CVAIRS.cpp

This example shows how to calculate credit value adjustment for an interest rate swap.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2015 Jose Aparicio
 
 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/qldefines.hpp>
#if !defined(BOOST_ALL_NO_LIB) && defined(BOOST_MSVC)
#  include <ql/auto_link.hpp>
#endif
#include <ql/instruments/vanillaswap.hpp>
#include <ql/instruments/makevanillaswap.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/pricingengines/swap/cvaswapengine.hpp>
#include <ql/termstructures/yield/piecewiseyieldcurve.hpp>
#include <ql/termstructures/yield/ratehelpers.hpp>
#include <ql/termstructures/credit/interpolatedhazardratecurve.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/actual360.hpp>
 
#include <iostream>
#include <iomanip>
 
using namespace std;
using namespace QuantLib;
 
/*
  This example reproduces Table 2 on page 11 of 
  A Formula for Interest Rate Swaps Valuation under
  Counterparty Risk in presence of Netting Agreements
  
  Damiano Brigo and Massimo Masetti; May 4, 2005
 */
 
int main(int, char* []) {
 
    try {
 
        std::cout << std::endl;
 
        Calendar calendar = TARGET();
        Date todaysDate(10, March, 2004);
        // must be a business day
        todaysDate = calendar.adjust(todaysDate);
 
        Settings::instance().evaluationDate() = todaysDate;
 
        auto yieldIndx = ext::make_shared<Euribor3M>();
        Size tenorsSwapMkt[] = {5, 10, 15, 20, 25, 30};
        
        // rates ignoring counterparty risk:
        Rate ratesSwapmkt[] = {.03249, .04074, .04463, .04675, .04775, .04811};
 
        vector<ext::shared_ptr<RateHelper>> swapHelpers;
        for(Size i=0; i<sizeof(tenorsSwapMkt)/sizeof(Size); i++)
            swapHelpers.push_back(ext::make_shared<SwapRateHelper>(
                Handle<Quote>(ext::make_shared<SimpleQuote>(ratesSwapmkt[i])),
                    tenorsSwapMkt[i] * Years,
                    TARGET(),
                    Quarterly,
                    ModifiedFollowing,
                    ActualActual(ActualActual::ISDA),
                    yieldIndx));
 
        auto swapTS = ext::make_shared<PiecewiseYieldCurve<Discount, LogLinear>>(
             2, TARGET(), swapHelpers, ActualActual(ActualActual::ISDA));
        swapTS->enableExtrapolation();
 
        auto riskFreeEngine =  ext::make_shared<DiscountingSwapEngine>(
                 Handle<YieldTermStructure>(swapTS));
 
        std::vector<Handle<DefaultProbabilityTermStructure>>
            defaultIntensityTS;
        
        Size defaultTenors[] = {0, 12, 36, 60, 84, 120, 180, 240, 300, 
                                360};// months
        // Three risk levels:
        Real intensitiesLow[] = {0.0036, 0.0036, 0.0065, 0.0099, 0.0111, 
                                 0.0177, 0.0177, 0.0177, 0.0177, 0.0177, 
                                 0.0177};
        Real intensitiesMedium[] = {0.0202, 0.0202, 0.0231, 0.0266, 0.0278, 
                                    0.0349, 0.0349, 0.0349, 0.0349, 0.0349,
                                    0.0349};
        Real intensitiesHigh[] = {0.0534, 0.0534, 0.0564, 0.06, 0.0614, 0.0696,
                                  0.0696, 0.0696, 0.0696, 0.0696, 0.0696};
        // Recovery rates:
        Real ctptyRRLow = 0.4, ctptyRRMedium = 0.35, ctptyRRHigh = 0.3;
 
        std::vector<Date> defaultTSDates;
        std::vector<Real> intesitiesVLow, intesitiesVMedium, intesitiesVHigh;
 
        for(Size i=0; i<sizeof(defaultTenors)/sizeof(Size); i++) {
            defaultTSDates.push_back(TARGET().advance(todaysDate, 
                Period(defaultTenors[i], Months)));
            intesitiesVLow.push_back(intensitiesLow[i]);
            intesitiesVMedium.push_back(intensitiesMedium[i]);
            intesitiesVHigh.push_back(intensitiesHigh[i]);
        }
 
        defaultIntensityTS.emplace_back(
            ext::make_shared<InterpolatedHazardRateCurve<BackwardFlat>>(defaultTSDates, intesitiesVLow,
                                                          Actual360(), TARGET()));
        defaultIntensityTS.emplace_back(
            ext::make_shared<InterpolatedHazardRateCurve<BackwardFlat>>(defaultTSDates, intesitiesVMedium,
                                                          Actual360(), TARGET()));
        defaultIntensityTS.emplace_back(
            ext::make_shared<InterpolatedHazardRateCurve<BackwardFlat>>(defaultTSDates, intesitiesVHigh,
                                                          Actual360(), TARGET()));
 
        Volatility blackVol = 0.15;   
        auto ctptySwapCvaLow = ext::make_shared<CounterpartyAdjSwapEngine>(
                 Handle<YieldTermStructure>(swapTS), 
                 blackVol,
                 defaultIntensityTS[0], 
                 ctptyRRLow);
 
        auto ctptySwapCvaMedium = ext::make_shared<CounterpartyAdjSwapEngine>(
                 Handle<YieldTermStructure>(swapTS), 
                 blackVol, 
                 defaultIntensityTS[1],
                 ctptyRRMedium);
        auto ctptySwapCvaHigh = ext::make_shared<CounterpartyAdjSwapEngine>(
                 Handle<YieldTermStructure>(swapTS), 
                 blackVol,
                 defaultIntensityTS[2],
                 ctptyRRHigh);
        
        defaultIntensityTS[0]->enableExtrapolation();
        defaultIntensityTS[1]->enableExtrapolation();
        defaultIntensityTS[2]->enableExtrapolation();
 
 
 
        // fixed leg
        Frequency fixedLegFrequency = Quarterly;
        BusinessDayConvention fixedLegConvention = ModifiedFollowing;
        DayCounter fixedLegDayCounter = ActualActual(ActualActual::ISDA);
        DayCounter floatingLegDayCounter = ActualActual(ActualActual::ISDA);
 
        Swap::Type swapType = Swap::Payer;
        auto yieldIndxS = ext::make_shared<Euribor3M>(Handle<YieldTermStructure>(swapTS));
        std::vector<VanillaSwap> riskySwaps;
        for(Size i=0; i<sizeof(tenorsSwapMkt)/sizeof(Size); i++) 
            riskySwaps.push_back(MakeVanillaSwap(tenorsSwapMkt[i]*Years,
                yieldIndxS,
                ratesSwapmkt[i], 
                0*Days)
            .withSettlementDays(2)
            .withFixedLegDayCount(fixedLegDayCounter)
            .withFixedLegTenor(Period(fixedLegFrequency))
            .withFixedLegConvention(fixedLegConvention)
            .withFixedLegTerminationDateConvention(fixedLegConvention)
            .withFixedLegCalendar(calendar)
            .withFloatingLegCalendar(calendar)
            .withNominal(100.)
            .withType(swapType));
 
        cout << "-- Correction in the contract fix rate in bp --" << endl;
        /* The paper plots correction to be substracted, here is printed
           with its sign 
        */
        for(Size i=0; i<riskySwaps.size(); i++) {
            cout << fixed << setprecision(3);
            cout << setw(4);
            riskySwaps[i].setPricingEngine(riskFreeEngine);
            // should recover the input here:
            Real nonRiskyFair = riskySwaps[i].fairRate();
            cout << tenorsSwapMkt[i];
            cout << setw(5);
 
            cout << " | " << io::rate(nonRiskyFair);
            cout << fixed << setprecision(2);
            cout << setw(5);
            // Low Risk:
            riskySwaps[i].setPricingEngine(ctptySwapCvaLow);
            cout << " | " << setw(6) 
                 << 10000.*(riskySwaps[i].fairRate() - nonRiskyFair);
            //cout << " | " << setw(6) << riskySwaps[i].NPV() ;
 
            // Medium Risk:
            riskySwaps[i].setPricingEngine(ctptySwapCvaMedium);
            cout << " | " << setw(6) 
                 << 10000.*(riskySwaps[i].fairRate() - nonRiskyFair);
            //cout << " | " << setw(6) << riskySwaps[i].NPV() ;
 
            riskySwaps[i].setPricingEngine(ctptySwapCvaHigh);
            cout << " | " << setw(6) 
                 << 10000.*(riskySwaps[i].fairRate() - nonRiskyFair);
            //cout << " | " << setw(6) << riskySwaps[i].NPV() ;
 
            cout << endl;
        }
 
        cout << endl;
 
        return 0;
    } catch (exception& e) {
        cerr << e.what() << endl;
        return 1;
    } catch (...) {
        cerr << "unknown error" << endl;
        return 1;
    }
}