noarbsabr.hpp

/* -*- 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.
*/
 
#ifndef quantlib_noarb_sabr
#define quantlib_noarb_sabr
 
#include <ql/qldefines.hpp>
#include <ql/types.hpp>
#include <ql/math/integrals/gausslobattointegral.hpp>
 
#include <vector>
 
namespace QuantLib {
 
namespace detail {
namespace NoArbSabrModel {
// parameter bounds
const Real beta_min = 0.01;
const Real beta_max = 0.99;
const Real expiryTime_max = 30.0;
const Real sigmaI_min = 0.05;
const Real sigmaI_max = 1.00;
const Real nu_min = 0.01;
const Real nu_max = 0.80;
const Real rho_min = -0.99;
const Real rho_max = 0.99;
// cutoff for phi(d0) / tau
// if beta = 0.99, d0 is below 1E-14 for
// bigger values than this
const Real phiByTau_cutoff = 124.587;
// number of mc simulations in tabulated
// absorption probabilities
const Real nsim = 2500000.0;
// small probability used for extrapolation
// of beta towards 1
const Real tiny_prob = 1E-5;
// minimum strike used for normal case integration
const Real strike_min = 1E-6;
// accuracy and max iterations for
// numerical integration
const Real i_accuracy = 1E-7;
const Size i_max_iterations = 10000;
// accuracy when adjusting the model forward
// to match the given forward
const Real forward_accuracy = 1E-6;
// step for searching the model forward
// in newton algorithm
const Real forward_search_step = 0.0010;
// lower bound for density evaluation
const Real density_lower_bound = 1E-50;
// threshold to identify a zero density
const Real density_threshold = 1E-100;
}
}
 
class NoArbSabrModel {
 
  public:
    NoArbSabrModel(Real expiryTime, Real forward, Real alpha, Real beta, Real nu, Real rho);
 
    Real optionPrice(Real strike) const;
    Real digitalOptionPrice(Real strike) const;
    Real density(const Real strike) const {
        return p(strike) * (1 - absProb_) / numericalIntegralOverP_;
    }
 
    Real forward() const { return externalForward_; }
    Real numericalForward() const { return numericalForward_; }
    Real expiryTime() const { return expiryTime_; }
    Real alpha() const { return alpha_; }
    Real beta() const { return beta_; }
    Real nu() const { return nu_; }
    Real rho() const { return rho_; }
 
    Real absorptionProbability() const { return absProb_; }
 
    private:
      Real p(Real f) const;
      Real forwardError(Real forward) const;
      const Real expiryTime_, externalForward_;
      const Real alpha_, beta_, nu_, rho_;
      Real absProb_, fmin_, fmax_;
      mutable Real forward_, numericalIntegralOverP_;
      mutable Real numericalForward_;
      ext::shared_ptr<GaussLobattoIntegral> integrator_;
      class integrand;
      class p_integrand;
};
 
namespace detail {
 
extern "C" const unsigned long sabrabsprob[1209600];
 
class D0Interpolator {
  public:
    D0Interpolator(Real forward, Real expiryTime, Real alpha, Real beta, Real nu, Real rho);
    Real operator()() const;
 
  private:
    Real phi(Real d0) const;
    Real d0(Real phi) const;
    const Real forward_, expiryTime_, alpha_, beta_, nu_, rho_, gamma_;
    Real sigmaI_;
    std::vector<Real> tauG_, sigmaIG_, rhoG_, nuG_, betaG_;
};
 
} // namespace detail
} // namespace QuantLib
 
#endif