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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Ferdinando Ametrano
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/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackvoltermstructure.hpp>
#include <ql/termstructures/volatility/equityfx/localvolsurface.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
const Date& LocalVolSurface::referenceDate() const {
return blackTS_->referenceDate();
}
DayCounter LocalVolSurface::dayCounter() const {
return blackTS_->dayCounter();
}
Date LocalVolSurface::maxDate() const {
return blackTS_->maxDate();
}
Real LocalVolSurface::minStrike() const {
return blackTS_->minStrike();
}
Real LocalVolSurface::maxStrike() const {
return blackTS_->maxStrike();
}
LocalVolSurface::LocalVolSurface(const Handle<BlackVolTermStructure>& blackTS,
Handle<YieldTermStructure> riskFreeTS,
Handle<YieldTermStructure> dividendTS,
Handle<Quote> underlying)
: LocalVolTermStructure(blackTS->businessDayConvention(), blackTS->dayCounter()),
blackTS_(blackTS), riskFreeTS_(std::move(riskFreeTS)), dividendTS_(std::move(dividendTS)),
underlying_(std::move(underlying)) {
registerWith(blackTS_);
registerWith(riskFreeTS_);
registerWith(dividendTS_);
registerWith(underlying_);
}
LocalVolSurface::LocalVolSurface(const Handle<BlackVolTermStructure>& blackTS,
Handle<YieldTermStructure> riskFreeTS,
Handle<YieldTermStructure> dividendTS,
Real underlying)
: LocalVolTermStructure(blackTS->businessDayConvention(), blackTS->dayCounter()),
blackTS_(blackTS), riskFreeTS_(std::move(riskFreeTS)), dividendTS_(std::move(dividendTS)),
underlying_(ext::shared_ptr<Quote>(new SimpleQuote(underlying))) {
registerWith(blackTS_);
registerWith(riskFreeTS_);
registerWith(dividendTS_);
}
void LocalVolSurface::accept(AcyclicVisitor& v) {
auto* v1 = dynamic_cast<Visitor<LocalVolSurface>*>(&v);
if (v1 != nullptr)
v1->visit(*this);
else
LocalVolTermStructure::accept(v);
}
Volatility LocalVolSurface::localVolImpl(Time t, Real underlyingLevel)
const {
DiscountFactor dr = riskFreeTS_->discount(t, true);
DiscountFactor dq = dividendTS_->discount(t, true);
Real forwardValue = underlying_->value()*dq/dr;
// strike derivatives
Real strike, y, dy, strikep, strikem;
Real w, wp, wm, dwdy, d2wdy2;
strike = underlyingLevel;
y = std::log(strike/forwardValue);
dy = ((std::fabs(y) > 0.001) ? Real(y*0.0001) : 0.000001);
strikep=strike*std::exp(dy);
strikem=strike/std::exp(dy);
w = blackTS_->blackVariance(t, strike, true);
wp = blackTS_->blackVariance(t, strikep, true);
wm = blackTS_->blackVariance(t, strikem, true);
dwdy = (wp-wm)/(2.0*dy);
d2wdy2 = (wp-2.0*w+wm)/(dy*dy);
// time derivative
Real dt, wpt, wmt, dwdt;
if (t==0.0) {
dt = 0.0001;
DiscountFactor drpt = riskFreeTS_->discount(t+dt, true);
DiscountFactor dqpt = dividendTS_->discount(t+dt, true);
Real strikept = strike*dr*dqpt/(drpt*dq);
wpt = blackTS_->blackVariance(t+dt, strikept, true);
QL_ENSURE(wpt>=w,
"decreasing variance at strike " << strike
<< " between time " << t << " and time " << t+dt);
dwdt = (wpt-w)/dt;
} else {
dt = std::min<Time>(0.0001, t/2.0);
DiscountFactor drpt = riskFreeTS_->discount(t+dt, true);
DiscountFactor drmt = riskFreeTS_->discount(t-dt, true);
DiscountFactor dqpt = dividendTS_->discount(t+dt, true);
DiscountFactor dqmt = dividendTS_->discount(t-dt, true);
Real strikept = strike*dr*dqpt/(drpt*dq);
Real strikemt = strike*dr*dqmt/(drmt*dq);
wpt = blackTS_->blackVariance(t+dt, strikept, true);
wmt = blackTS_->blackVariance(t-dt, strikemt, true);
QL_ENSURE(wpt>=w,
"decreasing variance at strike " << strike
<< " between time " << t << " and time " << t+dt);
QL_ENSURE(w>=wmt,
"decreasing variance at strike " << strike
<< " between time " << t-dt << " and time " << t);
dwdt = (wpt-wmt)/(2.0*dt);
}
if (dwdy==0.0 && d2wdy2==0.0) { // avoid /w where w might be 0.0
return std::sqrt(dwdt);
} else {
Real den1 = 1.0 - y/w*dwdy;
Real den2 = 0.25*(-0.25 - 1.0/w + y*y/w/w)*dwdy*dwdy;
Real den3 = 0.5*d2wdy2;
Real den = den1+den2+den3;
Real result = dwdt / den;
QL_ENSURE(result>=0.0,
"negative local vol^2 at strike " << strike
<< " and time " << t
<< "; the black vol surface is not smooth enough");
return std::sqrt(result);
}
}
}
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