//--------------------------------------------------------------------------
Distribution LossDistBinomial::operator()(Size n, Real volume,
Real probability) const {
//--------------------------------------------------------------------------
n_ = n;
probability_.clear();
probability_.resize(n_+1, 0.0);
Distribution dist (nBuckets_, 0.0, maximum_);
BinomialDistribution binomial (probability, n);
for (Size i = 0; i <= n; i++) {
if (volume_ * i <= maximum_) {
probability_[i] = binomial(i);
Size bucket = dist.locate(volume * i);
dist.addDensity (bucket, probability_[i] / dist.dx(bucket));
dist.addAverage (bucket, volume * i);
}
}
excessProbability_.clear();
excessProbability_.resize(n_+1, 0.0);
excessProbability_[n_] = probability_[n_];
for (int k = n_-1; k >= 0; k--)
excessProbability_[k] = excessProbability_[k+1] + probability_[k];
dist.normalize();
return dist;
}
//--------------------------------------------------------------------------
Distribution LossDistHomogeneous::operator()(Real volume,
const vector<Real>& p) const {
//--------------------------------------------------------------------------
volume_ = volume;
n_ = p.size();
probability_.clear();
probability_.resize(n_+1, 0.0);
vector<Real> prev;
probability_[0] = 1.0;
for (Size k = 0; k < n_; k++) {
prev = probability_;
probability_[0] = prev[0] * (1.0 - p[k]);
for (Size i = 1; i <= k; i++)
probability_[i] = prev[i-1] * p[k] + prev[i] * (1.0 - p[k]);
probability_[k+1] = prev[k] * p[k];
}
excessProbability_.clear();
excessProbability_.resize(n_+1, 0.0);
excessProbability_[n_] = probability_[n_];
for (int k = n_ - 1; k >= 0; k--)
excessProbability_[k] = excessProbability_[k+1] + probability_[k];
Distribution dist (nBuckets_, 0.0, maximum_);
for (Size i = 0; i <= n_; i++) {
if (volume * i <= maximum_) {
Size bucket = dist.locate(volume * i);
dist.addDensity (bucket, probability_[i] / dist.dx(bucket));
dist.addAverage (bucket, volume*i);
}
}
dist.normalize();
return dist;
}
//--------------------------------------------------------------------------
Distribution LossDistBucketing::operator()(const vector<Real>& nominals,
const vector<Real>& probabilities) const {
//--------------------------------------------------------------------------
QL_REQUIRE (nominals.size() == probabilities.size(), "sizes differ: "
<< nominals.size() << " vs " << probabilities.size());
vector<Real> p (nBuckets_, 0.0);
vector<Real> a (nBuckets_, 0.0);
vector<Real> ap (nBuckets_, 0.0);
p[0] = 1.0;
a[0] = 0.0;
Real dx = maximum_ / nBuckets_;
for (Size k = 1; k < nBuckets_; k++)
a[k] = dx * k + dx/2;
for (Size i = 0; i < nominals.size(); i++) {
Real L = nominals[i];
Real P = probabilities[i];
for (int k = a.size()-1; k >= 0; k--) {
if (p[k] > 0) {
int u = locateTargetBucket (a[k] + L, k);
QL_REQUIRE (u >= 0, "u=" << u << " at i=" << i << " k=" << k);
QL_REQUIRE (u >= k, "u=" << u << "<k=" << k << " at i=" << i);
Real dp = p[k] * P;
if (u == k)
a[k] += P * L;
else {
// no update of a[u] and p[u] if u is beyond grid end
if (u < int(nBuckets_)) {
// a[u] remains unchanged, if dp = 0
if (dp > 0.0) {
// on Windows, p[u]/dp could cause a NaN for
// some very small values of p[k].
// Writing the above as (p[u]/p[k])/P prevents
// the NaN. What can I say?
Real f = 1.0 / (1.0 + (p[u]/p[k]) / P);
a[u] = (1.0 - f) * a[u] + f * (a[k] + L);
}
/* formulation of Hull-White:
if (p[u] + dp > 0)
a[u] = (p[u] * a[u] + dp * (a[k] + L))
/ (p[u] + dp);
*/
p[u] += dp;
}
p[k] -= dp;
}
}
QL_REQUIRE(a[k] + epsilon_ >= dx * k && a[k] < dx * (k+1),
"a out of range at k=" << k << ", contract " << i);
}
}
Distribution dist (nBuckets_, 0.0, maximum_);
for (Size i = 0; i < nBuckets_; i++) {
dist.addDensity (i, p[i] / dx);
dist.addAverage (i, a[i]);
}
return dist;
}