distribution.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2008 Roland Lichters
 
 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 distribution.hpp
    \brief Discretized probability density and cumulative probability
*/
 
#ifndef quantlib_probability_distribution_hpp
#define quantlib_probability_distribution_hpp
 
#include <ql/types.hpp>
#include <vector>
 
namespace QuantLib {
 
    //! Discretized probability density and cumulative probability
    /*! Discretized probability density and cumulative probability
      \ingroup probability
    */
    class ManipulateDistribution;
    class Distribution {
    public:
        friend class ManipulateDistribution;
        Distribution (int nBuckets, Real xmin, Real xmax);
        Distribution() = default;
        ;
 
        void add (Real value);
        void addDensity (int bucket, Real value);
        void addAverage (int bucket, Real value);
        void normalize ();
 
        Size size () const { return size_; }
        Real x (Size k) { return x_.at(k); }
        std::vector<Real>& x () { return x_; }
        Real dx (Size k) { return dx_.at(k); }
        std::vector<Real>& dx () { return dx_; }
        Real dx (Real x);
 
        Real density (Size k) {
            normalize();
            return density_.at(k);
        }
        Real cumulative (Size k) {
            normalize();
            return cumulativeDensity_.at(k);
        }
        Real excess (Size k) {
            normalize();
            return excessProbability_.at(k);
        }
        Real cumulativeExcess (Size k) {
            normalize();
            return cumulativeExcessProbability_.at(k);
        }
        Real average (Size k) { return average_.at(k); }
 
        Real confidenceLevel (Real quantil);
        Real cumulativeDensity (Real x);
        Real cumulativeExcessProbability (Real a, Real b);
        Real expectedValue ();
        Real trancheExpectedValue (Real a, Real d);
 
        template <class F>
        Real expectedValue (F& f) {
            normalize();
            Real expected = 0;
            for (int i = 0; i < size_; i++) {
                Real x = x_[i] + dx_[i]/2;
                expected += f (x) * dx_[i] * density_[i];
            }
            return expected;
        }
 
        /*!
          Transform the loss distribution into the tranche loss distribution
          for losses L_T = min(L,D) - min(L,A).
          The effects are:
          1) shift the distribution to the left by A, then
          2) cut off at D-A, Pr(L_T > D-A) = 0
          3) ensure Pr(L_T >= 0) = 1, i.e. a density spike at L_T = 0
         */
        void tranche (Real attachmentPoint, Real detachmentPoint);
 
        /*
          index of the grid point to the left of x
        */
        int locate (Real x);
 
        /* Returns the average value conditional on values above
        the passed percentile probability */
        Real expectedShortfall (Real percValue);
    private:
        int size_;
        Real xmin_, xmax_;
        std::vector<int> count_;
        // x: coordinate of left hand cell bundary
        // dx: cell width
        std::vector<Real> x_, dx_;
        // density: probability density, densitx*dx = prob. of loss in cell i
        // cumulatedDensity: cumulated (integrated) from x = 0
        // excessProbability: cumulated from x_i to infinity
        // cumulativeExcessProbability: integrated excessProbability from x = 0
        std::vector<Real> density_, cumulativeDensity_;
        std::vector<Real> excessProbability_, cumulativeExcessProbability_;
        // average loss in cell i
        std::vector<Real> average_;
 
        int overFlow_, underFlow_;
        bool isNormalized_;
    };
 
    class ManipulateDistribution {
    public:
        static Distribution convolve (const Distribution& d1,
                                      const Distribution& d2);
    };
 
}
 
#endif