public double impliedVolatility(double targetValue, GeneralizedBlackScholesProcess process, double accuracy, int maxEvaluations, double minVol, double maxVol)
{
if (!(!isExpired()))
{
throw new ApplicationException("option expired");
}
SimpleQuote volQuote = new SimpleQuote();
GeneralizedBlackScholesProcess newProcess = ImpliedVolatilityHelper.clone(process, volQuote);
// engines are built-in for the time being
IPricingEngine engine = null;
switch (exercise_.type())
{
case Exercise.Type.European:
engine = new AnalyticBarrierEngine(newProcess);
break;
case Exercise.Type.American:
case Exercise.Type.Bermudan:
throw new ApplicationException("Engine not available for non-European barrier option");
default:
throw new ApplicationException("unknown exercise type");
}
return(ImpliedVolatilityHelper.calculate(this, engine, volQuote, targetValue, accuracy, maxEvaluations, minVol, maxVol));
}
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;
}
}