public double discountBondOption(Option.Type type,
double strike, double maturity,
double bondMaturity)
{
List <double> accrualStartTimes
= process_.accrualStartTimes();
List <double> accrualEndTimes
= process_.accrualEndTimes();
Utils.QL_REQUIRE(accrualStartTimes.First() <= maturity && accrualStartTimes.Last() >= maturity, () =>
"capet maturity does not fit to the process");
int i = accrualStartTimes.BinarySearch(maturity);
if (i < 0)
{
// The lower_bound() algorithm finds the first position in a sequence that value can occupy
// without violating the sequence's ordering
// if BinarySearch does not find value the value, the index of the prev minor item is returned
i = ~i + 1;
}
// impose limits. we need the one before last at max or the first at min
i = Math.Max(Math.Min(i, accrualStartTimes.Count - 1), 0);
Utils.QL_REQUIRE(i < process_.size() &&
Math.Abs(maturity - accrualStartTimes[i]) < 100 * Const.QL_EPSILON &&
Math.Abs(bondMaturity - accrualEndTimes[i]) < 100 * Const.QL_EPSILON, () =>
"irregular fixings are not (yet) supported");
double tenor = accrualEndTimes[i] - accrualStartTimes[i];
double forward = process_.initialValues()[i];
double capRate = (1.0 / strike - 1.0) / tenor;
double var = covarProxy_.integratedCovariance(i, i, process_.fixingTimes()[i]);
double dis = process_.index().forwardingTermStructure().link.discount(bondMaturity);
double black = Utils.blackFormula(
(type == Option.Type.Put ? Option.Type.Call : Option.Type.Put),
capRate, forward, Math.Sqrt(var));
double npv = dis * tenor * black;
return(npv / (1.0 + capRate * tenor));
}
public override void calculate()
{
if (!(arguments_.settlementType == Settlement.Type.Physical))
{
throw new ApplicationException("cash-settled swaptions not priced with Lfm engine");
}
double basisPoint = 1.0e-4;
VanillaSwap swap = arguments_.swap;
IPricingEngine pe = new DiscountingSwapEngine(discountCurve_);
swap.setPricingEngine(pe);
double correction = swap.spread *
Math.Abs(swap.floatingLegBPS() / swap.fixedLegBPS());
double fixedRate = swap.fixedRate - correction;
double fairRate = swap.fairRate() - correction;
SwaptionVolatilityMatrix volatility =
model_.getSwaptionVolatilityMatrix();
Date referenceDate = volatility.referenceDate();
DayCounter dayCounter = volatility.dayCounter();
double exercise = dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(0));
double swapLength =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates.Last())
- dayCounter.yearFraction(referenceDate,
arguments_.fixedResetDates[0]);
Option.Type w = arguments_.type == VanillaSwap.Type.Payer ?
Option.Type.Call : Option.Type.Put;
double vol = volatility.volatility(exercise, swapLength,
fairRate, true);
results_.value = (swap.fixedLegBPS() / basisPoint) *
Utils.blackFormula(w, fixedRate, fairRate, vol * Math.Sqrt(exercise));
}
public override double discountBondOption(Option.Type type,
double strike,
double maturity,
double bondMaturity)
{
double _a = a();
double v;
if (_a < Math.Sqrt(Const.QL_EPSILON))
{
v = sigma() * B(maturity, bondMaturity) * Math.Sqrt(maturity);
}
else
{
v = sigma() * B(maturity, bondMaturity) *
Math.Sqrt(0.5 * (1.0 - Math.Exp(-2.0 * _a * maturity)) / _a);
}
double f = termStructure().link.discount(bondMaturity);
double k = termStructure().link.discount(maturity) * strike;
return Utils.blackFormula(type, k, f, v);
}
protected double callSpreadPrice(double previousForward,
double nextForward,
double previousStrike,
double nextStrike,
double deflator,
double previousVariance,
double nextVariance)
{
double nextCall = Utils.blackFormula(Option.Type.Call, nextStrike, nextForward,
Math.Sqrt(nextVariance), deflator);
double previousCall = Utils.blackFormula(Option.Type.Call, previousStrike, previousForward,
Math.Sqrt(previousVariance), deflator);
Utils.QL_REQUIRE(nextCall < previousCall, () =>
"RangeAccrualPricerByBgm::callSpreadPrice: nextCall > previousCall" +
"\n nextCall: strike :" + nextStrike + "; variance: " + nextVariance +
" adjusted initial value " + nextForward +
"\n previousCall: strike :" + previousStrike + "; variance: " + previousVariance +
" adjusted initial value " + previousForward);
return((previousCall - nextCall) / (nextStrike - previousStrike));
}
public override void calculate()
{
Utils.QL_REQUIRE(arguments_.settlementMethod != Settlement.Method.ParYieldCurve, () =>
"cash-settled (ParYieldCurve) swaptions not priced with Lfm engine");
VanillaSwap swap = arguments_.swap;
IPricingEngine pe = new DiscountingSwapEngine(discountCurve_);
swap.setPricingEngine(pe);
double correction = swap.spread *
Math.Abs(swap.floatingLegBPS() / swap.fixedLegBPS());
double fixedRate = swap.fixedRate - correction;
double fairRate = swap.fairRate() - correction;
SwaptionVolatilityMatrix volatility =
model_.link.getSwaptionVolatilityMatrix();
Date referenceDate = volatility.referenceDate();
DayCounter dayCounter = volatility.dayCounter();
double exercise = dayCounter.yearFraction(referenceDate,
arguments_.exercise.date(0));
double swapLength =
dayCounter.yearFraction(referenceDate,
arguments_.fixedPayDates.Last())
- dayCounter.yearFraction(referenceDate,
arguments_.fixedResetDates[0]);
Option.Type w = arguments_.type == VanillaSwap.Type.Payer ?
Option.Type.Call : Option.Type.Put;
double vol = volatility.volatility(exercise, swapLength,
fairRate, true);
results_.value = (swap.fixedLegBPS() / Const.BASIS_POINT) *
Utils.blackFormula(w, fixedRate, fairRate, vol * Math.Sqrt(exercise));
}
public override double discountBondOption(Option.Type type, double strike, double maturity,
double bondMaturity)
{
double v;
double _a = a();
if (Math.Abs(maturity) < Const.QL_EPSILON)
{
v = 0.0;
}
else if (_a < Math.Sqrt(Const.QL_EPSILON))
{
v = sigma() * B(maturity, bondMaturity) * Math.Sqrt(maturity);
}
else
{
v = sigma() * B(maturity, bondMaturity) *
Math.Sqrt(0.5 * (1.0 - Math.Exp(-2.0 * _a * maturity)) / _a);
}
double f = discountBond(0.0, bondMaturity, r0_);
double k = discountBond(0.0, maturity, r0_) * strike;
return(Utils.blackFormula(type, k, f, v));
}
protected double optionletPrice(Option.Type optionType, double effStrike)
{
Date fixingDate = coupon_.fixingDate();
if (fixingDate <= Settings.evaluationDate())
{
// the amount is determined
double a;
double b;
if (optionType == Option.Type.Call)
{
a = coupon_.indexFixing();
b = effStrike;
}
else
{
a = effStrike;
b = coupon_.indexFixing();
}
return(Math.Max(a - b, 0.0) * accrualPeriod_ * discount_);
}
else
{
// not yet determined, use Black model
Utils.QL_REQUIRE(!capletVolatility().empty(), () => "missing optionlet volatility");
double stdDev = Math.Sqrt(capletVolatility().link.blackVariance(fixingDate, effStrike));
double shift = capletVolatility().link.displacement();
bool shiftedLn = capletVolatility().link.volatilityType() == VolatilityType.ShiftedLognormal;
double fixing =
shiftedLn
? Utils.blackFormula(optionType, effStrike, adjustedFixing(), stdDev, 1.0, shift)
: Utils.bachelierBlackFormula(optionType, effStrike, adjustedFixing(), stdDev, 1.0);
return(fixing * accrualPeriod_ * discount_);
}
}
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 double value(Option.Type type, double strike, double atmForward, double stdDev, double annuity,
double displacement = 0.0)
{
return(Utils.blackFormula(type, strike, atmForward, stdDev, annuity, displacement));
}
public override void calculate()
{
double value = 0.0;
double vega = 0.0;
int optionlets = arguments_.startDates.Count;
List <double> values = new InitializedList <double>(optionlets);
List <double> vegas = new InitializedList <double>(optionlets);
List <double> stdDevs = new InitializedList <double>(optionlets);
CapFloorType type = arguments_.type;
Date today = vol_.link.referenceDate();
Date settlement = discountCurve_.link.referenceDate();
for (int i = 0; i < optionlets; ++i)
{
Date paymentDate = arguments_.endDates[i];
if (paymentDate > settlement)
{
// discard expired caplets
double d = arguments_.nominals[i] *
arguments_.gearings[i] *
discountCurve_.link.discount(paymentDate) *
arguments_.accrualTimes[i];
double?forward = arguments_.forwards[i];
Date fixingDate = arguments_.fixingDates[i];
double sqrtTime = 0.0;
if (fixingDate > today)
{
sqrtTime = Math.Sqrt(vol_.link.timeFromReference(fixingDate));
}
if (type == CapFloorType.Cap || type == CapFloorType.Collar)
{
double?strike = arguments_.capRates[i];
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(vol_.link.blackVariance(fixingDate, strike.Value));
vegas[i] = Utils.blackFormulaStdDevDerivative(strike.Value, forward.Value, stdDevs[i], d, displacement_) * sqrtTime;
}
// include caplets with past fixing date
values[i] = Utils.blackFormula(Option.Type.Call, strike.Value,
forward.Value, stdDevs[i], d, displacement_);
}
if (type == CapFloorType.Floor || type == CapFloorType.Collar)
{
double?strike = arguments_.floorRates[i];
double floorletVega = 0.0;
if (sqrtTime > 0.0)
{
stdDevs[i] = Math.Sqrt(vol_.link.blackVariance(fixingDate, strike.Value));
floorletVega = Utils.blackFormulaStdDevDerivative(strike.Value, forward.Value, stdDevs[i], d, displacement_) * sqrtTime;
}
double floorlet = Utils.blackFormula(Option.Type.Put, strike.Value,
forward.Value, stdDevs[i], d, displacement_);
if (type == CapFloorType.Floor)
{
values[i] = floorlet;
vegas[i] = floorletVega;
}
else
{
// a collar is long a cap and short a floor
values[i] -= floorlet;
vegas[i] -= floorletVega;
}
}
value += values[i];
vega += vegas[i];
}
}
results_.value = value;
results_.additionalResults["vega"] = vega;
results_.additionalResults["optionletsPrice"] = values;
results_.additionalResults["optionletsVega"] = vegas;
results_.additionalResults["optionletsAtmForward"] = arguments_.forwards;
if (type != CapFloorType.Collar)
{
results_.additionalResults["optionletsStdDev"] = stdDevs;
}
}
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"
}
// critical commodity price
//public static double criticalPrice(StrikedTypePayoff payoff, double riskFreeDiscount, double dividendDiscount,
// double variance, double tolerance = 1e-6);
public static double criticalPrice(StrikedTypePayoff payoff, double riskFreeDiscount, double dividendDiscount,
double variance, double tolerance)
{
// Calculation of seed value, Si
double n = 2.0 * Math.Log(dividendDiscount / riskFreeDiscount) / (variance);
double m = -2.0 * Math.Log(riskFreeDiscount) / (variance);
double bT = Math.Log(dividendDiscount / riskFreeDiscount);
double qu, Su, h, Si;
switch (payoff.optionType())
{
case Option.Type.Call:
qu = (-(n - 1.0) + Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4.0 * m)) / 2.0;
Su = payoff.strike() / (1.0 - 1.0 / qu);
h = -(bT + 2.0 * Math.Sqrt(variance)) * payoff.strike() /
(Su - payoff.strike());
Si = payoff.strike() + (Su - payoff.strike()) *
(1.0 - Math.Exp(h));
break;
case Option.Type.Put:
qu = (-(n - 1.0) - Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4.0 * m)) / 2.0;
Su = payoff.strike() / (1.0 - 1.0 / qu);
h = (bT - 2.0 * Math.Sqrt(variance)) * payoff.strike() /
(payoff.strike() - Su);
Si = Su + (payoff.strike() - Su) * Math.Exp(h);
break;
default:
throw new ArgumentException("unknown option type");
}
// Newton Raphson algorithm for finding critical price Si
double Q, LHS, RHS, bi;
double forwardSi = Si * dividendDiscount / riskFreeDiscount;
double d1 = (Math.Log(forwardSi / payoff.strike()) + 0.5 * variance) /
Math.Sqrt(variance);
CumulativeNormalDistribution cumNormalDist = new CumulativeNormalDistribution();
double K = (riskFreeDiscount != 1.0 ? -2.0 * Math.Log(riskFreeDiscount) /
(variance * (1.0 - riskFreeDiscount)) : 0.0);
double temp = Utils.blackFormula(payoff.optionType(), payoff.strike(),
forwardSi, Math.Sqrt(variance)) * riskFreeDiscount;
switch (payoff.optionType())
{
case Option.Type.Call:
Q = (-(n - 1.0) + Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4 * K)) / 2;
LHS = Si - payoff.strike();
RHS = temp + (1 - dividendDiscount * cumNormalDist.value(d1)) * Si / Q;
bi = dividendDiscount * cumNormalDist.value(d1) * (1 - 1 / Q) +
(1 - dividendDiscount *
cumNormalDist.derivative(d1) / Math.Sqrt(variance)) / Q;
while (Math.Abs(LHS - RHS) / payoff.strike() > tolerance)
{
Si = (payoff.strike() + RHS - bi * Si) / (1 - bi);
forwardSi = Si * dividendDiscount / riskFreeDiscount;
d1 = (Math.Log(forwardSi / payoff.strike()) + 0.5 * variance)
/ Math.Sqrt(variance);
LHS = Si - payoff.strike();
double temp2 = Utils.blackFormula(payoff.optionType(), payoff.strike(),
forwardSi, Math.Sqrt(variance)) * riskFreeDiscount;
RHS = temp2 + (1 - dividendDiscount * cumNormalDist.value(d1)) * Si / Q;
bi = dividendDiscount * cumNormalDist.value(d1) * (1 - 1 / Q)
+ (1 - dividendDiscount *
cumNormalDist.derivative(d1) / Math.Sqrt(variance))
/ Q;
}
break;
case Option.Type.Put:
Q = (-(n - 1.0) - Math.Sqrt(((n - 1.0) * (n - 1.0)) + 4 * K)) / 2;
LHS = payoff.strike() - Si;
RHS = temp - (1 - dividendDiscount * cumNormalDist.value(-d1)) * Si / Q;
bi = -dividendDiscount *cumNormalDist.value(-d1) * (1 - 1 / Q)
- (1 + dividendDiscount * cumNormalDist.derivative(-d1)
/ Math.Sqrt(variance)) / Q;
while (Math.Abs(LHS - RHS) / payoff.strike() > tolerance)
{
Si = (payoff.strike() - RHS + bi * Si) / (1 + bi);
forwardSi = Si * dividendDiscount / riskFreeDiscount;
d1 = (Math.Log(forwardSi / payoff.strike()) + 0.5 * variance)
/ Math.Sqrt(variance);
LHS = payoff.strike() - Si;
double temp2 = Utils.blackFormula(payoff.optionType(), payoff.strike(),
forwardSi, Math.Sqrt(variance)) * riskFreeDiscount;
RHS = temp2 - (1 - dividendDiscount * cumNormalDist.value(-d1)) * Si / Q;
bi = -dividendDiscount *cumNormalDist.value(-d1) * (1 - 1 / Q)
- (1 + dividendDiscount * cumNormalDist.derivative(-d1)
/ Math.Sqrt(variance)) / Q;
}
break;
default:
throw new ArgumentException("unknown option type");
}
return(Si);
}
public override double value(double strike, Option.Type optionType, double deflator)
{
double variance = smile_.variance(strike);
return(deflator * Utils.blackFormula(optionType, strike, forwardValue_, Math.Sqrt(variance)));
}
public override void calculate()
{
double basisPoint = 1.0e-4;
Date exerciseDate = arguments_.exercise.date(0);
// the part of the swap preceding exerciseDate should be truncated
// to avoid taking into account unwanted cashflows
VanillaSwap swap = arguments_.swap;
double strike = swap.fixedRate;
// using the forecasting curve
swap.setPricingEngine(new DiscountingSwapEngine(swap.iborIndex().forwardingTermStructure()));
double atmForward = swap.fairRate();
// Volatilities are quoted for zero-spreaded swaps.
// Therefore, any spread on the floating leg must be removed
// with a corresponding correction on the fixed leg.
if (swap.spread != 0.0)
{
double correction = swap.spread * Math.Abs(swap.floatingLegBPS() / swap.fixedLegBPS());
strike -= correction;
atmForward -= correction;
results_.additionalResults["spreadCorrection"] = correction;
}
else
{
results_.additionalResults["spreadCorrection"] = 0.0;
}
results_.additionalResults["strike"] = strike;
results_.additionalResults["atmForward"] = atmForward;
// using the discounting curve
swap.setPricingEngine(new DiscountingSwapEngine(termStructure_));
double annuity;
switch (arguments_.settlementType)
{
case Settlement.Type.Physical: {
annuity = Math.Abs(swap.fixedLegBPS()) / basisPoint;
break;
}
case Settlement.Type.Cash: {
List <CashFlow> fixedLeg = swap.fixedLeg();
FixedRateCoupon firstCoupon = (FixedRateCoupon)fixedLeg[0];
DayCounter dayCount = firstCoupon.dayCounter();
double fixedLegCashBPS =
CashFlows.bps(fixedLeg,
new InterestRate(atmForward, dayCount, QLNet.Compounding.Compounded, Frequency.Annual), false,
termStructure_.link.referenceDate());
annuity = Math.Abs(fixedLegCashBPS / basisPoint);
break;
}
default:
throw new ApplicationException("unknown settlement type");
}
results_.additionalResults["annuity"] = annuity;
// the swap length calculation might be improved using the value date
// of the exercise date
double swapLength = volatility_.link.swapLength(exerciseDate,
arguments_.floatingPayDates.Last());
results_.additionalResults["swapLength"] = swapLength;
double variance = volatility_.link.blackVariance(exerciseDate,
swapLength,
strike);
double stdDev = Math.Sqrt(variance);
results_.additionalResults["stdDev"] = stdDev;
Option.Type w = (arguments_.type == VanillaSwap.Type.Payer) ?
Option.Type.Call : Option.Type.Put;
results_.value = Utils.blackFormula(w, strike, atmForward, stdDev, annuity);
double exerciseTime = volatility_.link.timeFromReference(exerciseDate);
results_.additionalResults["vega"] = Math.Sqrt(exerciseTime) *
Utils.blackFormulaStdDevDerivative(strike, atmForward, stdDev, annuity);
}
protected override double optionletImpl(Option.Type type, double strike, double forward, double stdDev,
double d)
{
return(Utils.blackFormula(type, strike, forward, stdDev, d));
}
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;
}
}
