMertonProcess stochProcess = new BlackScholesMertonProcess(x0Quote, foreignTS_, domesticTS_,
new Handle <BlackVolTermStructure>(blackVolTS));
IPricingEngine engineBS = new AnalyticBarrierEngine(stochProcess);
BlackDeltaCalculator blackDeltaCalculatorAtm = new BlackDeltaCalculator(
Option.Type.Call, atmVol_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_));
double atmStrike = blackDeltaCalculatorAtm.atmStrike(atmVol_.link.atmType());
double call25Vol = vol25Call_.link.value();
double put25Vol = vol25Put_.link.value();
BlackDeltaCalculator blackDeltaCalculatorPut25 = new BlackDeltaCalculator(
Option.Type.Put, vol25Put_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
put25Vol * Math.Sqrt(T_));
double put25Strike = blackDeltaCalculatorPut25.strikeFromDelta(-0.25);
BlackDeltaCalculator blackDeltaCalculatorCall25 = new BlackDeltaCalculator(
Option.Type.Call, vol25Call_.link.deltaType(), x0Quote.link.value(),
domesticTS_.link.discount(T_), foreignTS_.link.discount(T_),
call25Vol * Math.Sqrt(T_));
double call25Strike = blackDeltaCalculatorCall25.strikeFromDelta(0.25);
//here use vanna volga interpolated smile to price vanilla
List <double> strikes = new List <double>();
List <double> vols = new List <double>();
strikes.Add(put25Strike);
vols.Add(put25Vol);
strikes.Add(atmStrike);
vols.Add(atmVol_.link.value());
strikes.Add(call25Strike);
vols.Add(call25Vol);
VannaVolga vannaVolga = new VannaVolga(x0Quote.link.value(), domesticTS_.link.discount(T_),
foreignTS_.link.discount(T_), T_);
Interpolation interpolation = vannaVolga.interpolate(strikes, strikes.Count, vols);
interpolation.enableExtrapolation();
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
double strikeVol = interpolation.value(payoff.strike());
//vannila option price
double vanillaOption = Utils.blackFormula(payoff.optionType(), payoff.strike(),
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
strikeVol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//spot > barrier up&out 0
if (x0Quote.link.value() >= arguments_.barrier && arguments_.barrierType == Barrier.Type.UpOut)
{
results_.value = 0.0;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
//spot > barrier up&in vanilla
else if (x0Quote.link.value() >= arguments_.barrier && arguments_.barrierType == Barrier.Type.UpIn)
{
results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
//spot < barrier down&out 0
else if (x0Quote.link.value() <= arguments_.barrier && arguments_.barrierType == Barrier.Type.DownOut)
{
results_.value = 0.0;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
//spot < barrier down&in vanilla
else if (x0Quote.link.value() <= arguments_.barrier && arguments_.barrierType == Barrier.Type.DownIn)
{
results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;
results_.additionalResults["BarrierOutPrice"] = 0.0;
}
else
{
//set up BS barrier option pricing
//only calculate out barrier option price
// in barrier price = vanilla - out barrier
Barrier.Type barrierTyp;
if (arguments_.barrierType == Barrier.Type.UpOut)
{
barrierTyp = arguments_.barrierType;
}
else if (arguments_.barrierType == Barrier.Type.UpIn)
{
barrierTyp = Barrier.Type.UpOut;
}
else if (arguments_.barrierType == Barrier.Type.DownOut)
{
barrierTyp = arguments_.barrierType;
}
else
{
barrierTyp = Barrier.Type.DownOut;
}
BarrierOption barrierOption = new BarrierOption(barrierTyp,
arguments_.barrier.GetValueOrDefault(),
arguments_.rebate.GetValueOrDefault(),
(StrikedTypePayoff)arguments_.payoff,
arguments_.exercise);
barrierOption.setPricingEngine(engineBS);
//BS price with atm vol
double priceBS = barrierOption.NPV();
double priceAtmCallBS = Utils.blackFormula(Option.Type.Call, atmStrike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25CallBS = Utils.blackFormula(Option.Type.Call, call25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25PutBS = Utils.blackFormula(Option.Type.Put, put25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//market price
double priceAtmCallMkt = Utils.blackFormula(Option.Type.Call, atmStrike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
atmVol_.link.value() * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25CallMkt = Utils.blackFormula(Option.Type.Call, call25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
call25Vol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
double price25PutMkt = Utils.blackFormula(Option.Type.Put, put25Strike,
x0Quote.link.value() * foreignTS_.link.discount(T_) / domesticTS_.link.discount(T_),
put25Vol * Math.Sqrt(T_),
domesticTS_.link.discount(T_));
//Analytical Black Scholes formula for vanilla option
NormalDistribution norm = new NormalDistribution();
double d1atm = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) /
domesticTS_.link.discount(T_) / atmStrike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) /
(atmVolQuote.link.value() * Math.Sqrt(T_));
double vegaAtm_Analytical = x0Quote.link.value() * norm.value(d1atm) * Math.Sqrt(T_) *
foreignTS_.link.discount(T_);
double vannaAtm_Analytical = vegaAtm_Analytical / x0Quote.link.value() *
(1.0 - d1atm / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volgaAtm_Analytical = vegaAtm_Analytical * d1atm * (d1atm - atmVolQuote.link.value() * Math.Sqrt(T_)) /
atmVolQuote.link.value();
double d125call = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) /
domesticTS_.link.discount(T_) / call25Strike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) / (atmVolQuote.link.value() * Math.Sqrt(T_));
double vega25Call_Analytical = x0Quote.link.value() * norm.value(d125call) * Math.Sqrt(T_) *
foreignTS_.link.discount(T_);
double vanna25Call_Analytical = vega25Call_Analytical / x0Quote.link.value() *
(1.0 - d125call / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volga25Call_Analytical = vega25Call_Analytical * d125call *
(d125call - atmVolQuote.link.value() * Math.Sqrt(T_)) / atmVolQuote.link.value();
double d125Put = (Math.Log(x0Quote.link.value() * foreignTS_.link.discount(T_) /
domesticTS_.link.discount(T_) / put25Strike)
+ 0.5 * Math.Pow(atmVolQuote.link.value(), 2.0) * T_) / (atmVolQuote.link.value() * Math.Sqrt(T_));
double vega25Put_Analytical = x0Quote.link.value() * norm.value(d125Put) * Math.Sqrt(T_) *
foreignTS_.link.discount(T_);
double vanna25Put_Analytical = vega25Put_Analytical / x0Quote.link.value() *
(1.0 - d125Put / (atmVolQuote.link.value() * Math.Sqrt(T_)));
double volga25Put_Analytical = vega25Put_Analytical * d125Put *
(d125Put - atmVolQuote.link.value() * Math.Sqrt(T_)) / atmVolQuote.link.value();
//BS vega
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vega);
barrierOption.recalculate();
double vegaBarBS = (barrierOption.NPV() - priceBS) / sigmaShift_vega;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() - sigmaShift_vega);//setback
//BS volga
//vegaBar2
//base NPV
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_volga);
barrierOption.recalculate();
double priceBS2 = barrierOption.NPV();
//shifted npv
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vega);
barrierOption.recalculate();
double vegaBarBS2 = (barrierOption.NPV() - priceBS2) / sigmaShift_vega;
double volgaBarBS = (vegaBarBS2 - vegaBarBS) / sigmaShift_volga;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value()
- sigmaShift_volga
- sigmaShift_vega); //setback
//BS Delta
//base delta
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//shift forth
barrierOption.recalculate();
double priceBS_delta1 = barrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() - 2 * spotShift_delta);//shift back
barrierOption.recalculate();
double priceBS_delta2 = barrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//set back
double deltaBar1 = (priceBS_delta1 - priceBS_delta2) / (2.0 * spotShift_delta);
//shifted delta
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() + sigmaShift_vanna); //shift sigma
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta); //shift forth
barrierOption.recalculate();
priceBS_delta1 = barrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() - 2 * spotShift_delta);//shift back
barrierOption.recalculate();
priceBS_delta2 = barrierOption.NPV();
((SimpleQuote)x0Quote.currentLink()).setValue(x0Quote.link.value() + spotShift_delta);//set back
double deltaBar2 = (priceBS_delta1 - priceBS_delta2) / (2.0 * spotShift_delta);
double vannaBarBS = (deltaBar2 - deltaBar1) / sigmaShift_vanna;
((SimpleQuote)atmVolQuote.currentLink()).setValue(atmVolQuote.link.value() - sigmaShift_vanna);//set back
//Matrix
Matrix A = new Matrix(3, 3, 0.0);
//analytical
A[0, 0] = vegaAtm_Analytical;
A[0, 1] = vega25Call_Analytical;
A[0, 2] = vega25Put_Analytical;
A[1, 0] = vannaAtm_Analytical;
A[1, 1] = vanna25Call_Analytical;
A[1, 2] = vanna25Put_Analytical;
A[2, 0] = volgaAtm_Analytical;
A[2, 1] = volga25Call_Analytical;
A[2, 2] = volga25Put_Analytical;
Vector b = new Vector(3, 0.0);
b[0] = vegaBarBS;
b[1] = vannaBarBS;
b[2] = volgaBarBS;
//Vector q = inverse(A) * b; TODO implements transpose
Vector q = Matrix.inverse(A) * b;
//touch probability
CumulativeNormalDistribution cnd = new CumulativeNormalDistribution();
double mu = domesticTS_.link.zeroRate(T_, Compounding.Continuous).value() -
foreignTS_.link.zeroRate(T_, Compounding.Continuous).value() -
Math.Pow(atmVol_.link.value(), 2.0) / 2.0;
double h2 = (Math.Log(arguments_.barrier.GetValueOrDefault() / x0Quote.link.value()) + mu * T_) /
(atmVol_.link.value() * Math.Sqrt(T_));
double h2Prime = (Math.Log(x0Quote.link.value() / arguments_.barrier.GetValueOrDefault()) + mu * T_) /
(atmVol_.link.value() * Math.Sqrt(T_));
double probTouch = 0.0;
if (arguments_.barrierType == Barrier.Type.UpIn || arguments_.barrierType == Barrier.Type.UpOut)
{
probTouch = cnd.value(h2Prime) + Math.Pow(arguments_.barrier.GetValueOrDefault() / x0Quote.link.value(),
2.0 * mu / Math.Pow(atmVol_.link.value(), 2.0)) * cnd.value(-h2);
}
else
{
probTouch = cnd.value(-h2Prime) + Math.Pow(arguments_.barrier.GetValueOrDefault() / x0Quote.link.value(),
2.0 * mu / Math.Pow(atmVol_.link.value(), 2.0)) * cnd.value(h2);
}
double p_survival = 1.0 - probTouch;
double lambda = p_survival;
double adjust = q[0] * (priceAtmCallMkt - priceAtmCallBS)
+ q[1] * (price25CallMkt - price25CallBS)
+ q[2] * (price25PutMkt - price25PutBS);
double outPrice = priceBS + lambda * adjust;//
double inPrice;
//adapt Vanilla delta
if (adaptVanDelta_ == true)
{
outPrice += lambda * (bsPriceWithSmile_ - vanillaOption);
//capfloored by (0, vanilla)
outPrice = Math.Max(0.0, Math.Min(bsPriceWithSmile_, outPrice));
inPrice = bsPriceWithSmile_ - outPrice;
}
else
{
//capfloored by (0, vanilla)
outPrice = Math.Max(0.0, Math.Min(vanillaOption, outPrice));
inPrice = vanillaOption - outPrice;
}
if (arguments_.barrierType == Barrier.Type.DownOut || arguments_.barrierType == Barrier.Type.UpOut)
{
results_.value = outPrice;
}
else
{
results_.value = inPrice;
}
results_.additionalResults["VanillaPrice"] = vanillaOption;
results_.additionalResults["BarrierInPrice"] = inPrice;
results_.additionalResults["BarrierOutPrice"] = outPrice;
results_.additionalResults["lambda"] = lambda;
}
}
public override void update()
{
Vector tmp = new Vector(size_);
List <double> dx = new InitializedList <double>(size_ - 1),
S = new InitializedList <double>(size_ - 1);
for (int i = 0; i < size_ - 1; ++i)
{
dx[i] = xBegin_[i + 1] - xBegin_[i];
S[i] = (yBegin_[i + 1] - yBegin_[i]) / dx[i];
}
// first derivative approximation
if (da_ == CubicInterpolation.DerivativeApprox.Spline)
{
TridiagonalOperator L = new TridiagonalOperator(size_);
for (int i = 1; i < size_ - 1; ++i)
{
L.setMidRow(i, dx[i], 2.0 * (dx[i] + dx[i - 1]), dx[i - 1]);
tmp[i] = 3.0 * (dx[i] * S[i - 1] + dx[i - 1] * S[i]);
}
// left boundary condition
switch (leftType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setFirstRow(dx[1] * (dx[1] + dx[0]), (dx[0] + dx[1]) * (dx[0] + dx[1]));
tmp[0] = S[0] * dx[1] * (2.0 * dx[1] + 3.0 * dx[0]) + S[1] * dx[0] * dx[0];
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setFirstRow(1.0, 0.0);
tmp[0] = leftValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setFirstRow(2.0, 1.0);
tmp[0] = 3.0 * S[0] - leftValue_ * dx[0] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setFirstRow(1.0, 0.0);
tmp[0] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[0], this.xBegin_[1],
this.xBegin_[2], this.xBegin_[3],
this.yBegin_[0], this.yBegin_[1],
this.yBegin_[2], this.yBegin_[3],
this.xBegin_[0]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// right boundary condition
switch (rightType_)
{
case CubicInterpolation.BoundaryCondition.NotAKnot:
// ignoring end condition value
L.setLastRow(-(dx[size_ - 2] + dx[size_ - 3]) * (dx[size_ - 2] + dx[size_ - 3]),
-dx[size_ - 3] * (dx[size_ - 3] + dx[size_ - 2]));
tmp[size_ - 1] = -S[size_ - 3] * dx[size_ - 2] * dx[size_ - 2] -
S[size_ - 2] * dx[size_ - 3] * (3.0 * dx[size_ - 2] + 2.0 * dx[size_ - 3]);
break;
case CubicInterpolation.BoundaryCondition.FirstDerivative:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = rightValue_;
break;
case CubicInterpolation.BoundaryCondition.SecondDerivative:
L.setLastRow(1.0, 2.0);
tmp[size_ - 1] = 3.0 * S[size_ - 2] + rightValue_ * dx[size_ - 2] / 2.0;
break;
case CubicInterpolation.BoundaryCondition.Periodic:
// ignoring end condition value
throw new NotImplementedException("this end condition is not implemented yet");
case CubicInterpolation.BoundaryCondition.Lagrange:
L.setLastRow(0.0, 1.0);
tmp[size_ - 1] = cubicInterpolatingPolynomialDerivative(
this.xBegin_[size_ - 4], this.xBegin_[size_ - 3],
this.xBegin_[size_ - 2], this.xBegin_[size_ - 1],
this.yBegin_[size_ - 4], this.yBegin_[size_ - 3],
this.yBegin_[size_ - 2], this.yBegin_[size_ - 1],
this.xBegin_[size_ - 1]);
break;
default:
throw new ArgumentException("unknown end condition");
}
// solve the system
tmp = L.solveFor(tmp);
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM1)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i + 1] + dx[i]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
Q_[0, 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[0] * dx[0] * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i] + 1.0 / (size_ - 1) * dx[i - 1] * dx[i - 1] * dx[i - 1];
Q_[i, i + 1] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[i] * dx[i] * dx[i];
}
Q_[size_ - 1, size_ - 2] = 7.0 / 8 * 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2] * dx[size_ - 2] * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else if (da_ == CubicInterpolation.DerivativeApprox.SplineOM2)
{
Matrix T_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
T_[i, i] = dx[i] / 6.0;
T_[i, i + 1] = (dx[i] + dx[i + 1]) / 3.0;
T_[i, i + 2] = dx[i + 1] / 6.0;
}
Matrix S_ = new Matrix(size_ - 2, size_, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
S_[i, i] = 1.0 / dx[i];
S_[i, i + 1] = -(1.0 / dx[i + 1] + 1.0 / dx[i]);
S_[i, i + 2] = 1.0 / dx[i + 1];
}
Matrix Up_ = new Matrix(size_, 2, 0.0);
Up_[0, 0] = 1;
Up_[size_ - 1, 1] = 1;
Matrix Us_ = new Matrix(size_, size_ - 2, 0.0);
for (int i = 0; i < size_ - 2; ++i)
{
Us_[i + 1, i] = 1;
}
Matrix Z_ = Us_ * Matrix.inverse(T_ * Us_);
Matrix I_ = new Matrix(size_, size_, 0.0);
for (int i = 0; i < size_; ++i)
{
I_[i, i] = 1;
}
Matrix V_ = (I_ - Z_ * T_) * Up_;
Matrix W_ = Z_ * S_;
Matrix Q_ = new Matrix(size_, size_, 0.0);
Q_[0, 0] = 1.0 / (size_ - 1) * dx[0];
Q_[0, 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[0];
for (int i = 1; i < size_ - 1; ++i)
{
Q_[i, i - 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i] = 1.0 / (size_ - 1) * dx[i] + 1.0 / (size_ - 1) * dx[i - 1];
Q_[i, i + 1] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[i];
}
Q_[size_ - 1, size_ - 2] = 1.0 / 2 * 1.0 / (size_ - 1) * dx[size_ - 2];
Q_[size_ - 1, size_ - 1] = 1.0 / (size_ - 1) * dx[size_ - 2];
Matrix J_ = (I_ - V_ * Matrix.inverse(Matrix.transpose(V_) * Q_ * V_) * Matrix.transpose(V_) * Q_) * W_;
Vector Y_ = new Vector(size_);
for (int i = 0; i < size_; ++i)
{
Y_[i] = this.yBegin_[i];
}
Vector D_ = J_ * Y_;
for (int i = 0; i < size_ - 1; ++i)
{
tmp[i] = (Y_[i + 1] - Y_[i]) / dx[i] - (2.0 * D_[i] + D_[i + 1]) * dx[i] / 6.0;
}
tmp[size_ - 1] = tmp[size_ - 2] + D_[size_ - 2] * dx[size_ - 2] + (D_[size_ - 1] - D_[size_ - 2]) * dx[size_ - 2] / 2.0;
}
else
{
// local schemes
if (size_ == 2)
{
tmp[0] = tmp[1] = S[0];
}
else
{
switch (da_)
{
case CubicInterpolation.DerivativeApprox.FourthOrder:
throw new NotImplementedException("FourthOrder not implemented yet");
case CubicInterpolation.DerivativeApprox.Parabolic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
tmp[i] = (dx[i - 1] * S[i] + dx[i] * S[i - 1]) / (dx[i] + dx[i - 1]);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.FritschButland:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double Smin = Math.Min(S[i - 1], S[i]);
double Smax = Math.Max(S[i - 1], S[i]);
tmp[i] = 3.0 * Smin * Smax / (Smax + 2.0 * Smin);
}
// end points
tmp[0] = ((2.0 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[0] + dx[1]);
tmp[size_ - 1] = ((2.0 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] -
dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 2] + dx[size_ - 3]);
break;
case CubicInterpolation.DerivativeApprox.Akima:
tmp[0] = (Math.Abs(S[1] - S[0]) * 2 * S[0] * S[1] +
Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]) * S[0]) /
(Math.Abs(S[1] - S[0]) + Math.Abs(2 * S[0] * S[1] - 4 * S[0] * S[0] * S[1]));
tmp[1] = (Math.Abs(S[2] - S[1]) * S[0] + Math.Abs(S[0] - 2 * S[0] * S[1]) * S[1]) /
(Math.Abs(S[2] - S[1]) + Math.Abs(S[0] - 2 * S[0] * S[1]));
for (int i = 2; i < size_ - 2; ++i)
{
if ((S[i - 2].IsEqual(S[i - 1])) && (S[i].IsNotEqual(S[i + 1])))
{
tmp[i] = S[i - 1];
}
else if ((S[i - 2].IsNotEqual(S[i - 1])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = S[i];
}
else if (S[i].IsEqual(S[i - 1]))
{
tmp[i] = S[i];
}
else if ((S[i - 2].IsEqual(S[i - 1])) && (S[i - 1].IsNotEqual(S[i])) && (S[i].IsEqual(S[i + 1])))
{
tmp[i] = (S[i - 1] + S[i]) / 2.0;
}
else
{
tmp[i] = (Math.Abs(S[i + 1] - S[i]) * S[i - 1] + Math.Abs(S[i - 1] - S[i - 2]) * S[i]) /
(Math.Abs(S[i + 1] - S[i]) + Math.Abs(S[i - 1] - S[i - 2]));
}
}
tmp[size_ - 2] = (Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) * S[size_ - 3] +
Math.Abs(S[size_ - 3] - S[size_ - 4]) * S[size_ - 2]) /
(Math.Abs(2 * S[size_ - 2] * S[size_ - 3] - S[size_ - 2]) +
Math.Abs(S[size_ - 3] - S[size_ - 4]));
tmp[size_ - 1] =
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) *
S[size_ - 2] + Math.Abs(S[size_ - 2] - S[size_ - 3]) * 2 * S[size_ - 2] * S[size_ - 3]) /
(Math.Abs(4 * S[size_ - 2] * S[size_ - 2] * S[size_ - 3] - 2 * S[size_ - 2] * S[size_ - 3]) +
Math.Abs(S[size_ - 2] - S[size_ - 3]));
break;
case CubicInterpolation.DerivativeApprox.Kruger:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
if (S[i - 1] * S[i] < 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// slope will be between the slopes of the adjacent
// straight lines and should approach zero if the
// slope of either line approaches zero
tmp[i] = 2.0 / (1.0 / S[i - 1] + 1.0 / S[i]);
}
}
// end points
tmp[0] = (3.0 * S[0] - tmp[1]) / 2.0;
tmp[size_ - 1] = (3.0 * S[size_ - 2] - tmp[size_ - 2]) / 2.0;
break;
case CubicInterpolation.DerivativeApprox.Harmonic:
// intermediate points
for (int i = 1; i < size_ - 1; ++i)
{
double w1 = 2 * dx[i] + dx[i - 1];
double w2 = dx[i] + 2 * dx[i - 1];
if (S[i - 1] * S[i] <= 0.0)
{
// slope changes sign at point
tmp[i] = 0.0;
}
else
{
// weighted harmonic mean of S[i] and S[i-1] if they
// have the same sign; otherwise 0
tmp[i] = (w1 + w2) / (w1 / S[i - 1] + w2 / S[i]);
}
}
// end points [0]
tmp[0] = ((2 * dx[0] + dx[1]) * S[0] - dx[0] * S[1]) / (dx[1] + dx[0]);
if (tmp[0] * S[0] < 0.0)
{
tmp[0] = 0;
}
else if (S[0] * S[1] < 0)
{
if (Math.Abs(tmp[0]) > Math.Abs(3 * S[0]))
{
tmp[0] = 3 * S[0];
}
}
// end points [n-1]
tmp[size_ - 1] = ((2 * dx[size_ - 2] + dx[size_ - 3]) * S[size_ - 2] - dx[size_ - 2] * S[size_ - 3]) / (dx[size_ - 3] + dx[size_ - 2]);
if (tmp[size_ - 1] * S[size_ - 2] < 0.0)
{
tmp[size_ - 1] = 0;
}
else if (S[size_ - 2] * S[size_ - 3] < 0)
{
if (Math.Abs(tmp[size_ - 1]) > Math.Abs(3 * S[size_ - 2]))
{
tmp[size_ - 1] = 3 * S[size_ - 2];
}
}
break;
default:
throw new ArgumentException("unknown scheme");
}
}
}
monotonicityAdjustments_.Erase();
// Hyman monotonicity constrained filter
if (monotonic_)
{
double correction;
double pm, pu, pd, M;
for (int i = 0; i < size_; ++i)
{
if (i == 0)
{
if (tmp[i] * S[0] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]),
Math.Abs(3.0 * S[0]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else if (i == size_ - 1)
{
if (tmp[i] * S[size_ - 2] > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), Math.Abs(3.0 * S[size_ - 2]));
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
else
{
pm = (S[i - 1] * dx[i] + S[i] * dx[i - 1]) /
(dx[i - 1] + dx[i]);
M = 3.0 * Math.Min(Math.Min(Math.Abs(S[i - 1]), Math.Abs(S[i])),
Math.Abs(pm));
if (i > 1)
{
if ((S[i - 1] - S[i - 2]) * (S[i] - S[i - 1]) > 0.0)
{
pd = (S[i - 1] * (2.0 * dx[i - 1] + dx[i - 2])
- S[i - 2] * dx[i - 1]) /
(dx[i - 2] + dx[i - 1]);
if (pm * pd > 0.0 && pm * (S[i - 1] - S[i - 2]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pd)));
}
}
}
if (i < size_ - 2)
{
if ((S[i] - S[i - 1]) * (S[i + 1] - S[i]) > 0.0)
{
pu = (S[i] * (2.0 * dx[i] + dx[i + 1]) - S[i + 1] * dx[i]) /
(dx[i] + dx[i + 1]);
if (pm * pu > 0.0 && -pm * (S[i] - S[i - 1]) > 0.0)
{
M = Math.Max(M, 1.5 * Math.Min(
Math.Abs(pm), Math.Abs(pu)));
}
}
}
if (tmp[i] * pm > 0.0)
{
correction = tmp[i] / Math.Abs(tmp[i]) *
Math.Min(Math.Abs(tmp[i]), M);
}
else
{
correction = 0.0;
}
if (correction.IsNotEqual(tmp[i]))
{
tmp[i] = correction;
monotonicityAdjustments_[i] = true;
}
}
}
}
// cubic coefficients
for (int i = 0; i < size_ - 1; ++i)
{
a_[i] = tmp[i];
b_[i] = (3.0 * S[i] - tmp[i + 1] - 2.0 * tmp[i]) / dx[i];
c_[i] = (tmp[i + 1] + tmp[i] - 2.0 * S[i]) / (dx[i] * dx[i]);
}
primitiveConst_[0] = 0.0;
for (int i = 1; i < size_ - 1; ++i)
{
primitiveConst_[i] = primitiveConst_[i - 1]
+ dx[i - 1] *
(yBegin_[i - 1] + dx[i - 1] *
(a_[i - 1] / 2.0 + dx[i - 1] *
(b_[i - 1] / 3.0 + dx[i - 1] * c_[i - 1] / 4.0)));
}
}