/usr/include/ql/experimental/volatility/noarbsabrinterpolation.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
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 noarbsabrinterpolation.hpp
\brief noabr sabr interpolation between discrete points
*/
#ifndef quantlib_noarbsabr_interpolation_hpp
#define quantlib_noarbsabr_interpolation_hpp
#include <ql/math/interpolations/sabrinterpolation.hpp>
#include <ql/experimental/volatility/noarbsabrsmilesection.hpp>
#include <boost/make_shared.hpp>
#include <boost/assign/list_of.hpp>
namespace QuantLib {
namespace detail {
// we can directly use the smile section as the wrapper
typedef NoArbSabrSmileSection NoArbSabrWrapper;
struct NoArbSabrSpecs {
Size dimension() { return 4; }
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) {
SABRSpecs().defaultValues(params, paramIsFixed, forward, expiryTime, addParams);
// check if alpha / beta is admissable, otherwise adjust
// if possible (i.e. not fixed, otherwise an exception will
// be thrown from the model constructor anyway)
Real sigmaI = params[0] * std::pow(forward, params[1] - 1.0);
if (sigmaI < detail::NoArbSabrModel::sigmaI_min) {
if (!paramIsFixed[0])
params[0] = detail::NoArbSabrModel::sigmaI_min * (1.0 + eps()) /
std::pow(forward, params[1] - 1.0);
else {
if (!paramIsFixed[1])
params[1] = 1.0 +
std::log(detail::NoArbSabrModel::sigmaI_min *
(1.0 + eps()) / params[0]) /
std::log(forward);
}
}
if (sigmaI > detail::NoArbSabrModel::sigmaI_max) {
if (!paramIsFixed[0])
params[0] = detail::NoArbSabrModel::sigmaI_max * (1.0 - eps()) /
std::pow(forward, params[1] - 1.0);
else {
if (!paramIsFixed[1])
params[1] = 1.0 +
std::log(detail::NoArbSabrModel::sigmaI_max *
(1.0 - eps()) / params[0]) /
std::log(forward);
}
}
}
void guess(Array &values, const std::vector<bool> ¶mIsFixed,
const Real &forward, const Real expiryTime,
const std::vector<Real> &r, const std::vector<Real> &) {
Size j = 0;
if (!paramIsFixed[1])
values[1] = detail::NoArbSabrModel::beta_min +
(detail::NoArbSabrModel::beta_max -
detail::NoArbSabrModel::beta_min) *
r[j++];
if (!paramIsFixed[0]) {
Real sigmaI = detail::NoArbSabrModel::sigmaI_min +
(detail::NoArbSabrModel::sigmaI_max -
detail::NoArbSabrModel::sigmaI_min) *
r[j++];
sigmaI *= (1.0 - eps());
sigmaI += eps() / 2.0;
values[0] = sigmaI / std::pow(forward, values[1] - 1.0);
}
if (!paramIsFixed[2])
values[2] = detail::NoArbSabrModel::nu_min +
(detail::NoArbSabrModel::nu_max -
detail::NoArbSabrModel::nu_min) *
r[j++];
if (!paramIsFixed[3])
values[3] = detail::NoArbSabrModel::rho_min +
(detail::NoArbSabrModel::rho_max -
detail::NoArbSabrModel::rho_min) *
r[j++];
}
Array inverse(const Array &y, const std::vector<bool> ¶mIsFixed,
const std::vector<Real> ¶ms, const Real forward) {
Array x(4);
x[1] = std::tan((y[1] - detail::NoArbSabrModel::beta_min) /
(detail::NoArbSabrModel::beta_max -
detail::NoArbSabrModel::beta_min) *
M_PI +
M_PI / 2.0);
x[0] = std::tan((y[0] * std::pow(forward, y[1] - 1.0) -
detail::NoArbSabrModel::sigmaI_min) /
(detail::NoArbSabrModel::sigmaI_max -
detail::NoArbSabrModel::sigmaI_min) *
M_PI -
M_PI / 2.0);
x[2] = std::tan((y[2] - detail::NoArbSabrModel::nu_min) /
(detail::NoArbSabrModel::nu_max -
detail::NoArbSabrModel::nu_min) *
M_PI +
M_PI / 2.0);
x[3] = std::tan((y[3] - detail::NoArbSabrModel::rho_min) /
(detail::NoArbSabrModel::rho_max -
detail::NoArbSabrModel::rho_min) *
M_PI +
M_PI / 2.0);
return x;
}
Array direct(const Array &x, const std::vector<bool> ¶mIsFixed,
const std::vector<Real> ¶ms, const Real forward) {
Array y(4);
if (paramIsFixed[1])
y[1] = params[1];
else
y[1] = detail::NoArbSabrModel::beta_min +
(detail::NoArbSabrModel::beta_max -
detail::NoArbSabrModel::beta_min) *
(std::atan(x[1]) + M_PI / 2.0) / M_PI;
// we compute alpha from sigmaI using beta
// if alpha is fixed we have to check if beta is admissable
// and adjust if need be
if (paramIsFixed[0]) {
y[0] = params[0];
Real sigmaI = y[0] * std::pow(forward, y[1] - 1.0);
if (sigmaI < detail::NoArbSabrModel::sigmaI_min) {
y[1] = (1.0 +
std::log(detail::NoArbSabrModel::sigmaI_min *
(1.0 + eps()) / y[0]) /
std::log(forward));
}
if (sigmaI > detail::NoArbSabrModel::sigmaI_max) {
y[1] = (1.0 +
std::log(detail::NoArbSabrModel::sigmaI_max *
(1.0 - eps()) / y[0]) /
std::log(forward));
}
} else {
Real sigmaI = detail::NoArbSabrModel::sigmaI_min +
(detail::NoArbSabrModel::sigmaI_max -
detail::NoArbSabrModel::sigmaI_min) *
(std::atan(x[0]) + M_PI / 2.0) / M_PI;
y[0] = sigmaI / std::pow(forward, y[1] - 1.0);
}
if (paramIsFixed[2])
y[2] = params[2];
else
y[2] = detail::NoArbSabrModel::nu_min +
(detail::NoArbSabrModel::nu_max -
detail::NoArbSabrModel::nu_min) *
(std::atan(x[2]) + M_PI / 2.0) / M_PI;
if (paramIsFixed[3])
y[3] = params[3];
else
y[3] = detail::NoArbSabrModel::rho_min +
(detail::NoArbSabrModel::rho_max -
detail::NoArbSabrModel::rho_min) *
(std::atan(x[3]) + M_PI / 2.0) / M_PI;
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 NoArbSabrWrapper type;
boost::shared_ptr<type> instance(const Time t, const Real &forward,
const std::vector<Real> ¶ms,
const std::vector<Real> &) {
return boost::make_shared<type>(t, forward, params);
}
};
}
//! no arbitrage sabr smile interpolation between discrete volatility points.
class NoArbSabrInterpolation : public Interpolation {
public:
template <class I1, class I2>
NoArbSabrInterpolation(
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,
bool alphaIsFixed, bool betaIsFixed, bool nuIsFixed, bool rhoIsFixed,
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, const Real shift = 0.0) {
QL_REQUIRE(shift==0.0,"NoArbSabrInterpolation for non zero shift not implemented");
impl_ = boost::shared_ptr<Interpolation::Impl>(
new detail::XABRInterpolationImpl<I1, I2, detail::NoArbSabrSpecs>(
xBegin, xEnd, yBegin, t, forward,
boost::assign::list_of(alpha)(beta)(nu)(rho),
boost::assign::list_of(alphaIsFixed)(betaIsFixed)(nuIsFixed)(
rhoIsFixed),
vegaWeighted, endCriteria, optMethod, errorAccept, useMaxError,
maxGuesses));
coeffs_ = boost::dynamic_pointer_cast<
detail::XABRCoeffHolder<detail::NoArbSabrSpecs> >(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 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::NoArbSabrSpecs> > coeffs_;
};
//! no arbtrage sabr interpolation factory and traits
class NoArbSabr {
public:
NoArbSabr(Time t, Real forward, Real alpha, Real beta, Real nu, Real rho,
bool alphaIsFixed, bool betaIsFixed, bool nuIsFixed,
bool rhoIsFixed, 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),
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 NoArbSabrInterpolation(
xBegin, xEnd, yBegin, t_, forward_, alpha_, beta_, nu_, rho_,
alphaIsFixed_, betaIsFixed_, nuIsFixed_, rhoIsFixed_, vegaWeighted_,
endCriteria_, optMethod_, errorAccept_, useMaxError_, maxGuesses_);
}
static const bool global = true;
private:
Time t_;
Real forward_;
Real alpha_, beta_, nu_, rho_;
bool alphaIsFixed_, betaIsFixed_, nuIsFixed_, rhoIsFixed_;
bool vegaWeighted_;
const boost::shared_ptr<EndCriteria> endCriteria_;
const boost::shared_ptr<OptimizationMethod> optMethod_;
const Real errorAccept_;
const bool useMaxError_;
const Size maxGuesses_;
};
}
#endif
|