stoplightbounds.hpp

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/*
 Copyright (C) 2017 Quaternion Risk Management Ltd.
 All rights reserved.
 
 This file is part of ORE, a free-software/open-source library
 for transparent pricing and risk analysis - http://opensourcerisk.org
 
 ORE is free software: you can redistribute it and/or modify it
 under the terms of the Modified BSD License.  You should have received a
 copy of the license along with this program.
 The license is also available online at <http://opensourcerisk.org>
 
 This program is distributed on the basis that it will form a useful
 contribution to risk analytics and model standardisation, but WITHOUT
 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.
*/
 
/*!
  \file qle/math/stoplightbounds.hpp
  \brief compute stop light bounds for overlapping and correlated PL
 */
 
#pragma once
 
#include <ql/math/matrix.hpp>
#include <ql/math/matrixutilities/pseudosqrt.hpp>
#include <ql/types.hpp>
 
#include <vector>
 
namespace QuantExt {
using QuantLib::Matrix;
using QuantLib::Null;
using QuantLib::Real;
using QuantLib::SalvagingAlgorithm;
using QuantLib::Size;
 
/*! Computes the maximum number of exceptions n such that the probability of having less or equal to
  n exceptions is less than p for a given vector of stop light levels (0.95 = green, 0.9999 = red
  in the Basel approach). An overlapping PL over a given period is considered, possibly also several
  portfolios with correlated PL. If the parameter exceptions m is not null, cumProb is set to the
  probability of having less of equal to m exceptions (this is not affecting the return value).
*/
std::vector<Size> stopLightBounds(const std::vector<Real>& stopLightP, const Size observations,
                                  const Size numberOfDays = 10, const Real p = 0.99, const Size numberOfPortfolios = 1,
                                  const Matrix& correlation = Matrix(1, 1, 1.0), const Size samples = 1500000,
                                  const Size seed = 42,
                                  const SalvagingAlgorithm::Type salvaging = SalvagingAlgorithm::Spectral,
                                  const Size exceptions = Null<Size>(), Real* cumProb = nullptr);
 
/* Uses pretabulated values, throws if no suitable values are tabulated (single portfolio case only) */
std::vector<Size> stopLightBoundsTabulated(const std::vector<Real>& stopLightP, const Size observations,
                                           const Size numberOfDays = 10, const Real p = 0.99);
 
/* Same as above, but for non-overlapping and independent observations */
std::vector<Size> stopLightBounds(const std::vector<Real>& stopLightP, const Size observations, const Real p,
                                  const Size exceptions = Null<Size>(), Real* cumProb = nullptr);
 
/* Generate table of stop light bounds (observations_k, (b_1,k, b_2,k, ..., b_n,k) for a given vector of threshold
   probabilities {stopLightP[1], ..., stopLightP[n]} and a given vector of observations */
std::vector<std::pair<Size, std::vector<Size>>>
generateStopLightBoundTable(const std::vector<Size>& observations, const std::vector<Real>& stopLightP,
                            const Size samples, const Size seed, const Size numberOfDays = 10, const Real p = 0.99);
 
} // namespace QuantExt