public double weight(double strike, double forward, double stdDev, List <double?> addParams)
{
if (Convert.ToDouble(addParams[1]) == 0.0)
{
return(Utils.blackFormulaStdDevDerivative(strike, forward, stdDev, 1.0, addParams[0].Value));
}
else
{
return(Utils.bachelierBlackFormulaStdDevDerivative(strike, forward, stdDev, 1.0));
}
}
public double vega(double strike, double atmForward, double stdDev, double exerciseTime, double annuity,
double displacement = 0.0)
{
return(Math.Sqrt(exerciseTime) *
Utils.blackFormulaStdDevDerivative(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()
{
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);
}
public double weight(double strike, double forward, double stdDev, List <double?> addParams)
{
return(Utils.blackFormulaStdDevDerivative(strike, forward, stdDev, 1.0));
}
public override void update()
{
this.coeff_.updateModelInstance();
// we should also check that y contains positive values only
// we must update weights if it is vegaWeighted
if (vegaWeighted_)
{
coeff_.weights_.Clear();
double weightsSum = 0.0;
for (int i = 0; i < xBegin_.Count; i++)
{
double stdDev = Math.Sqrt((yBegin_[i]) * (yBegin_[i]) * this.coeff_.t_);
coeff_.weights_.Add(Utils.blackFormulaStdDevDerivative(xBegin_[i], forward_, stdDev));
weightsSum += coeff_.weights_.Last();
}
// weight normalization
for (int i = 0; i < coeff_.weights_.Count; i++)
{
coeff_.weights_[i] /= weightsSum;
}
}
// there is nothing to optimize
if (coeff_.paramIsFixed_.Aggregate((a, b) => b & a))
{
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
coeff_.XABREndCriteria_ = EndCriteria.Type.None;
return;
}
else
{
XABRError costFunction = new XABRError(this);
Vector guess = new Vector(coeff_.model_.dimension());
for (int i = 0; i < guess.size(); ++i)
{
guess[i] = coeff_.params_[i].Value;
}
int iterations = 0;
int freeParameters = 0;
double bestError = double.MaxValue;
Vector bestParameters = new Vector();
for (int i = 0; i < coeff_.model_.dimension(); ++i)
{
if (!coeff_.paramIsFixed_[i])
{
++freeParameters;
}
}
HaltonRsg halton = new HaltonRsg(freeParameters, 42);
EndCriteria.Type tmpEndCriteria;
double tmpInterpolationError;
do
{
if (iterations > 0)
{
Sample <List <double> > s = halton.nextSequence();
coeff_.model_.guess(guess, coeff_.paramIsFixed_, forward_, coeff_.t_, s.value);
for (int i = 0; i < coeff_.paramIsFixed_.Count; ++i)
{
if (coeff_.paramIsFixed_[i])
{
guess[i] = coeff_.params_[i].Value;
}
}
}
Vector inversedTransformatedGuess = new Vector(coeff_.model_.inverse(guess, coeff_.paramIsFixed_, coeff_.params_, forward_));
ProjectedCostFunction rainedXABRError = new ProjectedCostFunction(costFunction, inversedTransformatedGuess,
coeff_.paramIsFixed_);
Vector projectedGuess = new Vector(rainedXABRError.project(inversedTransformatedGuess));
NoConstraint raint = new NoConstraint();
Problem problem = new Problem(rainedXABRError, raint, projectedGuess);
tmpEndCriteria = optMethod_.minimize(problem, endCriteria_);
// TEST
// coeff_.params_[3] = 0.0099999966589763966;
// TEST
Vector projectedResult = new Vector(problem.currentValue());
Vector transfResult = new Vector(rainedXABRError.include(projectedResult));
//transfResult[3] = 0.0099999966589763966; ;
Vector result = coeff_.model_.direct(transfResult, coeff_.paramIsFixed_, coeff_.params_, forward_);
//result[3] = 0.0099999966589763966;
tmpInterpolationError = useMaxError_ ? interpolationMaxError()
: interpolationError();
if (tmpInterpolationError < bestError)
{
bestError = tmpInterpolationError;
bestParameters = result;
coeff_.XABREndCriteria_ = tmpEndCriteria;
}
} while (++iterations < maxGuesses_ &&
tmpInterpolationError > errorAccept_);
for (int i = 0; i < bestParameters.size(); ++i)
{
coeff_.params_[i] = bestParameters[i];
}
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
}
}
