Real SmileSection::volatility(Rate strike, VolatilityType volatilityType,
Real shift) const {
if(volatilityType == volatilityType_ && close(shift,this->shift()))
return volatility(strike);
Real atm = atmLevel();
QL_REQUIRE(atm != Null<Real>(),
"smile section must provide atm level to compute converted volatilties");
Option::Type type = strike >= atm ? Option::Call : Option::Put;
Real premium = optionPrice(strike,type);
Real premiumAtm = optionPrice(atm,type);
if (volatilityType == ShiftedLognormal) {
try {
return blackFormulaImpliedStdDev(type, strike, atm, premium,
1.0, shift) /
std::sqrt(exerciseTime());
} catch(...) {
return blackFormulaImpliedStdDevChambers(
type, strike, atm, premium, premiumAtm, 1.0, shift) /
std::sqrt(exerciseTime());
}
} else {
return bachelierBlackFormulaImpliedVol(type, strike, atm,
exerciseTime(), premium);
}
}
Real SmileSection::digitalOptionPrice(Rate strike,
Option::Type type,
Real discount,
Real gap) const {
Real m = volatilityType() == ShiftedLognormal ? -shift() : -QL_MAX_REAL;
Real kl = std::max(strike-gap/2.0,m);
Real kr = kl+gap;
return (type==Option::Call ? 1.0 : -1.0) *
(optionPrice(kl,type,discount)-optionPrice(kr,type,discount)) / gap;
}
Disposable<Array> SplineDensitySmileSection::setDensity(const Array& d) {
Array errors(c_.size()-2);
std::cout << "***************************" << std::endl;
Real signChanges = 0.0;
for(Size i=1;i<d_.size()-1;i++) {
d_[i] = d[i-1]*d[i-1];
std::cout << "knot " << i << " dens " << d_[i] << std::endl;
if( (d_[i]-d_[i-1]) * (d_[i+1]-d_[i]) < 0.0)
signChanges+=1.0;
}
if(signChanges > 0.0) signChanges -= 1.0;
density_->update();
update();
Real penalty =
1.0 + /*((std::exp(10.0* (f_ - expectation_) * (f_ - expectation_)) - 1.0) +*/
(std::exp((1.0 - adjustment_) * (1.0 - adjustment_)) - 1.0);
//(std::exp(signChanges)-1.0);
for (Size i = 1; i < c_.size() - 1; i++) {
errors[i-1] = (c_[i] - optionPrice(k_[i])) * penalty;
std::cout << "strike " << k_[i] << " market " << c_[i] << " spline " << c_[i] - errors[i-1] << std::endl;
}
std::cout << "penatly = " << penalty << std::endl;
return errors;
}
Real BdkSmileSection::volatilityImpl(Rate strike) const {
Real vol = 0.0;
try {
vol = blackFormulaImpliedStdDev(Option::Call, strike, f_,
optionPrice(strike)) /
sqrt(source_->exerciseTime());
}
catch (QuantLib::Error) {
}
return vol;
}
Real Gaussian1dSmileSection::volatilityImpl(Rate strike) const {
Real vol = 0.0;
try {
Option::Type type = strike >= atm_ ? Option::Call : Option::Put;
Real o = optionPrice(strike, type);
vol = blackFormulaImpliedStdDev(type, strike, atm_, o) /
sqrt(exerciseTime());
} catch (...) {
}
return vol;
}
Real SplineDensitySmileSection::setDensity(const Real d, const Size i) {
d_[i] = d*d;
density_->update();
update();
Real p = optionPrice(k_[i]);
std::cout << std::setprecision(16) << "strike " << k_[i] << " dens " << d << " market " << c_[i] << " spline " << p << " error " << (p-c_[i]) << std::endl;
return p-c_[i];
}
Real SplineDensitySmileSection::volatilityImpl(Rate strike) const {
strike = std::max(strike,0.00001); // assume only non shifted lognormal
// here ... TODO later ... (should be
// shifted lognormal with shift equal
// to minus lowerBound_
Option::Type type = strike >= f_ ? Option::Call : Option::Put;
Real p = optionPrice(strike,type);
Real vol = 0.0;
try {
vol = blackFormulaImpliedStdDev(type, strike, f_, p) /
sqrt(exerciseTime());
}
catch (...) {
}
return vol;
}
Real SplineDensitySmileSection::optionPrice(Rate strike, Option::Type type, Real discount) const {
if(type == Option::Put) return discount*(optionPrice(strike, Option::Call, 1.0) - f_ + strike);
//strike += expectation_-f_;
if(strike <= lowerBound_) return f_-strike;
if(strike >= upperBound_) return 0.0;
Real price = f_- lowerBound_;// + expectation_-f_;
// const std::vector<Real> &pa_ = density_->cCoefficients(); // just for our convenience
// const std::vector<Real> &pb_ = density_->bCoefficients();
// const std::vector<Real> &pc_ = density_->aCoefficients();
const std::vector<Real> &pd_ = d_;
for(Size j=0; j<=index(strike); j++) {
Real mu = std::min(k_[j+1],strike);
Real dk = mu - k_[j];
Real dk2 = dk*dk;
// price += (dk * (adjustment_*lambda_[j] - 1.0) + adjustment_*(
// 1.0 / 20.0 * pa_[j] * dk2*dk2*dk +
// 1.0 / 12.0 * pb_[j] * dk2*dk2 +
// 1.0 / 6.0 * pc_[j] * dk2*dk +
// 1.0 / 2.0 * pd_[j] * dk2));
// linear interpolation
Real pa=0.0,pb=0.0;
Real pc=(d_[j+1]-d_[j])/(k_[j+1]-k_[j]);
price += (dk * (adjustment_*lambda_[j] - 1.0) + adjustment_*(
1.0 / 20.0 * pa * dk2*dk2*dk +
1.0 / 12.0 * pb * dk2*dk2 +
1.0 / 6.0 * pc * dk2*dk +
1.0 / 2.0 * pd_[j] * dk2));
}
return price;
}
Real NoArbSabrSmileSection::volatilityImpl(Rate strike) const {
Real impliedVol = 0.0;
try {
Option::Type type;
if (strike >= forward_)
type = Option::Call;
else
type = Option::Put;
impliedVol =
blackFormulaImpliedStdDev(type, strike, forward_,
optionPrice(strike, type, 1.0), 1.0) /
std::sqrt(exerciseTime());
} catch (...) {
}
if (impliedVol == 0.0)
// fall back on Hagan 2002 expansion
impliedVol =
unsafeSabrVolatility(strike, forward_, exerciseTime(), params_[0],
params_[1], params_[2], params_[3]);
return impliedVol;
}