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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Mario Pucci
Copyright (C) 2013, 2015 Peter Caspers
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/math/comparison.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/settings.hpp>
#include <ql/termstructures/volatility/smilesection.hpp>
#include <utility>
using std::sqrt;
namespace QuantLib {
void SmileSection::update() {
if (isFloating_) {
referenceDate_ = Settings::instance().evaluationDate();
initializeExerciseTime();
}
}
void SmileSection::initializeExerciseTime() const {
QL_REQUIRE(exerciseDate_>=referenceDate_,
"expiry date (" << exerciseDate_ <<
") must be greater than reference date (" <<
referenceDate_ << ")");
exerciseTime_ = dc_.yearFraction(referenceDate_, exerciseDate_);
}
SmileSection::SmileSection(const Date& d,
DayCounter dc,
const Date& referenceDate,
const VolatilityType type,
const Rate shift)
: exerciseDate_(d), dc_(std::move(dc)), volatilityType_(type), shift_(shift) {
isFloating_ = referenceDate==Date();
if (isFloating_) {
registerWith(Settings::instance().evaluationDate());
referenceDate_ = Settings::instance().evaluationDate();
} else
referenceDate_ = referenceDate;
SmileSection::initializeExerciseTime();
}
SmileSection::SmileSection(Time exerciseTime,
DayCounter dc,
const VolatilityType type,
const Rate shift)
: isFloating_(false), dc_(std::move(dc)), exerciseTime_(exerciseTime), volatilityType_(type),
shift_(shift) {
QL_REQUIRE(exerciseTime_>=0.0,
"expiry time must be positive: " <<
exerciseTime_ << " not allowed");
}
Real SmileSection::optionPrice(Rate strike,
Option::Type type,
Real discount) const {
Real atm = atmLevel();
QL_REQUIRE(atm != Null<Real>(),
"smile section must provide atm level to compute option price");
// if lognormal or shifted lognormal,
// for strike at -shift, return option price even if outside
// minstrike, maxstrike interval
if (volatilityType() == ShiftedLognormal)
return blackFormula(type,strike,atm, std::fabs(strike+shift()) < QL_EPSILON ?
0.2 : Real(sqrt(variance(strike))),discount,shift());
else
return bachelierBlackFormula(type,strike,atm,sqrt(variance(strike)),discount);
}
Real SmileSection::digitalOptionPrice(Rate strike,
Option::Type type,
Real discount,
Real gap) const {
Real m = volatilityType() == ShiftedLognormal ? Real(-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;
}
Real SmileSection::density(Rate strike, Real discount, Real gap) const {
Real m = volatilityType() == ShiftedLognormal ? Real(-shift()) : -QL_MAX_REAL;
Real kl = std::max(strike-gap/2.0,m);
Real kr = kl+gap;
return (digitalOptionPrice(kl,Option::Call,discount,gap) -
digitalOptionPrice(kr,Option::Call,discount,gap)) / gap;
}
Real SmileSection::vega(Rate strike, Real discount) const {
Real atm = atmLevel();
QL_REQUIRE(atm != Null<Real>(),
"smile section must provide atm level to compute option vega");
if (volatilityType() == ShiftedLognormal)
return blackFormulaVolDerivative(strike,atmLevel(),
sqrt(variance(strike)),
exerciseTime(),discount,shift())*0.01;
else
QL_FAIL("vega for normal smilesection not yet implemented");
}
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);
}
}
}
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