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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012, 2013 Grzegorz Andruszkiewicz
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/catbonds/catrisk.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <boost/make_shared.hpp>
namespace QuantLib {
namespace {
Integer round(Real r) {
return (r > 0.0) ? Integer(floor(r + 0.5)) : Integer(ceil(r - 0.5));
}
}
EventSetSimulation::EventSetSimulation(boost::shared_ptr<std::vector<std::pair<Date, Real> > > events,
Date eventsStart,
Date eventsEnd,
Date start,
Date end)
: CatSimulation(start, end), events_(events), eventsStart_(eventsStart), eventsEnd_(eventsEnd), i_(0) {
years_ = end_.year()-start_.year();
if(eventsStart_.month()<start_.month()
|| (eventsStart_.month()==start_.month()
&& eventsStart_.dayOfMonth()<=start_.dayOfMonth())) {
periodStart_ = Date(start_.dayOfMonth(), start_.month(), eventsStart_.year());
} else {
periodStart_ = Date(start_.dayOfMonth(), start_.month(), eventsStart_.year()+1);
}
periodEnd_ = Date(end_.dayOfMonth(), end_.month(), periodStart_.year()+years_);
while(i_<events_->size() && (*events_)[i_].first<periodStart_) ++i_; //i points to the first element after the start of the relevant period.
}
bool EventSetSimulation::nextPath(std::vector< std::pair< Date, Real > >& path) {
path.resize(0);
if(periodEnd_>eventsEnd_) //Ran out of event data
return false;
while(i_<events_->size() && (*events_)[i_].first<periodStart_) {
++i_; //skip the elements between the previous period and this period
}
while(i_<events_->size() && (*events_)[i_].first<=periodEnd_){
std::pair<Date, Real> e(events_->at(i_).first+(start_.year() - periodStart_.year())*Years, events_->at(i_).second);
path.push_back(e);
++i_; //i points to the first element after the start of the relevant period.
}
if(start_+years_*Years<end_) {
periodStart_+=(years_+1)*Years;
periodEnd_+=(years_+1)*Years;
} else {
periodStart_+=years_*Years;
periodEnd_+=years_*Years;
}
return true;
}
EventSet::EventSet(boost::shared_ptr<std::vector<std::pair<Date, Real> > > events,
Date eventsStart,
Date eventsEnd)
: events_(events), eventsStart_(eventsStart), eventsEnd_(eventsEnd) {};
boost::shared_ptr<CatSimulation> EventSet::newSimulation(const Date& start, const Date& end) const{
return boost::make_shared<EventSetSimulation>(events_, eventsStart_, eventsEnd_, start, end);
}
BetaRiskSimulation::BetaRiskSimulation(Date start, Date end, Real maxLoss, Real lambda, Real alpha, Real beta)
: CatSimulation(start, end),
maxLoss_(maxLoss),
exponential_(rng_, boost::exponential_distribution<>(lambda)),
gammaAlpha_(rng_, boost::gamma_distribution<>(alpha)),
gammaBeta_(rng_, boost::gamma_distribution<>(beta))
{
ActualActual dayCounter;
dayCount_ = dayCounter.dayCount(start, end);
yearFraction_ = dayCounter.yearFraction(start, end);
}
Real BetaRiskSimulation::generateBeta()
{
Real X = gammaAlpha_();
Real Y = gammaBeta_();
return X*maxLoss_/(X+Y);
}
bool BetaRiskSimulation::nextPath(std::vector<std::pair<Date, Real> > &path)
{
path.resize(0);
Real eventFraction = exponential_();
while(eventFraction<=yearFraction_)
{
Integer days = round(eventFraction*dayCount_/yearFraction_);
Date eventDate = start_ + days*Days;
if(eventDate<=end_)
{
path.push_back(std::pair<Date, Real> (eventDate, generateBeta()));
}
else break;
eventFraction = exponential_();
}
return true;
}
BetaRisk::BetaRisk(Real maxLoss,
Real years,
Real mean,
Real stdDev)
: maxLoss_(maxLoss), lambda_(1.0/years) {
QL_REQUIRE(mean<maxLoss, "Mean "<<mean<<"of the loss distribution must be less than the maximum loss "<<maxLoss);
Real normalizedMean = mean/maxLoss;
Real normalizedVar = stdDev*stdDev/(maxLoss*maxLoss);
QL_REQUIRE(normalizedVar<normalizedMean*(1.0-normalizedMean), "Standard deviation of "<<stdDev<<" is impossible to achieve in gamma distribution with mean "<<mean);
Real nu = normalizedMean*(1.0-normalizedMean)/normalizedVar - 1.0;
alpha_=normalizedMean*nu;
beta_=(1.0-normalizedMean)*nu;
}
boost::shared_ptr<CatSimulation> BetaRisk::newSimulation(const Date& start, const Date& end) const {
return boost::make_shared<BetaRiskSimulation>(start, end, maxLoss_, lambda_, alpha_, beta_);
}
}
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