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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.
*/
#include <ql/experimental/credit/onefactorcopula.hpp>
using namespace std;
namespace QuantLib {
//-------------------------------------------------------------------------
Real OneFactorCopula::conditionalProbability(Real p, Real m) const {
//-------------------------------------------------------------------------
calculate ();
// FIXME
if (p < 1e-10) return 0;
Real c = correlation_->value();
Real res = cumulativeZ ((inverseCumulativeY (p) - sqrt(c) * m)
/ sqrt (1. - c));
QL_REQUIRE (res >= 0 && res <= 1,
"conditional probability " << res << "out of range");
return res;
}
//-------------------------------------------------------------------------
vector<Real> OneFactorCopula::conditionalProbability(
const vector<Real>& prob,
Real m) const {
//-------------------------------------------------------------------------
calculate ();
vector<Real> p (prob.size(), 0);
for (Size i = 0; i < p.size(); i++)
p[i] = conditionalProbability (prob[i], m);
return p;
}
//-------------------------------------------------------------------------
Real OneFactorCopula::cumulativeY (Real y) const {
//-------------------------------------------------------------------------
calculate ();
QL_REQUIRE (y_.size() > 0, "cumulative Y not tabulated yet");
// linear interpolation on the tabulated cumulative distribution of Y
if (y < y_.front())
return cumulativeY_.front();
for (Size i = 0; i < y_.size(); i++) {
if (y_[i] > y)
return ( (y_[i] - y) * cumulativeY_[i-1]
+ (y - y_[i-1]) * cumulativeY_[i] )
/ (y_[i] - y_[i-1]);
}
return cumulativeY_.back();
}
//-------------------------------------------------------------------------
Real OneFactorCopula::inverseCumulativeY (Real x) const {
//-------------------------------------------------------------------------
calculate ();
QL_REQUIRE (y_.size() > 0, "cumulative Y not tabulated yet");
// linear interpolation on the tabulated cumulative distribution of Y
if (x < cumulativeY_.front())
return y_.front();
for (Size i = 0; i < cumulativeY_.size(); i++) {
if (cumulativeY_[i] > x)
return ( (cumulativeY_[i] - x) * y_[i-1]
+ (x - cumulativeY_[i-1]) * y_[i] )
/ (cumulativeY_[i] - cumulativeY_[i-1]);
}
return y_.back();
}
//-------------------------------------------------------------------------
int OneFactorCopula::checkMoments (Real tolerance) const {
//-------------------------------------------------------------------------
calculate ();
Real norm = 0, mean = 0, var = 0;
for (Size i = 0; i < steps(); i++) {
norm += densitydm (i);
mean += m(i) * densitydm (i);
var += pow (m(i), 2) * densitydm (i);
}
QL_REQUIRE (fabs (norm - 1.0) < tolerance, "norm out of tolerance range");
QL_REQUIRE (fabs (mean) < tolerance, "mean out of tolerance range");
QL_REQUIRE (fabs (var - 1.0) < tolerance, "variance out of tolerance range");
// FIXME: define range for Y via cutoff quantil?
Real zMin = -10;
Real zMax = +10;
Size zSteps = 200;
norm = 0;
mean = 0;
var = 0;
for (Size i = 1; i < zSteps; i++) {
Real z1 = zMin + (zMax - zMin) / zSteps * (i - 1);
Real z2 = zMin + (zMax - zMin) / zSteps * i;
Real z = (z1 + z2) / 2;
Real densitydz = cumulativeZ (z2) - cumulativeZ (z1);
norm += densitydz;
mean += z * densitydz;
var += pow (z, 2) * densitydz;
}
QL_REQUIRE (fabs (norm - 1.0) < tolerance, "norm out of tolerance range");
QL_REQUIRE (fabs (mean) < tolerance, "mean out of tolerance range");
QL_REQUIRE (fabs (var - 1.0) < tolerance, "variance out of tolerance range");
// FIXME: define range for Y via cutoff quantil?
Real yMin = -10;
Real yMax = +10;
Size ySteps = 200;
norm = 0;
mean = 0;
var = 0;
for (Size i = 1; i < ySteps; i++) {
Real y1 = yMin + (yMax - yMin) / ySteps * (i - 1);
Real y2 = yMin + (yMax - yMin) / ySteps * i;
Real y = (y1 + y2) / 2;
Real densitydy = cumulativeY (y2) - cumulativeY (y1);
norm += densitydy;
mean += y * densitydy;
var += y * y * densitydy;
}
QL_REQUIRE (fabs (norm - 1.0) < tolerance, "norm out of tolerance range");
QL_REQUIRE (fabs (mean) < tolerance, "mean out of tolerance range");
QL_REQUIRE (fabs (var - 1.0) < tolerance, "variance out of tolerance range");
return 0;
}
}
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