Spread CallableBond::OAS(Real cleanPrice,
const Handle<YieldTermStructure>& engineTS,
const DayCounter& dayCounter,
Compounding compounding,
Frequency frequency,
Date settlement,
Real accuracy,
Size maxIterations,
Spread guess)
{
if (settlement == Date())
settlement = settlementDate();
Real dirtyPrice = cleanPrice + accruedAmount(settlement);
boost::function<Real(Real)> f = NPVSpreadHelper(*this);
OASHelper obj(f, dirtyPrice);
Brent solver;
solver.setMaxEvaluations(maxIterations);
Real step = 0.001;
Spread oas=solver.solve(obj, accuracy, guess, step);
return continuousToConv(oas,
*this,
engineTS,
dayCounter,
compounding,
frequency);
}
Volatility CalibrationHelper::impliedVolatility(Real targetValue,
Real accuracy,
Size maxEvaluations,
Volatility minVol,
Volatility maxVol) const {
ImpliedVolatilityHelper f(*this,targetValue);
Brent solver;
solver.setMaxEvaluations(maxEvaluations);
return solver.solve(f,accuracy,volatility_->value(),minVol,maxVol);
}
std::vector<Volatility> OptionletStripper2::spreadsVolImplied() const {
Brent solver;
std::vector<Volatility> result(nOptionExpiries_);
Volatility guess = 0.0001, minSpread = -0.1, maxSpread = 0.1;
for (Size j=0; j<nOptionExpiries_; ++j) {
ObjectiveFunction f(stripper1_, caps_[j], atmCapFloorPrices_[j]);
solver.setMaxEvaluations(maxEvaluations_);
Volatility root = solver.solve(f, accuracy_, guess,
minSpread, maxSpread);
result[j] = root;
}
return result;
}
Volatility CallableBond::impliedVolatility(
Real targetValue,
const Handle<YieldTermStructure>& discountCurve,
Real accuracy,
Size maxEvaluations,
Volatility minVol,
Volatility maxVol) const {
calculate();
QL_REQUIRE(!isExpired(), "instrument expired");
Volatility guess = 0.5*(minVol + maxVol);
blackDiscountCurve_.linkTo(*discountCurve, false);
ImpliedVolHelper f(*this,targetValue);
Brent solver;
solver.setMaxEvaluations(maxEvaluations);
return solver.solve(f, accuracy, guess, minVol, maxVol);
}
Volatility HestonBlackVolSurface::blackVolImpl(Time t, Real strike) const {
const boost::shared_ptr<HestonProcess> process = hestonModel_->process();
const DiscountFactor df = process->riskFreeRate()->discount(t, true);
const DiscountFactor div = process->dividendYield()->discount(t, true);
const Real spotPrice = process->s0()->value();
const Real fwd = spotPrice
* process->dividendYield()->discount(t, true)
/ process->riskFreeRate()->discount(t, true);
const PlainVanillaPayoff payoff(
fwd > strike ? Option::Put : Option::Call, strike);
const Real kappa = hestonModel_->kappa();
const Real theta = hestonModel_->theta();
const Real rho = hestonModel_->rho();
const Real sigma = hestonModel_->sigma();
const Real v0 = hestonModel_->v0();
const AnalyticHestonEngine::ComplexLogFormula cpxLogFormula
= AnalyticHestonEngine::Gatheral;
const AnalyticHestonEngine* const hestonEnginePtr = 0;
Real npv;
Size evaluations;
AnalyticHestonEngine::doCalculation(
df, div, spotPrice, strike, t,
kappa, theta, sigma, v0, rho,
payoff, integration_, cpxLogFormula,
hestonEnginePtr, npv, evaluations);
if (npv <= 0.0) return std::sqrt(theta);
Brent solver;
solver.setMaxEvaluations(10000);
const Volatility guess = std::sqrt(theta);
const Real accuracy = std::numeric_limits<Real>::epsilon();
const boost::function<Real(Real)> f = boost::bind(
&blackValue, payoff.optionType(), strike, fwd, t, _1, df, npv);
return solver.solve(f, accuracy, guess, 0.01);
}
Real InverseNonCentralChiSquareDistribution::operator()(Real x) const {
// first find the right side of the interval
Real upper = guess_;
Size evaluations = maxEvaluations_;
while (nonCentralDist_(upper) < x && evaluations > 0) {
upper*=2.0;
--evaluations;
}
// use a brent solver for the rest
Brent solver;
solver.setMaxEvaluations(evaluations);
return solver.solve(compose(std::bind2nd(std::minus<Real>(),x),
nonCentralDist_),
accuracy_, 0.75*upper,
(evaluations == maxEvaluations_)? 0.0: 0.5*upper,
upper);
}
Volatility CdsOption::impliedVolatility(
Real targetValue,
const Handle<YieldTermStructure>& termStructure,
const Handle<DefaultProbabilityTermStructure>& probability,
Real recoveryRate,
Real accuracy,
Size maxEvaluations,
Volatility minVol,
Volatility maxVol) const {
calculate();
QL_REQUIRE(!isExpired(), "instrument expired");
Volatility guess = 0.10;
ImpliedVolHelper f(*this, probability, recoveryRate,
termStructure, targetValue);
Brent solver;
solver.setMaxEvaluations(maxEvaluations);
return solver.solve(f, accuracy, guess, minVol, maxVol);
}
Volatility ImpliedVolatilityHelper::calculate(
const Instrument& instrument,
const PricingEngine& engine,
SimpleQuote& volQuote,
Real targetValue,
Real accuracy,
Natural maxEvaluations,
Volatility minVol,
Volatility maxVol) {
instrument.setupArguments(engine.getArguments());
engine.getArguments()->validate();
PriceError f(engine, volQuote, targetValue);
Brent solver;
solver.setMaxEvaluations(maxEvaluations);
Volatility guess = (minVol+maxVol)/2.0;
Volatility result = solver.solve(f, accuracy, guess,
minVol, maxVol);
return result;
}
CapPseudoDerivative::CapPseudoDerivative(boost::shared_ptr<MarketModel> inputModel,
Real strike,
Size startIndex,
Size endIndex, Real firstDF) : firstDF_(firstDF)
{
QL_REQUIRE(startIndex < endIndex, "for a cap pseudo derivative the start of the cap must be before the end");
QL_REQUIRE( endIndex <= inputModel->numberOfRates(), "for a cap pseudo derivative the end of the cap must before the end of the rates");
Size numberCaplets = endIndex-startIndex;
Size numberRates = inputModel->numberOfRates();
Size factors = inputModel->numberOfFactors();
LMMCurveState curve(inputModel->evolution().rateTimes());
curve.setOnForwardRates(inputModel->initialRates());
const Matrix& totalCovariance(inputModel->totalCovariance(inputModel->numberOfSteps()-1));
std::vector<Real> displacedImpliedVols(numberCaplets);
std::vector<Real> annuities(numberCaplets);
std::vector<Real> initialRates(numberCaplets);
std::vector<Real> expiries(numberCaplets);
Real capPrice =0.0;
Real guess=0.0;
Real minVol = 1e10;
Real maxVol =0.0;
for (Size j = startIndex; j < endIndex; ++j)
{
Size capletIndex = j - startIndex;
Time resetTime = inputModel->evolution().rateTimes()[j];
expiries[capletIndex] = resetTime;
Real sd = std::sqrt(totalCovariance[j][j]);
displacedImpliedVols[capletIndex] = std::sqrt(totalCovariance[j][j]/resetTime);
Real forward = inputModel->initialRates()[j];
initialRates[capletIndex] = forward;
Real annuity = curve.discountRatio(j+1,0)* inputModel->evolution().rateTaus()[j]*firstDF_;
annuities[capletIndex] = annuity;
Real displacement = inputModel->displacements()[j];
guess+= displacedImpliedVols[capletIndex]*(forward+displacement)/forward;
minVol =std::min(minVol, displacedImpliedVols[capletIndex]);
maxVol =std::max(maxVol, displacedImpliedVols[capletIndex]*(forward+displacement)/forward);
Real capletPrice = blackFormula(Option::Call,
strike,
forward,
sd,
annuity,
displacement
);
capPrice += capletPrice;
}
guess/=numberCaplets;
for (Size step =0; step < inputModel->evolution().numberOfSteps(); ++step)
{
Matrix thisDerivative(numberRates,factors,0.0);
for (Size rate =std::max(inputModel->evolution().firstAliveRate()[step],startIndex);
rate < endIndex; ++rate)
{
for (Size f=0; f < factors; ++f)
{
Real expiry = inputModel->evolution().rateTimes()[rate];
Real volDerivative = inputModel->pseudoRoot(step)[rate][f]
/(displacedImpliedVols[rate-startIndex]*expiry);
Real capletVega = blackFormulaVolDerivative(strike,inputModel->initialRates()[rate],
displacedImpliedVols[rate-startIndex]*std::sqrt(expiry),
expiry,
annuities[rate-startIndex],
inputModel->displacements()[rate]);
// note that the cap derivative is equal to one of the caplet ones so we lose a loop
thisDerivative[rate][f] = volDerivative*capletVega;
}
}
priceDerivatives_.push_back(thisDerivative);
}
QuickCap capPricer(strike, annuities, initialRates, expiries,capPrice);
Size maxEvaluations = 1000;
Real accuracy = 1E-6;
Brent solver;
solver.setMaxEvaluations(maxEvaluations);
impliedVolatility_ = solver.solve(capPricer,accuracy,guess,minVol*0.99,maxVol*1.01);
vega_ = capPricer.vega(impliedVolatility_);
for (Size step =0; step < inputModel->evolution().numberOfSteps(); ++step)
{
Matrix thisDerivative(numberRates,factors,0.0);
for (Size rate =std::max(inputModel->evolution().firstAliveRate()[step],startIndex);
rate < endIndex; ++rate)
{
for (Size f=0; f < factors; ++f)
{
thisDerivative[rate][f] = priceDerivatives_[step][rate][f]/vega_;
}
}
volatilityDerivatives_.push_back(thisDerivative);
}
}
void AnalyticCompoundOptionEngine::calculate() const {
QL_REQUIRE(strikeDaughter()>0.0,
"Daughter strike must be positive");
QL_REQUIRE(strikeMother()>0.0,
"Mother strike must be positive");
QL_REQUIRE(spot() >= 0.0, "negative or null underlying given");
/* Solver Setup ***************************************************/
Date helpDate(process_->riskFreeRate()->referenceDate());
Date helpMaturity=helpDate+(maturityDaughter()-maturityMother())*Days;
Real vol =process_->blackVolatility()->blackVol(helpMaturity,
strikeDaughter());
Time helpTimeToMat=process_->time(helpMaturity);
vol=vol*std::sqrt(helpTimeToMat);
DiscountFactor dividendDiscount =
process_->dividendYield()->discount(helpMaturity);
DiscountFactor riskFreeDiscount =
process_->riskFreeRate()->discount(helpMaturity);
boost::shared_ptr<ImpliedSpotHelper> f(
new ImpliedSpotHelper(dividendDiscount, riskFreeDiscount,
vol, payoffDaughter(), strikeMother()));
Brent solver;
solver.setMaxEvaluations(1000);
Real accuracy = 1.0e-6;
Real X=0.0;
Real sSolved=0.0;
sSolved=solver.solve(*f, accuracy, strikeDaughter(), 1.0e-6, strikeDaughter()*1000.0);
X=transformX(sSolved); // transform stock to return as in Wystup's book
/* Solver Setup Finished*****************************************/
Real phi=typeDaughter(); // -1 or 1
Real w=typeMother(); // -1 or 1
Real rho=std::sqrt(residualTimeMother()/residualTimeDaughter());
BivariateCumulativeNormalDistributionDr78 N2(w*rho) ;
DiscountFactor ddD=dividendDiscountDaughter();
DiscountFactor rdD=riskFreeDiscountDaughter();
//DiscountFactor ddM=dividendDiscountMother();
DiscountFactor rdM=riskFreeDiscountMother();
Real XmSM=X-stdDeviationMother();
Real S=spot();
Real dP=dPlus();
Real dPT12=dPlusTau12(sSolved);
Real vD=volatilityDaughter();
Real dM=dMinus();
Real strD=strikeDaughter();
Real strM=strikeMother();
Real rTM=residualTimeMother();
Real rTD=residualTimeDaughter();
Real rD=riskFreeRateDaughter();
Real dD=dividendRateDaughter();
Real tempRes=0.0;
Real tempDelta=0.0;
Real tempGamma=0.0;
Real tempVega=0.0;
Real tempTheta=0.0;
Real N2XmSM=N2(-phi*w*XmSM,phi*dP);
Real N2X=N2(-phi*w*X,phi*dM);
Real NeX=N_(-phi*w*e(X));
Real NX=N_(-phi*w*X);
Real NT12=N_(phi*dPT12);
Real ndP=n_(dP);
Real nXm=n_(XmSM);
Real invMTime=1/std::sqrt(rTM);
Real invDTime=1/std::sqrt(rTD);
tempRes=phi*w*S*ddD*N2XmSM-phi*w*strD*rdD*N2X-w*strM*rdM*NX;
tempDelta=phi*w*ddD*N2XmSM;
tempGamma=(ddD/(vD*S))*(invMTime*nXm*NT12+w*invDTime*ndP*NeX);
tempVega=ddD*S*((1/invMTime)*nXm*NT12+w*(1/invDTime)*ndP*NeX);
tempTheta+=phi*w*dD*S*ddD*N2XmSM-phi*w*rD*strD*rdD*N2X-w*rD*strM*rdM*NX;
tempTheta-=0.5*vD*S*ddD*(invMTime*nXm*NT12+w*invDTime*ndP*NeX);
results_.value=tempRes;
results_.delta=tempDelta;
results_.gamma=tempGamma;
results_.vega=tempVega;
results_.theta=tempTheta;
}
