/usr/include/ql/experimental/volatility/zabrinterpolation.hpp is in libquantlib0-dev 1.9.1-1.
This file is owned by root:root, with mode 0o644.
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/*
Copyright (C) 2014 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
<http://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 zabrinterpolation.hpp
\brief ZABR interpolation interpolation between discrete points
*/
#ifndef quantlib_zabr_interpolation_hpp
#define quantlib_zabr_interpolation_hpp
#include <ql/math/interpolations/xabrinterpolation.hpp>
#include <ql/experimental/volatility/zabrsmilesection.hpp>
#include <boost/make_shared.hpp>
#include <boost/assign/list_of.hpp>
namespace QuantLib {
namespace detail {
template <typename Evaluation> struct ZabrSpecs {
Size dimension() { return 5; }
Real eps() { return 0.000001; }
void defaultValues(std::vector<Real> ¶ms,
std::vector<bool> ¶mIsFixed, const Real &forward,
const Real expiryTime, const std::vector<Real>& addParams) {
if (params[1] == Null<Real>())
params[1] = 0.5;
if (params[0] == Null<Real>())
// adapt alpha to beta level
params[0] =
0.2 *
(params[1] < 0.9999 ? std::pow(forward, 1.0 - params[1]) : 1.0);
if (params[2] == Null<Real>())
params[2] = std::sqrt(0.4);
if (params[3] == Null<Real>())
params[3] = 0.0;
if (params[4] == Null<Real>())
params[4] = 1.0;
}
void guess(Array &values, const std::vector<bool> ¶mIsFixed,
const Real &forward, const Real expiryTime,
const std::vector<Real> &r, const std::vector<Real>& addParams) {
Size j = 0;
if (!paramIsFixed[1])
values[1] = (1.0 - 2E-6) * r[j++] + 1E-6;
if (!paramIsFixed[0]) {
values[0] = (1.0 - 2E-6) * r[j++] + 1E-6; // lognormal vol guess
// adapt this to beta level
if (values[1] < 0.999)
values[0] *= std::pow(forward, 1.0 - values[1]);
}
if (!paramIsFixed[2])
values[2] = 1.5 * r[j++] + 1E-6;
if (!paramIsFixed[3])
values[3] = (2.0 * r[j++] - 1.0) * (1.0 - 1E-6);
if (!paramIsFixed[4])
values[4] = r[j++] * 2.0;
}
Real eps1() { return .0000001; }
Real eps2() { return .9999; }
Real dilationFactor() { return 0.001; }
Array inverse(const Array &y, const std::vector<bool> &,
const std::vector<Real> &, const Real) {
Array x(5);
x[0] = y[0] < 25.0 + eps1() ? std::sqrt(y[0] - eps1())
: (y[0] - eps1() + 25.0) / 10.0;
x[1] = std::sqrt(-std::log(y[1]));
x[2] = std::tan(M_PI*(y[4]/5.0-0.5));
x[3] = std::asin(y[3] / eps2());
x[4] = std::tan(M_PI*(y[4]/1.9-0.5));
return x;
}
Array direct(const Array &x, const std::vector<bool> &,
const std::vector<Real> &, const Real) {
Array y(5);
y[0] = std::fabs(x[0]) < 5.0 ? x[0] * x[0] + eps1()
: (10.0 * std::fabs(x[0]) - 25.0) + eps1();
y[1] = std::fabs(x[1]) < std::sqrt(-std::log(eps1()))
? std::exp(-(x[1] * x[1]))
: eps1();
// limit nu to 5.00
y[2] = (std::atan(x[2])/M_PI + 0.5) * 5.0;
y[3] = std::fabs(x[3]) < 2.5 * M_PI
? eps2() * std::sin(x[3])
: eps2() * (x[3] > 0.0 ? 1.0 : (-1.0));
// limit gamma to 1.9
y[4] = (std::atan(x[4])/M_PI + 0.5) * 1.9;
return y;
}
Real weight(const Real strike, const Real forward, const Real stdDev,
const std::vector<Real> &addParams) {
return blackFormulaStdDevDerivative(strike, forward, stdDev, 1.0);
}
typedef ZabrSmileSection<Evaluation> type;
boost::shared_ptr<type> instance(const Time t, const Real &forward,
const std::vector<Real> ¶ms,
const std::vector<Real> &addParams) {
return boost::make_shared<type>(t, forward, params);
}
};
} // end namespace detail
//! zabr smile interpolation between discrete volatility points.
template <class Evaluation> class ZabrInterpolation : public Interpolation {
public:
template <class I1, class I2>
ZabrInterpolation(
const I1 &xBegin, // x = strikes
const I1 &xEnd,
const I2 &yBegin, // y = volatilities
Time t, // option expiry
const Real &forward, Real alpha, Real beta, Real nu, Real rho,
Real gamma, bool alphaIsFixed, bool betaIsFixed, bool nuIsFixed,
bool rhoIsFixed, bool gammaIsFixed, bool vegaWeighted = true,
const boost::shared_ptr<EndCriteria> &endCriteria =
boost::shared_ptr<EndCriteria>(),
const boost::shared_ptr<OptimizationMethod> &optMethod =
boost::shared_ptr<OptimizationMethod>(),
const Real errorAccept = 0.0020, const bool useMaxError = false,
const Size maxGuesses = 50) {
impl_ = boost::shared_ptr<
Interpolation::Impl>(new detail::XABRInterpolationImpl<
I1, I2,
detail::ZabrSpecs<Evaluation> >(
xBegin, xEnd, yBegin, t, forward,
boost::assign::list_of(alpha)(beta)(nu)(rho)(gamma),
boost::assign::list_of(alphaIsFixed)(betaIsFixed)(nuIsFixed)(
rhoIsFixed)(gammaIsFixed),
vegaWeighted, endCriteria, optMethod, errorAccept, useMaxError,
maxGuesses));
coeffs_ = boost::dynamic_pointer_cast<detail::XABRCoeffHolder<
detail::ZabrSpecs<Evaluation> > >(impl_);
}
Real expiry() const { return coeffs_->t_; }
Real forward() const { return coeffs_->forward_; }
Real alpha() const { return coeffs_->params_[0]; }
Real beta() const { return coeffs_->params_[1]; }
Real nu() const { return coeffs_->params_[2]; }
Real rho() const { return coeffs_->params_[3]; }
Real gamma() const { return coeffs_->params_[4]; }
Real rmsError() const { return coeffs_->error_; }
Real maxError() const { return coeffs_->maxError_; }
const std::vector<Real> &interpolationWeights() const {
return coeffs_->weights_;
}
EndCriteria::Type endCriteria() { return coeffs_->XABREndCriteria_; }
private:
boost::shared_ptr<detail::XABRCoeffHolder<detail::ZabrSpecs<Evaluation> > > coeffs_;
};
//! no arbtrage sabr interpolation factory and traits
template<class Evaluation> class Zabr {
public:
Zabr(Time t, Real forward, Real alpha, Real beta, Real nu, Real rho,
Real gamma, bool alphaIsFixed, bool betaIsFixed, bool nuIsFixed,
bool rhoIsFixed, bool gammaIsFixed, bool vegaWeighted = false,
const boost::shared_ptr<EndCriteria> endCriteria =
boost::shared_ptr<EndCriteria>(),
const boost::shared_ptr<OptimizationMethod> optMethod =
boost::shared_ptr<OptimizationMethod>(),
const Real errorAccept = 0.0020, const bool useMaxError = false,
const Size maxGuesses = 50)
: t_(t), forward_(forward), alpha_(alpha), beta_(beta), nu_(nu),
rho_(rho), alphaIsFixed_(alphaIsFixed), betaIsFixed_(betaIsFixed),
nuIsFixed_(nuIsFixed), rhoIsFixed_(rhoIsFixed),
gammaIsFixed_(gammaIsFixed), vegaWeighted_(vegaWeighted),
endCriteria_(endCriteria), optMethod_(optMethod),
errorAccept_(errorAccept), useMaxError_(useMaxError),
maxGuesses_(maxGuesses) {}
template <class I1, class I2>
Interpolation interpolate(const I1 &xBegin, const I1 &xEnd,
const I2 &yBegin) const {
return ZabrInterpolation<Evaluation>(
xBegin, xEnd, yBegin, t_, forward_, alpha_, beta_, nu_, rho_,
gamma_, alphaIsFixed_, betaIsFixed_, nuIsFixed_, rhoIsFixed_,
gammaIsFixed_, vegaWeighted_, endCriteria_, optMethod_,
errorAccept_, useMaxError_, maxGuesses_);
}
static const bool global = true;
private:
Time t_;
Real forward_;
Real alpha_, beta_, nu_, rho_, gamma_;
bool alphaIsFixed_, betaIsFixed_, nuIsFixed_, rhoIsFixed_, gammaIsFixed_;
bool vegaWeighted_;
const boost::shared_ptr<EndCriteria> endCriteria_;
const boost::shared_ptr<OptimizationMethod> optMethod_;
const Real errorAccept_;
const bool useMaxError_;
const Size maxGuesses_;
};
}
#endif
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