sabrinterpolation.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2006 Ferdinando Ametrano
 Copyright (C) 2007 Marco Bianchetti
 Copyright (C) 2007 François du Vignaud
 Copyright (C) 2007 Giorgio Facchinetti
 Copyright (C) 2006 Mario Pucci
 Copyright (C) 2006 StatPro Italia srl
 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 sabrinterpolation.hpp
    \brief SABR interpolation interpolation between discrete points
*/
 
#ifndef quantlib_sabr_interpolation_hpp
#define quantlib_sabr_interpolation_hpp
 
#include <ql/math/interpolations/xabrinterpolation.hpp>
#include <ql/termstructures/volatility/sabr.hpp>
#include <utility>
 
namespace QuantLib {
 
namespace detail {
 
class SABRWrapper {
  public:
    SABRWrapper(const Time t,
                const Real& forward,
                const std::vector<Real>& params,
                const std::vector<Real>& addParams)
    : t_(t), forward_(forward), params_(params), shift_(addParams.empty() ? 0.0 : addParams[0]) {
        QL_REQUIRE(forward_ + shift_ > 0.0, "forward+shift must be positive: "
                                                 << forward_ << " with shift "
                                                 << shift_ << " not allowed");
        validateSabrParameters(params[0], params[1], params[2], params[3]);
    }
    Real volatility(const Real x, const VolatilityType volatilityType) {
        return shiftedSabrVolatility(x, forward_, t_, params_[0], params_[1],
                                     params_[2], params_[3], shift_, volatilityType);
    }
 
  private:
    const Real t_, &forward_;
    const std::vector<Real> &params_;
    const Real shift_;
};
 
struct SABRSpecs {
    Size dimension() { return 4; }
    void defaultValues(std::vector<Real> &params, std::vector<bool> &,
                       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 ?
                                   Real(std::pow(forward + (addParams.empty() ? 0.0 : addParams[0]),
                                            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;
    }
    void guess(Array &values, const std::vector<bool> &paramIsFixed,
               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 + (addParams.empty() ? 0.0 : addParams[0]), 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);
    }
    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(4);
        x[0] = y[0] < 25.0 + eps1() ? Real(std::sqrt(y[0] - eps1()))
                                    : Real((y[0] - eps1() + 25.0) / 10.0);
        // y_[1] = std::tan(M_PI*(x[1] - 0.5))/dilationFactor();
        x[1] = std::sqrt(-std::log(y[1]));
        x[2] = y[2] < 25.0 + eps1() ? Real(std::sqrt(y[2] - eps1()))
                                    : Real((y[2] - eps1() + 25.0) / 10.0);
        x[3] = std::asin(y[3] / eps2());
        return x;
    }
    Array direct(const Array &x, const std::vector<bool> &,
                 const std::vector<Real> &, const Real) {
        Array y(4);
        y[0] = std::fabs(x[0]) < 5.0 ? Real(x[0] * x[0] + eps1())
                                     : Real((10.0 * std::fabs(x[0]) - 25.0) + eps1());
        // y_[1] = std::atan(dilationFactor_*x[1])/M_PI + 0.5;
        y[1] = std::fabs(x[1]) < std::sqrt(-std::log(eps1()))
                   ? std::exp(-(x[1] * x[1]))
                   : eps1();
        y[2] = std::fabs(x[2]) < 5.0 ? Real(x[2] * x[2] + eps1())
                                     : Real((10.0 * std::fabs(x[2]) - 25.0) + eps1());
        y[3] = std::fabs(x[3]) < 2.5 * M_PI
                   ? Real(eps2() * std::sin(x[3]))
                   : Real(eps2() * (x[3] > 0.0 ? 1.0 : (-1.0)));
        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,
                                            addParams[0]);
    }
    typedef SABRWrapper type;
    ext::shared_ptr<type> instance(const Time t, const Real &forward,
                                     const std::vector<Real> &params,
                                     const std::vector<Real> &addParams) {
        return ext::make_shared<type>(t, forward, params, addParams);
    }
};
}
 
//! %SABR smile interpolation between discrete volatility points.
/*! \ingroup interpolations
    \warning See the Interpolation class for information about the
             required lifetime of the underlying data.
*/
class SABRInterpolation : public Interpolation {
  public:
    template <class I1, class I2>
    SABRInterpolation(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 ext::shared_ptr<EndCriteria> &endCriteria =
                          ext::shared_ptr<EndCriteria>(),
                      const ext::shared_ptr<OptimizationMethod> &optMethod =
                          ext::shared_ptr<OptimizationMethod>(),
                      const Real errorAccept = 0.0020,
                      const bool useMaxError = false,
                      const Size maxGuesses = 50, const Real shift = 0.0,
                      const VolatilityType volatilityType = VolatilityType::ShiftedLognormal) {
 
        impl_ = ext::shared_ptr<Interpolation::Impl>(
            new detail::XABRInterpolationImpl<I1, I2, detail::SABRSpecs>(
                xBegin, xEnd, yBegin, t, forward,
                {alpha, beta, nu, rho},
                {alphaIsFixed, betaIsFixed, nuIsFixed, rhoIsFixed},
                vegaWeighted, endCriteria, optMethod, errorAccept, useMaxError,
                maxGuesses, {shift}, volatilityType));
    }
    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:
    const detail::XABRCoeffHolder<detail::SABRSpecs>& coeffs() const {
        return *dynamic_cast<detail::XABRCoeffHolder<detail::SABRSpecs>*>(impl_.get());
    }
};
 
//! %SABR interpolation factory and traits
/*! \ingroup interpolations */
class SABR {
  public:
    SABR(Time t,
         Real forward,
         Real alpha,
         Real beta,
         Real nu,
         Real rho,
         bool alphaIsFixed,
         bool betaIsFixed,
         bool nuIsFixed,
         bool rhoIsFixed,
         bool vegaWeighted = false,
         ext::shared_ptr<EndCriteria> endCriteria = ext::shared_ptr<EndCriteria>(),
         ext::shared_ptr<OptimizationMethod> optMethod = ext::shared_ptr<OptimizationMethod>(),
         const Real errorAccept = 0.0020,
         const bool useMaxError = false,
         const Size maxGuesses = 50,
         const Real shift = 0.0)
    : t_(t), forward_(forward), alpha_(alpha), beta_(beta), nu_(nu), rho_(rho),
      alphaIsFixed_(alphaIsFixed), betaIsFixed_(betaIsFixed), nuIsFixed_(nuIsFixed),
      rhoIsFixed_(rhoIsFixed), vegaWeighted_(vegaWeighted), endCriteria_(std::move(endCriteria)),
      optMethod_(std::move(optMethod)), errorAccept_(errorAccept), useMaxError_(useMaxError),
      maxGuesses_(maxGuesses), shift_(shift) {}
    template <class I1, class I2>
    Interpolation interpolate(const I1 &xBegin, const I1 &xEnd,
                              const I2 &yBegin) const {
        return SABRInterpolation(xBegin, xEnd, yBegin, t_, forward_, alpha_,
                                 beta_, nu_, rho_, alphaIsFixed_, betaIsFixed_,
                                 nuIsFixed_, rhoIsFixed_, vegaWeighted_,
                                 endCriteria_, optMethod_, errorAccept_,
                                 useMaxError_, maxGuesses_, shift_);
    }
    static const bool global = true;
 
  private:
    Time t_;
    Real forward_;
    Real alpha_, beta_, nu_, rho_;
    bool alphaIsFixed_, betaIsFixed_, nuIsFixed_, rhoIsFixed_;
    bool vegaWeighted_;
    const ext::shared_ptr<EndCriteria> endCriteria_;
    const ext::shared_ptr<OptimizationMethod> optMethod_;
    const Real errorAccept_;
    const bool useMaxError_;
    const Size maxGuesses_;
    const Real shift_;
};
}
 
#endif