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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/syntheticcdoengines.hpp>
#include <ql/experimental/credit/loss.hpp>
#include <ql/cashflows/fixedratecoupon.hpp>
#include <ql/time/daycounters/actualactual.hpp>
using namespace std;
namespace QuantLib {
//- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
void IntegralCDOEngine::calculate() const {
Date today = Settings::instance().evaluationDate();
const vector<Date>& dates = arguments_.schedule.dates();
results_.protectionValue = 0.0;
results_.premiumValue = 0.0;
results_.upfrontPremiumValue = 0.0;
results_.error = 0;
results_.expectedTrancheLoss.clear();
results_.expectedTrancheLoss.resize(dates.size(), 0.0);
// set remainingBasket_, results_.remainingNotional,
// vector results_.expectedTrancheLoss for all schedule dates
initialize();
Real e1 = 0;
if (arguments_.schedule.dates().front() > today)
e1 = expectedTrancheLoss (arguments_.schedule.dates()[0]);
for (Size i = 1; i < arguments_.schedule.size(); i++) {
Date d2 = arguments_.schedule.dates()[i];
if (d2 < today)
continue;
Date d1 = arguments_.schedule.dates()[i-1];
Date d, d0 = d1;
do {
d = NullCalendar().advance (d0 > today ? d0 : today,
stepSize_);
if (d > d2) d = d2;
Real e2 = expectedTrancheLoss (d);
results_.premiumValue
+= (results_.remainingNotional - e2)
* arguments_.runningRate
* arguments_.dayCounter.yearFraction (d0, d)
* arguments_.yieldTS->discount (d);
if (e2 < e1) results_.error ++;
results_.protectionValue
+= (e2 - e1) * arguments_.yieldTS->discount (d);
d0 = d;
e1 = e2;
}
while (d < d2);
}
if (arguments_.schedule.dates().front() >= today)
results_.upfrontPremiumValue
= results_.remainingNotional * arguments_.upfrontRate
* arguments_.yieldTS->discount(arguments_.schedule.dates()[0]);
if (arguments_.side == Protection::Buyer) {
results_.protectionValue *= -1;
results_.premiumValue *= -1;
results_.upfrontPremiumValue *= -1;
}
results_.value = results_.premiumValue - results_.protectionValue
+ results_.upfrontPremiumValue;
results_.errorEstimate = Null<Real>();
}
//- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
void MidPointCDOEngine::calculate() const {
Date today = Settings::instance().evaluationDate();
results_.premiumValue = 0.0;
results_.upfrontPremiumValue = 0.0;
results_.protectionValue = 0.0;
results_.expectedTrancheLoss.clear();
// set remainingBasket_, results_.remainingNotional,
// vector results_.expectedTrancheLoss for all schedule dates
initialize();
const vector<Date>& dates = arguments_.schedule.dates();
if (dates.front() > today)
results_.upfrontPremiumValue =
arguments_.upfrontRate * results_.remainingNotional;
vector<boost::shared_ptr<CashFlow> > premiumLeg =
FixedRateLeg(arguments_.schedule)
.withCouponRates(arguments_.runningRate, arguments_.dayCounter)
.withPaymentAdjustment(arguments_.paymentConvention)
.withNotionals(1.0);
Real e1 = 0;
if (dates[0] > today)
e1 = expectedTrancheLoss (dates[0]);
for (Size i = 0; i < premiumLeg.size(); i++) {
boost::shared_ptr<Coupon> coupon =
boost::dynamic_pointer_cast<Coupon>(premiumLeg[i]);
Date paymentDate = coupon->date();
Date startDate = std::max(coupon->accrualStartDate(),
arguments_.yieldTS->referenceDate());
Date endDate = coupon->accrualEndDate();
Date defaultDate = startDate + (endDate-startDate)/2;
if (paymentDate <= today)
continue;
Real e2 = expectedTrancheLoss(paymentDate);
results_.premiumValue += (results_.remainingNotional - e2)
* coupon->amount()
* arguments_.yieldTS->discount(paymentDate);
Real discount = arguments_.yieldTS->discount(defaultDate);
results_.premiumValue += coupon->accruedAmount(defaultDate)
* discount * (e2 - e1);
results_.protectionValue += discount * (e2 - e1);
e1 = e2;
}
if (arguments_.side == Protection::Buyer) {
results_.protectionValue *= -1;
results_.premiumValue *= -1;
results_.upfrontPremiumValue *= -1;
}
results_.value = results_.premiumValue - results_.protectionValue
+ results_.upfrontPremiumValue;
results_.errorEstimate = Null<Real>();
}
//- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
void MonteCarloCDOEngine1::defaultScenarios() const {
results_.expectedTrancheLoss.clear();
const vector<Date>& dates = arguments_.schedule.dates();
Date today = Settings::instance().evaluationDate();
Real tmax = ActualActual().yearFraction(today, dates.back());
QL_REQUIRE(tmax >= 0, "tmax < 0");
/*
1) Generate a vector of random default times in the single-factor
Gaussian Copula framework
2) Work out cumulative portfolio and tranche loss for each scenario
3) Map cumulative tranche losses to schedule dates
4) Average over many scenarios
*/
const boost::shared_ptr<Pool> pool = remainingBasket_->pool();
vector<vector<Real> > cumulativeTrancheLoss(samples_, vector<Real>());
results_.expectedTrancheLoss.resize(dates.size(), 0.0);
for (Size i = 0; i < samples_; i++) {
rdm_->nextSequence(tmax);
cumulativeTrancheLoss[i].resize(dates.size(), 0.0);
remainingBasket_->updateScenarioLoss();
for (Size k = 0; k < dates.size(); k++) {
cumulativeTrancheLoss[i][k]
= remainingBasket_->scenarioTrancheLoss(dates[k]);
// aggregate
results_.expectedTrancheLoss[k] += cumulativeTrancheLoss[i][k];
}
}
// normalize
for (Size i = 0; i < dates.size(); i++)
results_.expectedTrancheLoss[i] /= samples_;
}
//- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
void MonteCarloCDOEngine2::calculate() const {
Date today = Settings::instance().evaluationDate();
results_.protectionValue = 0.0;
results_.premiumValue = 0.0;
results_.expectedTrancheLoss.clear();
// set remainingBasket_, results_.remainingNotional,
initialize();
const vector<Date>& dates = arguments_.schedule.dates();
if (dates.front() > today)
results_.upfrontPremiumValue =
arguments_.upfrontRate * results_.remainingNotional;
Real tmax = ActualActual().yearFraction(today, dates.back());
//Real tmin = ActualActual().yearFraction(today, dates.front());
QL_REQUIRE(tmax >= 0, "tmax < 0");
vector<boost::shared_ptr<CashFlow> > premiumLeg =
FixedRateLeg(arguments_.schedule)
.withNotionals(1.0)
.withCouponRates(arguments_.runningRate, arguments_.dayCounter)
.withPaymentAdjustment(arguments_.paymentConvention);
boost::shared_ptr<Pool> pool = remainingBasket_->pool();
vector<Real> premiumValue(samples_, 0.0);
vector<Real> protectionValue(samples_, 0.0);
vector<Real> value(samples_, 0.0);
vector<Real> fairPremium(samples_, 0.0);
vector<vector<Real> > cumulativeTrancheLoss(samples_, vector<Real>());
for (Size i = 0; i < samples_; i++) { //================================
/******************************************************************
* (1) Compute default times
******************************************************************/
rdm_->nextSequence(tmax);
/******************************************************************
* (2) Cumulative tranche loss to schedule dates
******************************************************************/
cumulativeTrancheLoss[i].resize(dates.size(), 0.0);
remainingBasket_->updateScenarioLoss();
for (Size k = 0; k < dates.size(); k++)
cumulativeTrancheLoss[i][k]
= remainingBasket_->scenarioTrancheLoss(dates[k]);
/*****************************************************************
* (3) Contribution of this scenario to the protection leg
* - Loop through all incremental tranche loss events between
* start and end date
* - Pay and discount these increments as they occur
*****************************************************************/
vector<Loss> increments = remainingBasket_->scenarioIncrementalTrancheLosses(dates.front(), dates.back());
for (Size k = 0; k < increments.size(); k++)
protectionValue[i] += increments[k].amount
* arguments_.yieldTS->discount(increments[k].time);
/*****************************************************************
* (4) Contribution of this scenario to the premium leg
* - Loop through all coupon periods
* - Pay coupon at period end on effective notional
* - Effective notional:
* - Start with remaining notional minus cumulative loss
* on the tranche until period start =: N
* - Reduce N for each loss in the period by subtracting the
* the incremental tranche loss weighted with the time
* to period end
*****************************************************************/
for (Size j = 0; j < premiumLeg.size(); j++) {
boost::shared_ptr<Coupon> coupon =
boost::dynamic_pointer_cast<Coupon>(premiumLeg[j]);
Date startDate = std::max(coupon->accrualStartDate(),
arguments_.yieldTS->referenceDate());
Date endDate = coupon->accrualEndDate();
Date paymentDate = coupon->date();
if (paymentDate <= today)
continue;
Real t1 = ActualActual().yearFraction(today, startDate);
Real t2 = ActualActual().yearFraction(today, endDate);
Real PL = cumulativeTrancheLoss[i][j];
Real N = results_.remainingNotional - PL;
for (Size k = 0; k < increments.size(); k++) {
Real t = increments[k].time;
if (t <= t1) continue;
if (t >= t2) break;
N -= (t2-t) / (t2-t1) * increments[k].amount;
}
Real discount = arguments_.yieldTS->discount(paymentDate);
premiumValue[i] += N * coupon->amount() * discount;
}
/*****************
* Aggregate
*****************/
results_.premiumValue += premiumValue[i];
results_.protectionValue += protectionValue[i];
value[i] = premiumValue[i] - protectionValue[i]
+ results_.upfrontPremiumValue;
for (Size k = 0; k < dates.size(); k++)
results_.expectedTrancheLoss[k] += cumulativeTrancheLoss[i][k];
/*
cout.setf (ios::fixed, ios::floatfield);
cout << setprecision(0);
for (Size k = 0; k < dates.size(); k++)
cout << setw(3) << cumulativeTrancheLoss[i][k] << " ";
cout << endl;
cout << setprecision(2);
for (Size k = 0; k < pool->size(); k++) {
const string name = pool->names()[k];
Real t = pool->getTime(name);
if (t < 6)
cout << setw(10) << name << " " << setw(5) << t << endl;
}
*/
} // end of loop over samples ==========================================
/*****************************************
* Expected values, normalize, switch sign
*****************************************/
results_.premiumValue /= samples_;
results_.protectionValue /= samples_;
for (Size k = 0; k < dates.size(); k++)
results_.expectedTrancheLoss[k] /= samples_;
if (arguments_.side == Protection::Buyer) {
results_.protectionValue *= -1;
results_.premiumValue *= -1;
results_.upfrontPremiumValue *= -1;
}
results_.value = results_.premiumValue - results_.protectionValue
+ results_.upfrontPremiumValue;
/*************************************************
* Error estimates - NPV
*************************************************/
Real avg = 0.0;
Real var = 0.0;
for (Size i = 0; i < samples_; i++) {
var += value[i] * value[i];
avg += value[i];
}
avg /= samples_;
var /= samples_;
results_.errorEstimate = sqrt(var - avg * avg);
/*****************************************************
* Error estimates - fair premium
* http://math.nyu.edu/~atm262/files/spring06/ircm/cdo
*****************************************************/
/*
Real x = 0.0, xx = 0.0, y = 0.0, yy = 0.0, xy = 0.0;
for (Size i = 0; i < samples_; i++) {
Real dx = protectionValue[i] - results_.upfrontPremiumValue;
Real dy = premiumValue[i];
x += dx;
xx += dx * dx;
y += dy;
yy += dy * dy;
xy += dx * dy;
}
x /= samples_;
y /= samples_;
xx /= samples_;
yy /= samples_;
xy /= samples_;
Real v = x*x/(y*y) * (xx/(x*x) + yy/(y*y) - 2.0 * xy/(x*y));
Real stdFairPremium = sqrt(v) * arguments_.runningRate;
*/
}
}
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