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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2002, 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.
*/
/*! \file localvolcurve.hpp
\brief Local volatility curve derived from a Black curve
*/
#ifndef quantlib_localvolcurve_hpp
#define quantlib_localvolcurve_hpp
#include <ql/termstructures/volatility/equityfx/blackvariancecurve.hpp>
#include <ql/termstructures/volatility/equityfx/localvoltermstructure.hpp>
namespace QuantLib {
//! Local volatility curve derived from a Black curve
class LocalVolCurve : public LocalVolTermStructure {
public:
LocalVolCurve(const Handle<BlackVarianceCurve>& curve)
: LocalVolTermStructure(curve->businessDayConvention(),
curve->dayCounter()),
blackVarianceCurve_(curve) {
registerWith(blackVarianceCurve_);
}
//! \name TermStructure interface
//@{
const Date& referenceDate() const override { return blackVarianceCurve_->referenceDate(); }
Calendar calendar() const override { return blackVarianceCurve_->calendar(); }
DayCounter dayCounter() const override { return blackVarianceCurve_->dayCounter(); }
Date maxDate() const override { return blackVarianceCurve_->maxDate(); }
//@}
//! \name VolatilityTermStructure interface
//@{
Real minStrike() const override { return QL_MIN_REAL; }
Real maxStrike() const override { return QL_MAX_REAL; }
//@}
//! \name Visitability
//@{
void accept(AcyclicVisitor&) override;
//@}
protected:
Volatility localVolImpl(Time, Real) const override;
private:
Handle<BlackVarianceCurve> blackVarianceCurve_;
};
// inline definitions
inline void LocalVolCurve::accept(AcyclicVisitor& v) {
auto* v1 = dynamic_cast<Visitor<LocalVolCurve>*>(&v);
if (v1 != nullptr)
v1->visit(*this);
else
LocalVolTermStructure::accept(v);
}
/*! The relation
\f[
\int_0^T \sigma_L^2(t)dt = \sigma_B^2 T
\f]
holds, where \f$ \sigma_L(t) \f$ is the local volatility at
time \f$ t \f$ and \f$ \sigma_B(T) \f$ is the Black
volatility for maturity \f$ T \f$. From the above, the formula
\f[
\sigma_L(t) = \sqrt{\frac{\mathrm{d}}{\mathrm{d}t}\sigma_B^2(t)t}
\f]
can be deduced which is here implemented.
*/
inline Volatility LocalVolCurve::localVolImpl(Time t, Real dummy) const {
Time dt = (1.0/365.0);
Real var1 = blackVarianceCurve_->blackVariance(t, dummy, true);
Real var2 = blackVarianceCurve_->blackVariance(t+dt, dummy, true);
Real derivative = (var2-var1)/dt;
return std::sqrt(derivative);
}
}
#endif
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