BermudanSwaption.cpp

This example prices a bermudan swaption using different models calibrated to market swaptions. The calibration examples include Hull and White's using both an analytic formula as well as numerically, and Black and Karasinski's model. Using these three calibrations, Bermudan swaptions are priced for at-the-money, out-of-the-money and in-the-money volatilities.

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

 
#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/swaption.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/pricingengines/swaption/treeswaptionengine.hpp>
#include <ql/pricingengines/swaption/jamshidianswaptionengine.hpp>
#include <ql/pricingengines/swaption/g2swaptionengine.hpp>
#include <ql/pricingengines/swaption/fdhullwhiteswaptionengine.hpp>
#include <ql/pricingengines/swaption/fdg2swaptionengine.hpp>
#include <ql/models/shortrate/calibrationhelpers/swaptionhelper.hpp>
#include <ql/models/shortrate/onefactormodels/blackkarasinski.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/cashflows/coupon.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/utilities/dataformatters.hpp>
 
#include <iostream>
#include <iomanip>
 
using namespace QuantLib;
 
//Number of swaptions to be calibrated to...
 
Size numRows = 5;
Size numCols = 5;
 
Integer swapLengths[] = {
      1,     2,     3,     4,     5};
Volatility swaptionVols[] = {
  0.1490, 0.1340, 0.1228, 0.1189, 0.1148,
  0.1290, 0.1201, 0.1146, 0.1108, 0.1040,
  0.1149, 0.1112, 0.1070, 0.1010, 0.0957,
  0.1047, 0.1021, 0.0980, 0.0951, 0.1270,
  0.1000, 0.0950, 0.0900, 0.1230, 0.1160};
 
void calibrateModel(
          const ext::shared_ptr<ShortRateModel>& model,
          const std::vector<ext::shared_ptr<BlackCalibrationHelper>>& swaptions) {
 
    std::vector<ext::shared_ptr<CalibrationHelper>> helpers(swaptions.begin(), swaptions.end());
    LevenbergMarquardt om;
    model->calibrate(helpers, om,
                     EndCriteria(400, 100, 1.0e-8, 1.0e-8, 1.0e-8));
 
    // Output the implied Black volatilities
    for (Size i=0; i<numRows; i++) {
        Size j = numCols - i -1; // 1x5, 2x4, 3x3, 4x2, 5x1
        Size k = i*numCols + j;
        Real npv = swaptions[i]->modelValue();
        Volatility implied = swaptions[i]->impliedVolatility(npv, 1e-4,
                                                             1000, 0.05, 0.50);
        Volatility diff = implied - swaptionVols[k];
 
        std::cout << i+1 << "x" << swapLengths[j]
                  << std::setprecision(5) << std::noshowpos
                  << ": model " << std::setw(7) << io::volatility(implied)
                  << ", market " << std::setw(7)
                  << io::volatility(swaptionVols[k])
                  << " (" << std::setw(7) << std::showpos
                  << io::volatility(diff) << std::noshowpos << ")\n";
    }
}
 
int main(int, char* []) {
 
    try {
 
        std::cout << std::endl;
 
        Date todaysDate(15, February, 2002);
        Calendar calendar = TARGET();
        Date settlementDate(19, February, 2002);
        Settings::instance().evaluationDate() = todaysDate;
 
        // flat yield term structure impling 1x5 swap at 5%
        auto flatRate = ext::make_shared<SimpleQuote>(0.04875825);
        Handle<YieldTermStructure> rhTermStructure(
            ext::make_shared<FlatForward>(
                      settlementDate, Handle<Quote>(flatRate),
                                      Actual365Fixed()));
 
        // Define the ATM/OTM/ITM swaps
        Frequency fixedLegFrequency = Annual;
        BusinessDayConvention fixedLegConvention = Unadjusted;
        BusinessDayConvention floatingLegConvention = ModifiedFollowing;
        DayCounter fixedLegDayCounter = Thirty360(Thirty360::European);
        Frequency floatingLegFrequency = Semiannual;
        Swap::Type type = Swap::Payer;
        Rate dummyFixedRate = 0.03;
        auto indexSixMonths = ext::make_shared<Euribor6M>(rhTermStructure);
 
        Date startDate = calendar.advance(settlementDate,1,Years,
                                          floatingLegConvention);
        Date maturity = calendar.advance(startDate,5,Years,
                                         floatingLegConvention);
        Schedule fixedSchedule(startDate,maturity,Period(fixedLegFrequency),
                               calendar,fixedLegConvention,fixedLegConvention,
                               DateGeneration::Forward,false);
        Schedule floatSchedule(startDate,maturity,Period(floatingLegFrequency),
                               calendar,floatingLegConvention,floatingLegConvention,
                               DateGeneration::Forward,false);
 
        auto swap = ext::make_shared<VanillaSwap>(
            type, 1000.0,
            fixedSchedule, dummyFixedRate, fixedLegDayCounter,
            floatSchedule, indexSixMonths, 0.0,
            indexSixMonths->dayCounter());
        swap->setPricingEngine(ext::make_shared<DiscountingSwapEngine>(rhTermStructure));
        Rate fixedATMRate = swap->fairRate();
        Rate fixedOTMRate = fixedATMRate * 1.2;
        Rate fixedITMRate = fixedATMRate * 0.8;
 
        auto atmSwap = ext::make_shared<VanillaSwap>(
            type, 1000.0,
            fixedSchedule, fixedATMRate, fixedLegDayCounter,
            floatSchedule, indexSixMonths, 0.0,
            indexSixMonths->dayCounter());
        auto otmSwap = ext::make_shared<VanillaSwap>(
            type, 1000.0,
            fixedSchedule, fixedOTMRate, fixedLegDayCounter,
            floatSchedule, indexSixMonths, 0.0,
            indexSixMonths->dayCounter());
        auto itmSwap = ext::make_shared<VanillaSwap>(
            type, 1000.0,
            fixedSchedule, fixedITMRate, fixedLegDayCounter,
            floatSchedule, indexSixMonths, 0.0,
            indexSixMonths->dayCounter());
 
        // defining the swaptions to be used in model calibration
        std::vector<Period> swaptionMaturities;
        swaptionMaturities.emplace_back(1, Years);
        swaptionMaturities.emplace_back(2, Years);
        swaptionMaturities.emplace_back(3, Years);
        swaptionMaturities.emplace_back(4, Years);
        swaptionMaturities.emplace_back(5, Years);
 
        std::vector<ext::shared_ptr<BlackCalibrationHelper>> swaptions;
 
        // List of times that have to be included in the timegrid
        std::list<Time> times;
 
        Size i;
        for (i=0; i<numRows; i++) {
            Size j = numCols - i -1; // 1x5, 2x4, 3x3, 4x2, 5x1
            Size k = i*numCols + j;
            auto vol = ext::make_shared<SimpleQuote>(swaptionVols[k]);
 
            swaptions.push_back(ext::make_shared<SwaptionHelper>(
                               swaptionMaturities[i],
                               Period(swapLengths[j], Years),
                               Handle<Quote>(vol),
                               indexSixMonths,
                               indexSixMonths->tenor(),
                               indexSixMonths->dayCounter(),
                               indexSixMonths->dayCounter(),
                               rhTermStructure));
 
            swaptions.back()->addTimesTo(times);
        }
 
        // Building time-grid
        TimeGrid grid(times.begin(), times.end(), 30);
 
 
        // defining the models
        auto modelG2 = ext::make_shared<G2>(rhTermStructure);
        auto modelHW = ext::make_shared<HullWhite>(rhTermStructure);
        auto modelHW2 = ext::make_shared<HullWhite>(rhTermStructure);
        auto modelBK = ext::make_shared<BlackKarasinski>(rhTermStructure);
 
 
        // model calibrations
 
        std::cout << "G2 (analytic formulae) calibration" << std::endl;
        for (i=0; i<swaptions.size(); i++)
            swaptions[i]->setPricingEngine(ext::make_shared<G2SwaptionEngine>(modelG2, 6.0, 16));
 
        calibrateModel(modelG2, swaptions);
        std::cout << "calibrated to:\n"
                  << "a     = " << modelG2->params()[0] << ", "
                  << "sigma = " << modelG2->params()[1] << "\n"
                  << "b     = " << modelG2->params()[2] << ", "
                  << "eta   = " << modelG2->params()[3] << "\n"
                  << "rho   = " << modelG2->params()[4]
                  << std::endl << std::endl;
 
 
 
        std::cout << "Hull-White (analytic formulae) calibration" << std::endl;
        for (i=0; i<swaptions.size(); i++)
            swaptions[i]->setPricingEngine(ext::make_shared<JamshidianSwaptionEngine>(modelHW));
 
        calibrateModel(modelHW, swaptions);
        std::cout << "calibrated to:\n"
                  << "a = " << modelHW->params()[0] << ", "
                  << "sigma = " << modelHW->params()[1]
                  << std::endl << std::endl;
 
        std::cout << "Hull-White (numerical) calibration" << std::endl;
        for (i=0; i<swaptions.size(); i++)
            swaptions[i]->setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW2, grid));
 
        calibrateModel(modelHW2, swaptions);
        std::cout << "calibrated to:\n"
                  << "a = " << modelHW2->params()[0] << ", "
                  << "sigma = " << modelHW2->params()[1]
                  << std::endl << std::endl;
 
        std::cout << "Black-Karasinski (numerical) calibration" << std::endl;
        for (i=0; i<swaptions.size(); i++)
            swaptions[i]->setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelBK, grid));
 
        calibrateModel(modelBK, swaptions);
        std::cout << "calibrated to:\n"
                  << "a = " << modelBK->params()[0] << ", "
                  << "sigma = " << modelBK->params()[1]
                  << std::endl << std::endl;
 
 
        // ATM Bermudan swaption pricing
 
        std::cout << "Payer bermudan swaption "
                  << "struck at " << io::rate(fixedATMRate)
                  << " (ATM)" << std::endl;
 
        std::vector<Date> bermudanDates;
        const std::vector<ext::shared_ptr<CashFlow>>& leg =
            swap->fixedLeg();
        for (i=0; i<leg.size(); i++) {
            auto coupon = ext::dynamic_pointer_cast<Coupon>(leg[i]);
            bermudanDates.push_back(coupon->accrualStartDate());
        }
 
        auto bermudanExercise = ext::make_shared<BermudanExercise>(bermudanDates);
 
        Swaption bermudanSwaption(atmSwap, bermudanExercise);
 
        // Do the pricing for each model
 
        // G2 price the European swaption here, it should switch to bermudan
        bermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelG2, 50));
        std::cout << "G2 (tree):      " << bermudanSwaption.NPV() << std::endl;
        bermudanSwaption.setPricingEngine(ext::make_shared<FdG2SwaptionEngine>(modelG2));
        std::cout << "G2 (fdm) :      " << bermudanSwaption.NPV() << std::endl;
 
        bermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW, 50));
        std::cout << "HW (tree):      " << bermudanSwaption.NPV() << std::endl;
        bermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW));
        std::cout << "HW (fdm) :      " << bermudanSwaption.NPV() << std::endl;
 
        bermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW2, 50));
        std::cout << "HW (num, tree): " << bermudanSwaption.NPV() << std::endl;
        bermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW2));
        std::cout << "HW (num, fdm) : " << bermudanSwaption.NPV() << std::endl;
 
        bermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelBK, 50));
        std::cout << "BK:             " << bermudanSwaption.NPV() << std::endl;
 
 
        // OTM Bermudan swaption pricing
 
        std::cout << "Payer bermudan swaption "
                  << "struck at " << io::rate(fixedOTMRate)
                  << " (OTM)" << std::endl;
 
        Swaption otmBermudanSwaption(otmSwap,bermudanExercise);
 
        // Do the pricing for each model
        otmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelG2, 300));
        std::cout << "G2 (tree):       " << otmBermudanSwaption.NPV()
                  << std::endl;
        otmBermudanSwaption.setPricingEngine(ext::make_shared<FdG2SwaptionEngine>(modelG2));
        std::cout << "G2 (fdm) :       " << otmBermudanSwaption.NPV()
                  << std::endl;
 
        otmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW, 50));
        std::cout << "HW (tree):       " << otmBermudanSwaption.NPV()
                  << std::endl;
        otmBermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW));
        std::cout << "HW (fdm) :       " << otmBermudanSwaption.NPV()
                  << std::endl;
 
        otmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW2, 50));
        std::cout << "HW (num, tree):  " << otmBermudanSwaption.NPV()
                  << std::endl;
        otmBermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW2));
        std::cout << "HW (num, fdm):   " << otmBermudanSwaption.NPV()
                  << std::endl;
 
        otmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelBK, 50));
        std::cout << "BK:              " << otmBermudanSwaption.NPV()
                  << std::endl;
 
 
        // ITM Bermudan swaption pricing
 
        std::cout << "Payer bermudan swaption "
                  << "struck at " << io::rate(fixedITMRate)
                  << " (ITM)" << std::endl;
 
        Swaption itmBermudanSwaption(itmSwap,bermudanExercise);
 
        // Do the pricing for each model
        itmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelG2, 50));
        std::cout << "G2 (tree):       " << itmBermudanSwaption.NPV()
                  << std::endl;
        itmBermudanSwaption.setPricingEngine(ext::make_shared<FdG2SwaptionEngine>(modelG2));
        std::cout << "G2 (fdm) :       " << itmBermudanSwaption.NPV()
                  << std::endl;
 
        itmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW, 50));
        std::cout << "HW (tree):       " << itmBermudanSwaption.NPV()
                  << std::endl;
        itmBermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW));
        std::cout << "HW (fdm) :       " << itmBermudanSwaption.NPV()
                  << std::endl;
 
        itmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelHW2, 50));
        std::cout << "HW (num, tree):  " << itmBermudanSwaption.NPV()
                  << std::endl;
        itmBermudanSwaption.setPricingEngine(ext::make_shared<FdHullWhiteSwaptionEngine>(modelHW2));
        std::cout << "HW (num, fdm) :  " << itmBermudanSwaption.NPV()
                  << std::endl;
 
        itmBermudanSwaption.setPricingEngine(ext::make_shared<TreeSwaptionEngine>(modelBK, 50));
        std::cout << "BK:              " << itmBermudanSwaption.NPV()
                  << std::endl;
 
        return 0;
    } catch (std::exception& e) {
        std::cerr << e.what() << std::endl;
        return 1;
    } catch (...) {
        std::cerr << "unknown error" << std::endl;
        return 1;
    }
}