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【C++】开源：量化金融计算库QuantLib配置与使用

news 来源：原创 2024/7/6 1:22:16

😏★,°:.☆(￣▽￣)/$:.°★ 😏
这篇文章主要介绍量化交易库QuantLib配置与使用。
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文章目录

- :smirk:1. 项目介绍
- :blush:2. 环境配置
- :satisfied:3. 使用说明

😏1. 项目介绍

官网：https://www.quantlib.org/

项目Github地址：https://github.com/lballabio/QuantLib

QuantLib（Quantitative Finance Library）是一个开源的跨平台软件框架，专为量化金融领域设计和开发。它提供了丰富的金融工具和计算功能，用于衍生品定价、风险管理、投资组合管理等多个领域。以下是关于QuantLib的一些主要特点和用途：

1.开源跨平台：QuantLib是完全开源的，可以在不同操作系统上运行，包括Windows、Linux和Mac OS X。这使得它成为量化金融研究和开发的理想工具，能够在不同的环境中使用和定制。

2.丰富的金融工具：QuantLib支持多种金融工具和衍生品的定价和分析，包括利率衍生品（如利率互换、利率期权）、股票衍生品（如期权）、信用衍生品（如信用违约掉期）、外汇衍生品等。

3.数值方法和模型支持：QuantLib提供了广泛的数值方法和模型，用于衍生品定价和风险管理，如蒙特卡洛模拟、有限差分法、解析方法等。它支持的模型包括Black-Scholes模型、Heston模型、Libor Market Model等。

4.投资组合和风险管理：QuantLib能够处理复杂的投资组合和风险管理需求，包括风险测度、对冲分析、压力测试等，为金融机构和量化交易员提供重要的决策支持工具。

5.易于集成和扩展：QuantLib的设计允许用户根据特定需求进行定制和扩展，通过C++编程接口提供了灵活的扩展性，同时也支持Python等编程语言的接口，使得QuantLib能够与其他系统和库集成使用。

😊2. 环境配置

Ubuntu环境安装QuantLib库：

git clone https://github.com/lballabio/QuantLib # 或者下载release版本 1.34
mkdir build && cd build
cmake ..
make
sudo make install

程序g++编译：g++ -o main main.cpp -lQuantLib

😆3. 使用说明

下面是一个简单示例，计算零息债券的定价：

#include <ql/quantlib.hpp>
#include <iostream>using namespace QuantLib;int main() {// 设置评估日期Date today = Date::todaysDate();Settings::instance().evaluationDate() = today;// 定义债券参数Real faceAmount = 1000.0; // 债券面值Rate couponRate = 0.05; // 年利率Date maturity = today + Period(1, Years); // 到期时间// 创建收益率曲线Rate marketRate = 0.03; // 市场利率Handle<YieldTermStructure> discountCurve(boost::shared_ptr<YieldTermStructure>(new FlatForward(today, marketRate, Actual360())));// 创建零息债券ZeroCouponBond bond(0, NullCalendar(), faceAmount, maturity, Following, 100.0, today);// 创建定价引擎并设置参数bond.setPricingEngine(boost::shared_ptr<PricingEngine>(new DiscountingBondEngine(discountCurve)));// 计算债券价格Real bondPrice = bond.NPV();std::cout << "Zero-coupon bond price: " << bondPrice << std::endl;return 0;
}

此外，还有官方示例里的BasketLosses 计算一组金融资产损失示例（看起来还是很复杂的）：

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- *//*!
Copyright (C) 2009 Mark JoshiThis 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/models/marketmodels/marketmodel.hpp>
#include <ql/models/marketmodels/accountingengine.hpp>
#include <ql/models/marketmodels/pathwiseaccountingengine.hpp>
#include <ql/models/marketmodels/products/multiproductcomposite.hpp>
#include <ql/models/marketmodels/products/multistep/multistepswap.hpp>
#include <ql/models/marketmodels/products/multistep/callspecifiedmultiproduct.hpp>
#include <ql/models/marketmodels/products/multistep/exerciseadapter.hpp>
#include <ql/models/marketmodels/products/multistep/multistepnothing.hpp>
#include <ql/models/marketmodels/products/multistep/multistepinversefloater.hpp>
#include <ql/models/marketmodels/products/pathwise/pathwiseproductswap.hpp>
#include <ql/models/marketmodels/products/pathwise/pathwiseproductinversefloater.hpp>
#include <ql/models/marketmodels/products/pathwise/pathwiseproductcallspecified.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/models/marketmodels/callability/swapratetrigger.hpp>
#include <ql/models/marketmodels/callability/swapbasissystem.hpp>
#include <ql/models/marketmodels/callability/swapforwardbasissystem.hpp>
#include <ql/models/marketmodels/callability/nothingexercisevalue.hpp>
#include <ql/models/marketmodels/callability/collectnodedata.hpp>
#include <ql/models/marketmodels/callability/lsstrategy.hpp>
#include <ql/models/marketmodels/callability/upperboundengine.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/models/marketmodels/browniangenerators/mtbrowniangenerator.hpp>
#include <ql/models/marketmodels/browniangenerators/sobolbrowniangenerator.hpp>
#include <ql/models/marketmodels/evolvers/lognormalfwdratepc.hpp>
#include <ql/models/marketmodels/evolvers/lognormalfwdrateeuler.hpp>
#include <ql/models/marketmodels/pathwisegreeks/bumpinstrumentjacobian.hpp>
#include <ql/models/marketmodels/utilities.hpp>
#include <ql/methods/montecarlo/genericlsregression.hpp>
#include <ql/legacy/libormarketmodels/lmlinexpcorrmodel.hpp>
#include <ql/legacy/libormarketmodels/lmextlinexpvolmodel.hpp>
#include <ql/time/schedule.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/math/integrals/segmentintegral.hpp>
#include <ql/math/statistics/convergencestatistics.hpp>
#include <ql/termstructures/volatility/abcd.hpp>
#include <ql/termstructures/volatility/abcdcalibration.hpp>
#include <ql/math/optimization/simplex.hpp>
#include <ql/quotes/simplequote.hpp>
#include <sstream>
#include <iostream>
#include <ctime>using namespace QuantLib;std::vector<std::vector<Matrix>>
theVegaBumps(bool factorwiseBumping, const ext::shared_ptr<MarketModel>& marketModel, bool doCaps) {Real multiplierCutOff = 50.0;Real projectionTolerance = 1E-4;Size numberRates= marketModel->numberOfRates();std::vector<VolatilityBumpInstrumentJacobian::Cap> caps;if (doCaps){Rate capStrike = marketModel->initialRates()[0];for (Size i=0; i< numberRates-1; i=i+1){VolatilityBumpInstrumentJacobian::Cap nextCap;nextCap.startIndex_ = i;nextCap.endIndex_ = i+1;nextCap.strike_ = capStrike;caps.push_back(nextCap);}}std::vector<VolatilityBumpInstrumentJacobian::Swaption> swaptions(numberRates);for (Size i=0; i < numberRates; ++i){swaptions[i].startIndex_ = i;swaptions[i].endIndex_ = numberRates;}VegaBumpCollection possibleBumps(marketModel,factorwiseBumping);OrthogonalizedBumpFinder  bumpFinder(possibleBumps,swaptions,caps,multiplierCutOff, // if vector length grows by more than this discardprojectionTolerance);      // if vector projection before scaling less than this discardstd::vector<std::vector<Matrix>> theBumps;bumpFinder.GetVegaBumps(theBumps);return theBumps;}int Bermudan()
{Size numberRates =20;Real accrual = 0.5;Real firstTime = 0.5;std::vector<Real> rateTimes(numberRates+1);for (Size i=0; i < rateTimes.size(); ++i)rateTimes[i] = firstTime + i*accrual;std::vector<Real> paymentTimes(numberRates);std::vector<Real> accruals(numberRates,accrual);for (Size i=0; i < paymentTimes.size(); ++i)paymentTimes[i] = firstTime + (i+1)*accrual;Real fixedRate = 0.05;std::vector<Real> strikes(numberRates,fixedRate);Real receive = -1.0;// 0. a payer swapMultiStepSwap payerSwap(rateTimes, accruals, accruals, paymentTimes,fixedRate, true);// 1. the equivalent receiver swapMultiStepSwap receiverSwap(rateTimes, accruals, accruals, paymentTimes,fixedRate, false);//exercise schedule, we can exercise on any rate time except the last onestd::vector<Rate> exerciseTimes(rateTimes);exerciseTimes.pop_back();// naive exercise strategy, exercise above a trigger levelstd::vector<Rate> swapTriggers(exerciseTimes.size(), fixedRate);SwapRateTrigger naifStrategy(rateTimes, swapTriggers, exerciseTimes);// Longstaff-Schwartz exercise strategystd::vector<std::vector<NodeData>> collectedData;std::vector<std::vector<Real>> basisCoefficients;// control that does nothing, need it because some control is expectedNothingExerciseValue control(rateTimes);//    SwapForwardBasisSystem basisSystem(rateTimes,exerciseTimes);SwapBasisSystem basisSystem(rateTimes,exerciseTimes);// rebate that does nothing, need it because some rebate is expected// when you break a swap nothing happens.NothingExerciseValue nullRebate(rateTimes);CallSpecifiedMultiProduct dummyProduct =CallSpecifiedMultiProduct(receiverSwap, naifStrategy,ExerciseAdapter(nullRebate));const EvolutionDescription& evolution = dummyProduct.evolution();// parameters for modelsSize seed = 12332; // for Sobol generatorSize trainingPaths = 65536;Size paths = 16384;Size vegaPaths = 16384*64;std::cout << "training paths, " << trainingPaths << "\n";std::cout << "paths, " << paths << "\n";std::cout << "vega Paths, " << vegaPaths << "\n";
#ifdef _DEBUGtrainingPaths = 512;paths = 1024;vegaPaths = 1024;
#endif// set up a calibration, this would typically be done by using a calibratorReal rateLevel =0.05;Real initialNumeraireValue = 0.95;Real volLevel = 0.11;Real beta = 0.2;Real gamma = 1.0;Size numberOfFactors = std::min<Size>(5,numberRates);Spread displacementLevel =0.02;// set up vectorsstd::vector<Rate> initialRates(numberRates,rateLevel);std::vector<Volatility> volatilities(numberRates, volLevel);std::vector<Spread> displacements(numberRates, displacementLevel);ExponentialForwardCorrelation correlations(rateTimes,volLevel, beta,gamma);FlatVol  calibration(volatilities,ext::make_shared<ExponentialForwardCorrelation>(correlations),evolution,numberOfFactors,initialRates,displacements);auto marketModel = ext::make_shared<FlatVol>(calibration);// we use a factory since there is data that will only be known laterSobolBrownianGeneratorFactory generatorFactory(SobolBrownianGenerator::Diagonal, seed);std::vector<Size> numeraires( moneyMarketMeasure(evolution));// the evolver will actually evolve the ratesLogNormalFwdRatePc  evolver(marketModel,generatorFactory,numeraires   // numeraires for each step);auto evolverPtr = ext::make_shared<LogNormalFwdRatePc>(evolver);int t1= clock();// gather data before computing exercise strategycollectNodeData(evolver,receiverSwap,basisSystem,nullRebate,control,trainingPaths,collectedData);int t2 = clock();// calculate the exercise strategy's coefficientsgenericLongstaffSchwartzRegression(collectedData,basisCoefficients);// turn the coefficients into an exercise strategyLongstaffSchwartzExerciseStrategy exerciseStrategy(basisSystem, basisCoefficients,evolution, numeraires,nullRebate, control);//  bermudan swaption to enter into the payer swapCallSpecifiedMultiProduct bermudanProduct =CallSpecifiedMultiProduct(MultiStepNothing(evolution),exerciseStrategy, payerSwap);//  callable receiver swapCallSpecifiedMultiProduct callableProduct =CallSpecifiedMultiProduct(receiverSwap, exerciseStrategy,ExerciseAdapter(nullRebate));// lower bound: evolve all 4 products togheterMultiProductComposite allProducts;allProducts.add(payerSwap);allProducts.add(receiverSwap);allProducts.add(bermudanProduct);allProducts.add(callableProduct);allProducts.finalize();AccountingEngine accounter(evolverPtr,Clone<MarketModelMultiProduct>(allProducts),initialNumeraireValue);SequenceStatisticsInc stats;accounter.multiplePathValues (stats,paths);int t3 = clock();std::vector<Real> means(stats.mean());for (Real mean : means)std::cout << mean << "\n";std::cout << " time to build strategy, " << (t2-t1)/static_cast<Real>(CLOCKS_PER_SEC)<< ", seconds.\n";std::cout << " time to price, " << (t3-t2)/static_cast<Real>(CLOCKS_PER_SEC)<< ", seconds.\n";// vegas// do it twice once with factorwise bumping, once withoutSize pathsToDoVegas = vegaPaths;for (Size i=0; i < 4; ++i){bool allowFactorwiseBumping = i % 2 > 0 ;bool doCaps = i / 2 > 0 ;LogNormalFwdRateEuler evolverEuler(marketModel,generatorFactory,numeraires) ;MarketModelPathwiseSwap receiverPathwiseSwap(  rateTimes,accruals,strikes,receive);Clone<MarketModelPathwiseMultiProduct> receiverPathwiseSwapPtr(receiverPathwiseSwap.clone());//  callable receiver swapCallSpecifiedPathwiseMultiProduct callableProductPathwise(receiverPathwiseSwapPtr,exerciseStrategy);Clone<MarketModelPathwiseMultiProduct> callableProductPathwisePtr(callableProductPathwise.clone());std::vector<std::vector<Matrix>> theBumps(theVegaBumps(allowFactorwiseBumping,marketModel,doCaps));PathwiseVegasOuterAccountingEngineaccountingEngineVegas(ext::make_shared<LogNormalFwdRateEuler>(evolverEuler),callableProductPathwisePtr,marketModel,theBumps,initialNumeraireValue);std::vector<Real> values,errors;accountingEngineVegas.multiplePathValues(values,errors,pathsToDoVegas);std::cout << "vega output \n";std::cout << " factorwise bumping " << allowFactorwiseBumping << "\n";std::cout << " doCaps " << doCaps << "\n";Size r=0;std::cout << " price estimate, " << values[r++] << "\n";for (Size i=0; i < numberRates; ++i, ++r)std::cout << " Delta, " << i << ", " << values[r] << ", " << errors[r] << "\n";Real totalVega = 0.0;for (; r < values.size(); ++r){std::cout << " vega, " << r - 1 -  numberRates<< ", " << values[r] << " ," << errors[r] << "\n";totalVega +=  values[r];}std::cout << " total Vega, " << totalVega << "\n";}// upper boundMTBrownianGeneratorFactory uFactory(seed+142);auto upperEvolver = ext::make_shared<LogNormalFwdRatePc>(ext::make_shared<FlatVol>(calibration),uFactory,numeraires   // numeraires for each step);std::vector<ext::shared_ptr<MarketModelEvolver>> innerEvolvers;std::valarray<bool> isExerciseTime =   isInSubset(evolution.evolutionTimes(),    exerciseStrategy.exerciseTimes());for (Size s=0; s < isExerciseTime.size(); ++s){if (isExerciseTime[s]){MTBrownianGeneratorFactory iFactory(seed+s);auto e = ext::make_shared<LogNormalFwdRatePc>(ext::make_shared<FlatVol>(calibration),uFactory,numeraires,  // numeraires for each steps);innerEvolvers.push_back(e);}}UpperBoundEngine uEngine(upperEvolver,  // does outer pathsinnerEvolvers, // for sub-simulations that do continuation valuesreceiverSwap,nullRebate,receiverSwap,nullRebate,exerciseStrategy,initialNumeraireValue);Statistics uStats;Size innerPaths = 255;Size outerPaths =256;int t4 = clock();uEngine.multiplePathValues(uStats,outerPaths,innerPaths);Real upperBound = uStats.mean();Real upperSE = uStats.errorEstimate();int t5=clock();std::cout << " Upper - lower is, " << upperBound << ", with standard error " << upperSE << "\n";std::cout << " time to compute upper bound is,  " << (t5-t4)/static_cast<Real>(CLOCKS_PER_SEC) << ", seconds.\n";return 0;
}int InverseFloater(Real rateLevel)
{Size numberRates =20;Real accrual = 0.5;Real firstTime = 0.5;Real strike =0.15;Real fixedMultiplier = 2.0;Real floatingSpread =0.0;bool payer = true;std::vector<Real> rateTimes(numberRates+1);for (Size i=0; i < rateTimes.size(); ++i)rateTimes[i] = firstTime + i*accrual;std::vector<Real> paymentTimes(numberRates);std::vector<Real> accruals(numberRates,accrual);std::vector<Real> fixedStrikes(numberRates,strike);std::vector<Real> floatingSpreads(numberRates,floatingSpread);std::vector<Real> fixedMultipliers(numberRates,fixedMultiplier);for (Size i=0; i < paymentTimes.size(); ++i)paymentTimes[i] = firstTime + (i+1)*accrual;MultiStepInverseFloater inverseFloater(rateTimes,accruals,accruals,fixedStrikes,fixedMultipliers,floatingSpreads,paymentTimes,payer);//exercise schedule, we can exercise on any rate time except the last onestd::vector<Rate> exerciseTimes(rateTimes);exerciseTimes.pop_back();// naive exercise strategy, exercise above a trigger levelReal trigger =0.05;std::vector<Rate> swapTriggers(exerciseTimes.size(), trigger);SwapRateTrigger naifStrategy(rateTimes, swapTriggers, exerciseTimes);// Longstaff-Schwartz exercise strategystd::vector<std::vector<NodeData>> collectedData;std::vector<std::vector<Real>> basisCoefficients;// control that does nothing, need it because some control is expectedNothingExerciseValue control(rateTimes);SwapForwardBasisSystem basisSystem(rateTimes,exerciseTimes);
//    SwapBasisSystem basisSystem(rateTimes,exerciseTimes);// rebate that does nothing, need it because some rebate is expected// when you break a swap nothing happens.NothingExerciseValue nullRebate(rateTimes);CallSpecifiedMultiProduct dummyProduct =CallSpecifiedMultiProduct(inverseFloater, naifStrategy,ExerciseAdapter(nullRebate));const EvolutionDescription& evolution = dummyProduct.evolution();// parameters for modelsSize seed = 12332; // for Sobol generatorSize trainingPaths = 65536;Size paths = 65536;Size vegaPaths =16384;#ifdef _DEBUGtrainingPaths = 8192;paths = 8192;vegaPaths = 1024;
#endifstd::cout <<  " inverse floater \n";std::cout << " fixed strikes :  "  << strike << "\n";std::cout << " number rates :  " << numberRates << "\n";std::cout << "training paths, " << trainingPaths << "\n";std::cout << "paths, " << paths << "\n";std::cout << "vega Paths, " << vegaPaths << "\n";// set up a calibration, this would typically be done by using a calibrator//Real rateLevel =0.08;std::cout << " rate level " <<  rateLevel << "\n";Real initialNumeraireValue = 0.95;Real volLevel = 0.11;Real beta = 0.2;Real gamma = 1.0;Size numberOfFactors = std::min<Size>(5,numberRates);Spread displacementLevel =0.02;// set up vectorsstd::vector<Rate> initialRates(numberRates,rateLevel);std::vector<Volatility> volatilities(numberRates, volLevel);std::vector<Spread> displacements(numberRates, displacementLevel);ExponentialForwardCorrelation correlations(rateTimes,volLevel, beta,gamma);FlatVol  calibration(volatilities,ext::make_shared<ExponentialForwardCorrelation>(correlations),evolution,numberOfFactors,initialRates,displacements);auto marketModel = ext::make_shared<FlatVol>(calibration);// we use a factory since there is data that will only be known laterSobolBrownianGeneratorFactory generatorFactory(SobolBrownianGenerator::Diagonal, seed);std::vector<Size> numeraires( moneyMarketMeasure(evolution));// the evolver will actually evolve the ratesLogNormalFwdRatePc  evolver(marketModel,generatorFactory,numeraires   // numeraires for each step);auto evolverPtr = ext::make_shared<LogNormalFwdRatePc>(evolver);int t1= clock();// gather data before computing exercise strategycollectNodeData(evolver,inverseFloater,basisSystem,nullRebate,control,trainingPaths,collectedData);int t2 = clock();// calculate the exercise strategy's coefficientsgenericLongstaffSchwartzRegression(collectedData,basisCoefficients);// turn the coefficients into an exercise strategyLongstaffSchwartzExerciseStrategy exerciseStrategy(basisSystem, basisCoefficients,evolution, numeraires,nullRebate, control);//  callable receiver swapCallSpecifiedMultiProduct callableProduct =CallSpecifiedMultiProduct(inverseFloater, exerciseStrategy,ExerciseAdapter(nullRebate));MultiProductComposite allProducts;allProducts.add(inverseFloater);allProducts.add(callableProduct);allProducts.finalize();AccountingEngine accounter(evolverPtr,Clone<MarketModelMultiProduct>(allProducts),initialNumeraireValue);SequenceStatisticsInc stats;accounter.multiplePathValues (stats,paths);int t3 = clock();std::vector<Real> means(stats.mean());for (Real mean : means)std::cout << mean << "\n";std::cout << " time to build strategy, " << (t2-t1)/static_cast<Real>(CLOCKS_PER_SEC)<< ", seconds.\n";std::cout << " time to price, " << (t3-t2)/static_cast<Real>(CLOCKS_PER_SEC)<< ", seconds.\n";// vegas// do it twice once with factorwise bumping, once withoutSize pathsToDoVegas = vegaPaths;for (Size i=0; i < 4; ++i){bool allowFactorwiseBumping = i % 2 > 0 ;bool doCaps = i / 2 > 0 ;LogNormalFwdRateEuler evolverEuler(marketModel,generatorFactory,numeraires) ;MarketModelPathwiseInverseFloater pathwiseInverseFloater(rateTimes,accruals,accruals,fixedStrikes,fixedMultipliers,floatingSpreads,paymentTimes,payer);Clone<MarketModelPathwiseMultiProduct> pathwiseInverseFloaterPtr(pathwiseInverseFloater.clone());//  callable inverse floaterCallSpecifiedPathwiseMultiProduct callableProductPathwise(pathwiseInverseFloaterPtr,exerciseStrategy);Clone<MarketModelPathwiseMultiProduct> callableProductPathwisePtr(callableProductPathwise.clone());std::vector<std::vector<Matrix>> theBumps(theVegaBumps(allowFactorwiseBumping,marketModel,doCaps));PathwiseVegasOuterAccountingEngineaccountingEngineVegas(ext::make_shared<LogNormalFwdRateEuler>(evolverEuler),//         pathwiseInverseFloaterPtr,callableProductPathwisePtr,marketModel,theBumps,initialNumeraireValue);std::vector<Real> values,errors;accountingEngineVegas.multiplePathValues(values,errors,pathsToDoVegas);std::cout << "vega output \n";std::cout << " factorwise bumping " << allowFactorwiseBumping << "\n";std::cout << " doCaps " << doCaps << "\n";Size r=0;std::cout << " price estimate, " << values[r++] << "\n";for (Size i=0; i < numberRates; ++i, ++r)std::cout << " Delta, " << i << ", " << values[r] << ", " << errors[r] << "\n";Real totalVega = 0.0;for (; r < values.size(); ++r){std::cout << " vega, " << r - 1 -  numberRates<< ", " << values[r] << " ," << errors[r] << "\n";totalVega +=  values[r];}std::cout << " total Vega, " << totalVega << "\n";}// upper boundMTBrownianGeneratorFactory uFactory(seed+142);auto upperEvolver = ext::make_shared<LogNormalFwdRatePc>(ext::make_shared<FlatVol>(calibration),uFactory,numeraires   // numeraires for each step);std::vector<ext::shared_ptr<MarketModelEvolver>> innerEvolvers;std::valarray<bool> isExerciseTime =   isInSubset(evolution.evolutionTimes(),    exerciseStrategy.exerciseTimes());for (Size s=0; s < isExerciseTime.size(); ++s){if (isExerciseTime[s]){MTBrownianGeneratorFactory iFactory(seed+s);auto e = ext::make_shared<LogNormalFwdRatePc>(ext::make_shared<FlatVol>(calibration),uFactory,numeraires ,  // numeraires for each steps);innerEvolvers.push_back(e);}}UpperBoundEngine uEngine(upperEvolver,  // does outer pathsinnerEvolvers, // for sub-simulations that do continuation valuesinverseFloater,nullRebate,inverseFloater,nullRebate,exerciseStrategy,initialNumeraireValue);Statistics uStats;Size innerPaths = 255;Size outerPaths =256;int t4 = clock();uEngine.multiplePathValues(uStats,outerPaths,innerPaths);Real upperBound = uStats.mean();Real upperSE = uStats.errorEstimate();int t5=clock();std::cout << " Upper - lower is, " << upperBound << ", with standard error " << upperSE << "\n";std::cout << " time to compute upper bound is,  " << (t5-t4)/static_cast<Real>(CLOCKS_PER_SEC) << ", seconds.\n";return 0;
}int main()
{try {for (Size i=5; i < 10; ++i)InverseFloater(i/100.0);return 0;} catch (std::exception& e) {std::cerr << e.what() << std::endl;return 1;} catch (...) {std::cerr << "unknown error" << std::endl;return 1;}
}