| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
| 2 | |
| 3 | /* |
| 4 | Copyright (C) 2008 Roland Lichters |
| 5 | |
| 6 | This file is part of QuantLib, a free-software/open-source library |
| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
| 8 | |
| 9 | QuantLib is free software: you can redistribute it and/or modify it |
| 10 | under the terms of the QuantLib license. You should have received a |
| 11 | copy of the license along with this program; if not, please email |
| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
| 13 | <http://quantlib.org/license.shtml>. |
| 14 | |
| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
| 18 | */ |
| 19 | |
| 20 | #include <ql/event.hpp> |
| 21 | #include <ql/experimental/credit/cdo.hpp> |
| 22 | #include <utility> |
| 23 | |
| 24 | using namespace std; |
| 25 | |
| 26 | namespace QuantLib { |
| 27 | |
| 28 | CDO::CDO(Real attachment, |
| 29 | Real detachment, |
| 30 | vector<Real> nominals, |
| 31 | const vector<Handle<DefaultProbabilityTermStructure> >& basket, |
| 32 | Handle<OneFactorCopula> copula, |
| 33 | bool protectionSeller, |
| 34 | Schedule premiumSchedule, |
| 35 | Rate premiumRate, |
| 36 | DayCounter dayCounter, |
| 37 | Rate recoveryRate, |
| 38 | Rate upfrontPremiumRate, |
| 39 | Handle<YieldTermStructure> yieldTS, |
| 40 | Size nBuckets, |
| 41 | const Period& integrationStep) |
| 42 | : attachment_(attachment), detachment_(detachment), nominals_(std::move(nominals)), |
| 43 | basket_(basket), copula_(std::move(copula)), protectionSeller_(protectionSeller), |
| 44 | premiumSchedule_(std::move(premiumSchedule)), premiumRate_(premiumRate), |
| 45 | dayCounter_(std::move(dayCounter)), recoveryRate_(recoveryRate), |
| 46 | upfrontPremiumRate_(upfrontPremiumRate), yieldTS_(std::move(yieldTS)), nBuckets_(nBuckets), |
| 47 | integrationStep_(integrationStep) { |
| 48 | |
| 49 | QL_REQUIRE (!basket.empty(), "basket is empty" ); |
| 50 | QL_REQUIRE (attachment_ >= 0 && attachment_ < detachment_ |
| 51 | && detachment_ <= 1, |
| 52 | "illegal attachment/detachment point" ); |
| 53 | |
| 54 | registerWith (h: yieldTS_); |
| 55 | registerWith (h: copula_); |
| 56 | for (auto& i : basket_) |
| 57 | registerWith(h: i); |
| 58 | |
| 59 | QL_REQUIRE (nominals_.size() <= basket_.size(), |
| 60 | "nominal vector size too large" ); |
| 61 | |
| 62 | if (nominals_.size() < basket_.size()) { |
| 63 | Size n = basket_.size() - nominals_.size(); |
| 64 | Real back = nominals_.back(); |
| 65 | for (Size i = 0; i < n; i++) |
| 66 | nominals_.push_back(x: back); |
| 67 | } |
| 68 | |
| 69 | QL_REQUIRE (nominals_.size() == basket_.size(), |
| 70 | "nominal size " << nominals_.size() |
| 71 | << " != basket size " << basket_.size()); |
| 72 | |
| 73 | nominal_ = 0; |
| 74 | for (Size i = 0; i < nominals_.size(); i++) { |
| 75 | lgds_.push_back (x: nominals_[i] * (1.0 - recoveryRate_)); |
| 76 | nominal_ += nominals_[i]; |
| 77 | lgd_ += lgds_[i]; |
| 78 | } |
| 79 | xMax_ = detachment_ * nominal_; |
| 80 | xMin_ = attachment_ * nominal_; |
| 81 | } |
| 82 | |
| 83 | |
| 84 | bool CDO::isExpired () const { |
| 85 | return detail::simple_event(premiumSchedule_.dates().back()) |
| 86 | .hasOccurred(refDate: yieldTS_->referenceDate()); |
| 87 | } |
| 88 | |
| 89 | |
| 90 | void CDO::setupExpired() const { |
| 91 | Instrument::setupExpired(); |
| 92 | } |
| 93 | |
| 94 | |
| 95 | Real CDO::expectedTrancheLoss (Date d) const { |
| 96 | if (d <= basket_.front()->referenceDate()) |
| 97 | return 0; |
| 98 | |
| 99 | vector<Real> defProb (basket_.size()); |
| 100 | for (Size j = 0; j < basket_.size(); j++) |
| 101 | defProb[j] = basket_[j]->defaultProbability (d); |
| 102 | |
| 103 | LossDistBucketing op (nBuckets_, xMax_); |
| 104 | Distribution dist = copula_->integral (f: op, nominals: lgds_, probabilities: defProb); |
| 105 | |
| 106 | return dist.trancheExpectedValue (a: xMin_, d: xMax_); |
| 107 | |
| 108 | // The following causes two errors in test against literature values. |
| 109 | // FIXME: Investigate accuracy. |
| 110 | // return dist.cumulativeExcessProbability (xMin_, xMax_); |
| 111 | |
| 112 | // TranchePayoff func (xMin_, xMax_); |
| 113 | // return (dist.expectedValue (func) |
| 114 | // + (xMax_ - xMin_) * (1.0 - dist.cumulatedProbability (xMax_))); |
| 115 | } |
| 116 | |
| 117 | |
| 118 | void CDO::performCalculations() const { |
| 119 | |
| 120 | QL_REQUIRE(!yieldTS_.empty(), "no yield term structure set" ); |
| 121 | |
| 122 | errorEstimate_ = Null<Real>(); |
| 123 | |
| 124 | NPV_ = 0.0; |
| 125 | premiumValue_ = 0; |
| 126 | protectionValue_ = 0; |
| 127 | error_ = 0; |
| 128 | |
| 129 | /* Expectations e1 and e2 are portfolio loss given default, |
| 130 | i.e. with recovery already "bult in". Multiplication by |
| 131 | (1-r) is therefore not necessary, neither in premium nor |
| 132 | protection value calculation. |
| 133 | */ |
| 134 | |
| 135 | Real e1 = 0; |
| 136 | Date today = yieldTS_->referenceDate(); |
| 137 | if (premiumSchedule_[0] > today) |
| 138 | e1 = expectedTrancheLoss (d: premiumSchedule_[0]); |
| 139 | |
| 140 | for (Size i = 1; i < premiumSchedule_.size(); i++) { |
| 141 | Date d2 = premiumSchedule_[i]; |
| 142 | if (d2 < today) |
| 143 | continue; |
| 144 | |
| 145 | Date d1 = premiumSchedule_[i-1]; |
| 146 | |
| 147 | Date d, d0 = d1; |
| 148 | do { |
| 149 | d = NullCalendar().advance (date: d0 > today ? d0 : today, |
| 150 | period: integrationStep_); |
| 151 | if (d > d2) |
| 152 | d = d2; |
| 153 | |
| 154 | Real e2 = expectedTrancheLoss (d); |
| 155 | |
| 156 | premiumValue_ += (xMax_ - xMin_ - e2) |
| 157 | * premiumRate_ * dayCounter_.yearFraction (d1: d0, d2: d) |
| 158 | * yieldTS_->discount (d); |
| 159 | |
| 160 | if (e2 < e1) { |
| 161 | error_ ++; |
| 162 | } |
| 163 | |
| 164 | protectionValue_ -= (e2 - e1) * yieldTS_->discount (d); |
| 165 | |
| 166 | d0 = d; |
| 167 | e1 = e2; |
| 168 | } |
| 169 | while (d < d2); |
| 170 | } |
| 171 | |
| 172 | if (premiumSchedule_[0] >= today) |
| 173 | upfrontPremiumValue_ = (xMax_ - xMin_) * upfrontPremiumRate_ * |
| 174 | yieldTS_->discount(d: premiumSchedule_[0]); |
| 175 | else |
| 176 | upfrontPremiumValue_ = 0.0; |
| 177 | |
| 178 | if (!protectionSeller_) { |
| 179 | premiumValue_ *= -1; |
| 180 | upfrontPremiumValue_ *= -1; |
| 181 | protectionValue_ *= -1; |
| 182 | } |
| 183 | |
| 184 | NPV_ = premiumValue_ + protectionValue_ + upfrontPremiumValue_; |
| 185 | } |
| 186 | |
| 187 | |
| 188 | Rate CDO::premiumValue () const { |
| 189 | calculate(); |
| 190 | return premiumValue_; |
| 191 | } |
| 192 | |
| 193 | Rate CDO::protectionValue () const { |
| 194 | calculate(); |
| 195 | return protectionValue_; |
| 196 | } |
| 197 | |
| 198 | Size CDO::error () const { |
| 199 | calculate(); |
| 200 | return error_; |
| 201 | } |
| 202 | |
| 203 | Rate CDO::fairPremium () const { |
| 204 | calculate(); |
| 205 | return - premiumRate_ * protectionValue_ / premiumValue_; |
| 206 | } |
| 207 | |
| 208 | } |
| 209 | |