book

Advanced Quantitative Finance with Modern C++: Interest Rate Modeling and Advanced Derivatives

Name: Advanced Quantitative Finance with Modern C++: Interest Rate Modeling and Advanced Derivatives
Author: Aaron De La Rosa
ISBN: 9798868820595

by Aaron De La Rosa

January 2026

Intermediate to advanced

1087 pages

23h 46m

English

Apress

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Advanced Quantitative Finance with Modern C++
Introduction
What Readers Will LearnWho This Book Is ForUser LevelAdvancedCompiling C++23 Codes
Acknowledgments
Table of Contents
About the Author
About the Technical Reviewer
1. Black–Scholes PDE for a European Call Option Using Finite Difference Methods
1.1 Overview1.2 Black–Scholes PDE FormulaDerivation of the Black–Scholes PDETerminal Condition for a European Call OptionBoundary ConditionsBasic ImplementationOverview of the Class Structure1.3 Implementation of the Classes Described, Focusing on the Core Functionality for a European Call Option Using the Explicit Euler FDMCode AnalysisStructurePayOff and VanillaOption ClassesConvectionDiffusionPDE (Abstract) and BlackScholesPDEFDMBase (Abstract) and FDMEulerExplicitmain()Analysis of the Results1.4 Implementing Single-Factor Black–Scholes and Its Partial Differential Equation (PDE) Using Finite Difference Methods (FDMs) for European Option Pricing, via the Explicit Euler Method in C++23 (Four Header Files and Five Source Files): Full ImplementationPayOff (Abstract Base Class)PayOffCall (Derived Class)PayOffPut (Derived Class)PayOffCall ImplementationPayOffPut ImplementationClass DefinitionConstructorsDependenciesDefault ConstructorParameterized ConstructorConvectionDiffusionPDE (Abstract Base Class)BlackScholesPDE (Derived Class)DependenciesConstructorPDE CoefficientsBoundary and Initial ConditionsDependenciesFDMBase (Abstract Base Class)MembersPure Virtual FunctionFDMEulerExplicit (Derived Class)OverridesDependenciescalculate_step_sizesset_initial_conditionscalculate_boundary_conditionscalculate_inner_domainstep_marchDependenciesIncludes Necessary HeadersDefines Option ParametersNumerical Grid ParametersCreates ObjectsRuns a Finite Difference MethodProgram TerminationAnalysis of the OutputFormatStructureAt t = 0 (Maturity)As Time Progresses (t > 0)PurposeLimitationsKey ComponentsAxesSurface PlotColor BarInterpretationContextAxesSurface BehaviorConnection to Code1.5 Solving the Black–Scholes PDE Using Finite Difference Methods: Crank–Nicolson SchemeGrid SetupFinite Difference ApproximationsCrank–Nicolson SchemeApply Boundary and Terminal ConditionsStability and ConvergenceAdvantages and Limitations of FDMComparison with Analytical Solution1.6 FDM Simulation Using the Crank–Nicolson Scheme for European Call Option Pricing (Five Header and Six Source Files): Full ImplementationBlack_Scholes.hPrivate MembersPublic MembersVanilla_Option.hPrivate MembersPublic MembersGetter Methodspayoff.hPublic MembersPrivate MembersPublic Membersfdm.hProtected MembersPublic MembersPrivate MembersPublic Memberspde.hPublic MembersPublic MembersOverridden MethodsBlack_Scholes.cppIncluded HeadersConstructornorm_cdf MethodValue MethodVanilla_Option.cppIncluded HeadersDefault ConstructorParameterized Constructorpayoff.cppIncluded HeadersConstructorPayoff Functionfdm.cppIncluded HeadersFDMBase ConstructorFDMCrankNicolson Constructorcalculate_coefficients Methodsolve_tridiagonal Methodstep_march Methodpde.cppIncluded HeadersConstructorPDE Coefficient Methodsdiff_coeffconv_coeffzero_coeffsource_coeffBoundary and Initial Condition Methodsboundary_leftboundary_rightinit_condmain.cppIncluded HeadersMain Function SetupOption and PDE SetupFDM Time MarchingFDM Price InterpolationAnalytical Black–Scholes PriceError HandlingSummaryVisualizationPlotting1.7 ConclusionKey TakeawaysDerivation and Understanding of the Black–Scholes PDEImplementation of Numerical SchemesAccuracy and Stability AnalysisPractical InsightsWhat This Enables Going Forward
2. Random Number Generation (RNG)
2.1 Overview2.2 Random Number Generator Class HierarchyDesigning the RNG Class HierarchyMersenneTwisterRNGCommon ApplicationsAdvantages2.3 Basic Implementation in C++23 Using MersenneTwisterRNG (Two Header and Two Source Files)random.hmt_rng.hmt_rng.cppmain.cpp2.4 Quasi-random Sequences: Low-Discrepancy Sequences for Efficient SamplingDiscrepancy and EfficiencyHow Quasi-random Sequences WorkProminent Low-Discrepancy SequencesSobol Sequence2.5 Sobol Sequence: Basic ImplementationConceptsStructures and ClassesClass StatUtilityHow a Sequence Is GeneratedSample Generationmain FunctionKey ObservationsDimensional InterpretationVisualizationX-Axis (Dimension 1) and Y-Axis (Dimension 2)Blue DotsKey Features of a Sobol Sequence in This PlotScrambling (If Applied)Sobol Sequence Use Cases2.6 Monte Carlo Sobol Sequence for Option PricingKey Concepts in a Sobol SequenceWhy Do We Use the Sobol Sequence in Monte Carlo Simulations?Why Use Monte Carlo Sobol to Price Options?Sobol for Path SimulationAccuracy and EfficiencyAdvantages of Sobol Sequence in Monte Carlo Option PricingImplementationSobol Sequence GenerationFunctionsStatUtility ClassMonte Carlo Pricing via MonteCarloMethod::MonteCarloSobolAlgorithm Flow2.7 Monte Carlo Faure Quasi-random SequenceKey StepsKey StepsKey StepsKey InsightsSummary2.8 MonteCarloFaureQuasiRandom: ImplementationStatUtility ClassKey StepsInitialize VariablesMonte Carlo Loop (M Simulations)Compute Statisticsmain()2.9 Random Walk Using Boost LibraryKey Changes with BoostSeeding with TimeEnhanced FlexibilityWhy Use Boost?Random Walk Using the Boost Library: ImplementationConstructorMain.functionSummary2.10 Conclusion
3. Vasicek, Black–Scholes, and Black (1976) Models for Option Pricing and Bond Valuation with QuantLib
3.1 Vasicek ModelApplicationsLimitationsKey FeaturesApplicationsComparison with the CIR ModelVolatility DependenceAdvantagesLimitationsDataEstimate Vasicek Model ParametersSimulate Future Interest Rate PathsBond Option Pricing Using the Vasicek ModelKey FunctionsMain FunctionInterpretationOut-of-the-Money OptionLow Volatility (sigma = 0.02)Short Option Maturity (One Year)Mean-Reverting Interest RatesDiscounting Effect3.2 Vasicek Model for Interest Rate DynamicsKey ComponentsVasicek ModelVisualization Using Data Saved As csv.fileGraph ComponentsLines and ShadingSimulated PathMean ReversionVolatility and Standard DeviationSummary3.3 Vasicek Model Yield Curve with Expected Short-Rate DynamicsImplementationKey ComponentsVisualization Using Data Saved As csv.fileGraph ComponentsLines and ShadingYield CurveExpected Short RateStandard DeviationBehaviorSummaryYields3.4 Black–Scholes Price for a European Put Option on a Coupon BondKey ComponentsOutputAnalysis of the OutputDifferences3.5 Black Model (1976) for Pricing Options on Bond FuturesImplementationKey ComponentsMain FunctionOutputAnalysis of the OutputSensitivity Insight3.6 Bond Pricing, Duration, and Convexity (Two Header and Three Source Files)bond.hHeader Guards and PragmaNamespaceEnum ClassBond ClassMethodsbond.cppAnalysisConstructorgetBondPrice()getPaymentFrequency()Setters and GettersbondDuration.hHeader Guards and PragmaIncludesNamespaceBondDuration ClassMethodsPrivate MemberbondDuration.cppIncludesConstructorcalculateMacaulayDuration()calculateDuration()calculateConvexity()main.cppIncludesNamespacetestBondDuration FunctionTest Case 1: Semi-annual BondTest Case 2: Annual BondTest Case 3: Invalid Payment Typemain FunctionTesting an Invalid Payment Type3.7 Bond Valuation Using QuantLib and Boost Libraries in C++23: Updated for 2025 Market Conditions with Realistic Euribor6M and Bond QuotesImplementationSetup and IncludesDate and Calendar SetupDiscounting Yield Curve ConstructionBond DetailsEURIBOR Forecasting Curve ConstructionBond Definitions and PricingError HandlingDifferences from the Previous CodeMarket DataSummaryOutputOutput AnalysisDatesBond Metrics TableColumnsRowsNet Present Value (NPV)Clean PriceDirty PriceAccrued CouponPrevious CouponNext CouponYieldSample Indirect Computations (Floating-Rate Bond)Summary3.8 Conclusion
4. Advanced Interest Rate Models: Hull–White/Black–Karasinski and Callable Bond Pricing Using QuantLib
4.1 Hull–White Extended Vasicek ModelFeatures of the Hull–White ModelHull–White vs. VasicekApplicationsLimitationsAnalytical SolutionsHull–White Model (Simulated Interest Rate Path)Code AnalysisFunction simulateHullAndWhiteMain FunctionLimitationsOutputOutput AnalysisOutput StructureColumnsRowsKey ObservationsInterest Rate DynamicsExample FluctuationsNegative Interest RatesVolatility and RangeTime-Dependent ParametersUse CaseLimitations4.2 Implementing the Hull–White Model for the Estimation of the Interest Rate Tree and Forward Interest Rates in C++23IncludesGraphNode (Represents a Node in the Trinomial Tree)GraphStepHWCalculatorMethodsMain Function BehaviorCalculationsOutputAnalysis of the OutputStep-by-Step Tree EvolutionConclusion4.3 Caplet Pricing Using the Hull–White Model by Calibrating to Market Cash Prices and the Black Model Formula in C++23Code AnalysisKey Financial ConceptsCode StructureMain FunctionKey Financial ConceptsCaplets and CapsHull–White ModelCalibrationBlack–Scholes ModelCode Limitations and NotesGrid SearchNegative Mean ReversionError HandlingUnused CodeNormalizationOutput AnalysisSummary4.4 Estimating Arrow–Debreu, Zero-Coupon Bond, Caplet, and Swaption Prices Using Black–KarasinskiCode AnalysisAnalysis of the OutputSummary4.5 Pricing a Callable Fixed-Rate Bond Using Hull–White with Reversion Parameters and QuantLib/Boost LibrariesCode AnalysisSummaryKey ObservationsOutputAnalysis of the OutputSummary4.6 Conclusion

5. Advanced Fixed Income and Credit Default Swap (CDS) Using QuantLib
5.1 Overview of the Cox–Ingersoll–Ross ModelDefinitionKey FeaturesApplicationsAdvantagesLimitationsPractical Applications5.2 Cox–Ingersoll–Ross ModelImplementationsimulateCIR Functionmain FunctionExecutionSummaryConclusionOutput5.3 Zero-Coupon Bond Pricing and Yield to Maturity Using the CIR ModelImplementationCode AnalysisValidation FunctionsCIRParameters Structcompute_AB Functionprice_bond Functiongenerate_yield_curve Functionmain FunctionExecutionConclusionOutputAnalysis of the OutputCIR Model Yield CurveObservationsCIR Model Bond Pricing (Single Maturity)OutputInterpretationKey InsightsComparison with Previous OutputsSummary5.4 Overview of the Black–Derman–Toy ModelKey Features5.5 Black–Derman–Toy Short–Rate Model CalibratedImplementationCode AnalysisBlackDermanToy ClassPrivate MembersPrivate MethodsinitializeBondPricesinitializeFirstNodeupdateProbabilitiescalculateBondPriceWithUsolveForUcalculateRatesAndDiscountscalculateBondPriceprintTreePublic Method: buildBDTmain FunctionSetupKey FeaturesOutputOutput AnalysisKey ParametersInitializationCalibrated Median RatesStructureBond Price CalibrationKey InsightsComparison with Other ModelsSummary5.6 Callable and Puttable Bond Price Using the Black–Derman–Toy Model CalibratedImplementationCode AnalysispriceBondBDT Functionmain FunctionExecutionKey FeaturesCallable/Puttable FeaturesComparison to Previous ModelsSummaryOutputAnalysis of the OutputKey InsightsCallable vs. PuttableBDT ModelYield Curve ContextPotential Output AnomaliesSummary5.7 Overview of the Black ‘76 ModelKey FeaturesApplicationsLimitations5.8 Caplet and Floorlet Pricing Using the Black ‘76 ModelImplementationCode Analysisnormal_density Functionboole_rule Functionnormal_cdf Functionblack76_cap_floor Functionmain FunctionSetupExecutionKey FeaturesLimitationsOutputAnalysis of the Output5.9 Interest Rate Swap ValuationKey FeaturesOverviewApplicationsKey Components (Example)5.10 Interest Rate Swap Valuation with Fixed Payer and Floating PayerImplementationCode AnalysisOutput AnalysisFixed-Payer SwapFloating-Payer SwapVisualization (First Chart)SummaryBlue Bar (Fixed-Payer Swap)Purple Bar (Floating-Payer Swap)Summary5.11 Credit Default Swap (CDS) Using QuantLib and Boost LibrariesImplementationCode AnalysisExample 1: Basic CDS Calibration and Repricing (example01())Key StepsSet Up Market DataBootstrap Hazard Rate CurveReprice CDS InstrumentsCompute and Print for Each CDSSummaryPotential Output Snippet (Based on Code Logic)Example 2: ISDA-Compliant CDS Pricing with Yield and Credit Curves (example02())Key StepsSetupBuild ISDA Yield CurveReference CDS and PricingBootstrap Credit Curve from Single CDSPrice Sample TradeSummaryPotential Output SnippetExample 3: Multi-point Credit Curve Bootstrapping (example03())Key StepsSetupBuild ISDA Yield CurveBootstrap ISDA Credit CurvePricing EngineSummaryPotential Output SnippetGeneral Notes on the CodeOutputOutput AnalysisExample 1 Output: Basic CDS Calibration and RepricingCalibrated Hazard Rate ValuesSurvival Probability ValuesRepricing of Quoted CDSsAnalysisExample 2 Output: ISDA-Compliant CDS PricingCDS ScheduleAnalysisISDA Rate CurveAnalysisAccrual and Reference Trade NPVISDA Credit CurveAnalysisSample Trade NPVAnalysisExample 3 Output: Multi-point Credit Curve BootstrappingISDA Yield CurveAnalysisISDA Credit CurveAnalysisSummaryExample 1Example 2Example 3Using OutputVisualization5.12 Conclusion
6. Short-Rate Models and Lattice Methods: Black–Derman–Toy, Hull–White, and FRA with QuantLib
6.1 Overview6.2 Building Binomial Short-Rate Trees for Black–Derman–ToyImplementationIncludesInitialize the Short-Rate TreeInitialize the First Short RateBuild the Tree via Calibration (Years 2 and Beyond)Root-Finding Setup (Newton–Raphson)Newton–Raphson IterationConstruct the Rate Tree at Time iCompute the Model Bond Price Using Backward InductionCompute the Derivative of Model Price w.r.t GuessApply Newton–Raphson UpdateOutput: Print the Tree and Check AccuracyBond Price Matching6.3 Black–Derman–Toy Tree Calibrated to the Yield Vector of the Yield CurveImplementationKey ConceptsMain Components of the CodeInputsInitializationTree Data StructuresTree ConstructionNewton–Raphson CalibrationOutputAnalysis of the OutputVisualization6.4 Black–Derman–Toy Tree Calibrated to the Yield Curve and Volatility CurveAdvanced ImplementationKey Concepts and StepsCompute Market Bond PricesInitialize Tree at t = 0Calibrate Tree Step by Step (i = 1 to N-1)Newton–Raphson IterationArrow–Debreu ProbabilitiesValidationAlternative ApplicationsOutputAnalysis of the OutputContinuous CompoundingDiscrete CompoundingVisualizationBDT Tree StructureContinuous Compounding (Left)Discrete Compounding (Right)CalibrationPurpose of the Comparison6.5 Calibrated Black–Derman–Toy Lattice for American and European Swaption ValuationImplementationKey ParametersBuilding the BDT Lattice: buildBDTLattice( )BDT Lattice OverviewComputing the Swap Rate: computeSwapRate( )Pricing a European Swaption: priceEuropeanSwaption( )Pricing an American Swaption: priceAmericanSwaption( )Debugging OutputSummaryOutputAnalysis of the OutputSummaryVisualizationKey FeaturesSummary6.6 Building a Hull–White Tree Calibrated to the Initial Short-Term StructureKey GoalsKey ConceptsBasic ImplementationIncludesOutputAnalysis of the OutputSummaryVisualizationKey Features of the Model and Tree6.7 Zero-Coupon Bond Pricing Using the Hull–White TreeImplementationIncludesSummaryOutputAnalysis of the OutputConclusionVisualization6.8 FRA (Forward Rate Agreement) Using QuantLib and Boost LibrariesKey FeaturesUsesBasic ExampleAdvanced ImplementationCode AnalysisOutput AnalysisGeneral ContextKey ObservationsSummaryVisualization6.9 Conclusion
7. Advanced Interest Rate Lattice Models: Lognormal Hull–White (BK) Trees and QuantLib Applications (Bootstrapping and Repo)
7.1 Lognormal Hull–White (Black–Karasinski) TreeImplementationIncludesData Structures for the TreeTree ConstructionTransition ProbabilitiesHull–White Iteration: Solving for α(t)Debug OutputSummaryOutputWhat the Output RepresentsStructure of the TreeKey Numbers in OutputInterpretationSummaryVisualizationKey Features of the PlotNodes and PathsModel DynamicsUsage7.2 Building a Lognormal Hull–White (Black–Karasinski) Tree for Bond PricingC++ CodeImplementationLognormal Hull–White/Black–KarasinskiStep-by-Step Tree ConstructionFinal Time StepSummaryOutputAnalysis of the OutputVisualizationKey Features of the GraphLines and MarkersImplicationsSummary7.3 Lognormal Hull–White (Black–Karasinski) Model Calibrated to Yield and Volatility CurvesImplementationCode AnalysisData Structures for the TreeTree ConstructionTransition ProbabilitiesHull–White Iteration: Solving for α(t)Discount Factor UpdateDebug OutputOutputAnalysis of the OutputSummaryVisualizationStructureHeatmap OverlayColor Bar (Right Side): Vertical Scale for Short RatesDynamics VisualizedModel Parameters (Inferred)7.4 Multi-curve Bootstrapping Using QuantLib and Boost Libraries for a Five-Year SwapImplementationCode AnalysisGlobal SettingsBuilding the €STR CurveBuilding the Euribor6M CurveDefining Swaps to PriceSummaryOutputAnalysis of the OutputDate InformationFirst Pricing Section (Initial Market Quotes)Second Pricing Section (After Market Change)Summary7.5 REPO Using QuantLib and Boost LibrariesImplementationCode AnalysisRepo ParametersBond ParametersBond Curve and Bond CreationRepo Curve and Bond Forward CreationSummaryOutputAnalysis of the OutputSummary7.6 Conclusion
8. Multi-factor Interest Rate Models: G2++, Hull–White, Libor Market Model, and Ho–Lee Applications
8.1 Two-Factor Gaussian Model (G2++)How to Build a G2++ Tree?ImplementationImplementationCode AnalysisKey Components and FunctionalityG2PlusPlusTree Classbuild_statescompute_probabilitiesfit_yield_curveprice_bondrunmainSummaryOutput8.2 Two-Factor Hull–White Model (1994) for Zero-Coupon Bond Price and CapletKey FeaturesAdvantages over One-Factor ModelsApplicationsImplementationCode AnalysisModel Parameters: HW2FParamsMarket Bond Prices: getMarketBondPricesCalibrating Drift φ(t): calibratePhiPath Simulation: simulateHW2FPathBond Pricing Function: zeroCouponBondPriceCaplet Pricing (Monte Carlo): priceCapletCalibration Stub: calibrateParametersMain Function OverviewSummaryOutputAnalysis of the OutputKey Observations8.3 Two-Factor Hull–White Model (1994) for Zero-Coupon Bond and Caplet Pricing: Advanced ImplementationCode AnalysisKey Components and Their RolesHW2FParams StructgetMarketBondPricescalibratePhisimulateHW2FPatB and A FunctionszeroCouponBondPriceForwardRatepriceCapletcalibrateParametersmain FunctionSummaryOutputAnalysis of the Output8.4 Two-Factor Hull–White Model for Zero-Coupon Bond PriceImplementationCode AnalysisMarket Bond Price GenerationAnalytical FunctionsBond Price Interpolation and Forward Rateφ(t) CalibrationZero-Coupon Bond PricingSimulating Short-Rate PathsCoupon Bond PricingMain FunctionOutputAnalysis of the Output8.5 The Hull–White Libor Market Model (LMM), a.k.a the LMM with Hull–White Volatility or Simply the LMM-HW ModelLMM (Libor Market Model)Hull–White (HW) ExtensionLMM DynamicsBasic ImplementationCode AnalysisLIBOR Rate StructureVolatility Function AbstractionHull–White Volatility Model for LIBORForward CurveThetaEvolving the LIBOR RatesEvolving the Short RateSimulation FunctionMain FunctionOutputAnalysis of the OutputInterpretation of the OutputVisualization8.6 Hull–White LMM Calibration and Caplet Pricing Using the Eigen/Dense LibraryKey ComponentsImplementationCode Analysis: Key Structures and FunctionsLiborRate StructureVolatilityFunction and HullWhiteVolatilitymarketForwardRatescomputeThetacalibrateHullWhiteevolveLiborRatesevolveShortRatepriceCapletsimulateLMMHullWhitemain FunctionSummaryInitializationCalibrationSimulationCaplet PricingDependenciesConclusionOutputAnalysis of the OutputCalibration OutputCaplet Pricing OutputCaplet PricePractical Implications8.7 Ho–Lee Model for Zero-Coupon Bond PricingImplementationCode AnalysisSummaryConclusionVisualizationExplanation8.8 Conclusion
9. Heath–Jarrow–Morton and BGM Models: Advanced Forward Rate Dynamics and Derivative Pricing with Boost
9.1 Heath–Jarrow–Morton Model (1992)The Heath–Jarrow–Morton (HJM) FrameworkKey Concepts of the HJM FrameworkForward Rate as the Core VariableNo-Arbitrage ConditionZero-Coupon Bond PricingFlexibility in Volatility StructureSteps in Using the HJM FrameworkAdvantages of the HJM FrameworkLimitationsPractical ApplicationsMain Advantages of the HJM FrameworkSummaryBasic ImplementationCode AnalysisLibraries and SetupHJM Simulation FunctionRandom Number GenerationTime Steps and StorageForward Rate SimulationMain FunctionForward Rate RepresentationOutputOutput AnalysisVisualizationSummary9.2 Heath–Jarrow–Morton Model with No-Arbitrage Drift and Zero-Coupon Bond Pricing Using Multiple MaturitiesBasic ImplementationCode AnalysisKey Components and FunctionalitycomputeDriftpriceZeroCouponBondsimulateHJMmainSummaryKey OutputsLimitationsFinal ObservationsOutputOutput AnalysisVisualization9.3 Heath–Jarrow–Morton Model with No-Arbitrage Drift and Zero-Coupon Bond Pricing, Swaption Valuation, and Caplet and Floorlet PricingImplementationCode AnalysiscomputeDriftpriceZeroCouponBondcomputeDiscountFactorpriceSwaptionpriceCap and priceFloorsimulateHJMOutputAnalysis of the OutputForward Rates TableZero-Coupon Bond PricesPayer Swaption PricesCap PricesFloor PricesSummaryVisualization9.4 Brace, Gatarek, and Musiela (BGM, 1997) Model for Cap Pricing (with the Boost Library)Implementation Using the Boost LibraryCode AnalysisMain Function: cap_bgmCompute LIBOR Forward Rates (LFRs)Compute Integrated Volatility (BGM)Compute d1 for Caplet Pricing (BGM)Compute Caplet Prices (BGM)Total Cap Price (BGM)Black's Model for ComparisonTotal Cap Price (Black)Return ValueMain FunctionKey Differences Between BGM and Black ModelsOutputAnalysis of the OutputWhat Is a Cap?Interpretation of the PricesWhy Are the Prices Different?Volatility StructureModel AssumptionsNumerical DifferenceFinancial SignificanceSummary9.5 Brace, Gatarek, and Musiela (BGM, 1997) Model for Caps and Floors Using Multi-strike Prices and the Boost LibraryOverview of Caps and Floors, the BGM Model, and the Black ModelImplementation Using the Boost LibraryCode AnalysisHeaders and Utility FunctionsPricingResult StructureMain Pricing Function: cap_floor_bgmCompute LIBOR Forward RatesCompute Integrated Volatility (BGM)ProcessDebug Output (Forward Rates and Volatilities)Compute d1 for BGM PricingCompute Caplet and Floorlet Prices (BGM)Total Cap and Floor Prices (BGM)Black Model for ComparisonTotal Cap and Floor Prices (Black)Return ResultsMain FunctionSummaryOutputAnalysis of the OutputTable StructureUnderstanding Caps and FloorsBGM vs. BlackTrends and InsightsCap Prices Decrease with StrikeFloor Prices Increase with StrikeBGM vs. Black ModelForward Rates and VolatilityPractical ImplicationsSummaryVisualization9.6 Brace, Gatarek, and Musiela (BGM, 1997) Model for Caps, Floors, and Swaptions Using Multi-strike Prices and the Boost LibraryCode StructureImplementation Using the Boost LibraryCode Analysisnorm_cdfvector_norm_squaredPricingResult StructureMain Pricing Function: cap_floor_swaption_bgmCompute Integrated VolatilityDebug OutputCompute d1 for Caplets/FloorletsPrice Caplets and Floorlets (BGM)Total Cap and Floor Prices (BGM)Black Model for Caps and FloorsSwaption PricingSwap RateSwaption VolatilityBlack Swaption PriceReturn ResultsMain FunctionExecutionFinancial ConceptSwaptionsBGM vs. BlackVolatility CalibrationConclusionOutputAnalysis of the OutputOutput StructureAnalysis of ResultsForward Rates and Swap RateVolatilityModel ComparisonFinancial InterpretationSummaryVisualization9.7 Conclusion
10. Monte Carlo LFR Dynamics and Advanced Fixed-Income Derivatives: Convertible Bonds and Gaussian Model with QuantLib
10.1 Monte Carlo Simulation of the LFR (Libor Forward Rate) Dynamics to Price a European Swaption Using the Eigen/Dense LibraryImplementationCode AnalysisLibrariesPreprocessor DirectivesHelper FunctionsnormalCDF(double x)blackSwaptionPricegetVolatilitycomputeDriftMain Function: priceSwaptionMonteCarloRandom Number GenerationCorrelation MatrixForward Rate SimulationPayoff CalculationFinal PriceMain FunctionFinancial and Numerical TechniquesSummaryOutputAnalysis of the OutputContext of the SimulationKey ObservationsControl Variate EffectivenessAt-the-Money SwaptionForward Rate DynamicsPayoff StatisticsSignificanceForward Rates in OutputSignificanceSwap Rate DistributionSignificanceSwap Rate VolatilitySignificanceBlack Model PriceSignificanceFinal Swaption PriceSignificanceVisualizationOverall ContextDistribution of Swap Rates at MaturitySample Forward Rate PathsDistribution of Discounted PayoffsKey InsightsSwap Rate DistributionForward Rate PathsPayoff DistributionComparison with C++ Output10.2 Convertible Bonds Using QuantLib and Boost LibrariesImplementationCode AnalysisWhat the Code ComputesKey LibrariesIncludes and SetupParameter DefinitionDate and Schedule SetupCall/Put and Dividend SchedulesPricing Setup and Binomial ModelsPricing Loop and OutputsAdditional MetricsJarrow-RuddGreeksError Handling and ExitOutputAnalysis of the OutputBond ParametersCall and Put SchedulesColumnsRowsValuesAdditional Metrics (Jarrow–Rudd)Sensitivity Analysis (Underlying Price vs. NPV)Greeks for European Bond (Finite Difference)Key InsightsVisualization10.3 Gaussian Model Using QuantLib and Boost LibrariesImplementationCode AnalysisHeader IncludesHelper FunctionsprintBasketprintModelCalibrationMain FunctionKey ConceptsOutputOutput AnalysisAnalysisCalibration Basket (Naive Mode)AnalysisBasket DetailsGSR Model Calibration (Naive Basket)AnalysisColumnsBermudan Swaption NPV (Naive Calibration)AnalysisCalibration Basket (MaturityStrikeByDeltaGamma Mode)AnalysisDetailsGSR Model Recalibration (MaturityStrikeByDeltaGamma)AnalysisBermudan Swaption NPV (Deal Strike Calibration)AnalysisLinear Amortizing Nominal ScheduleAnalysisBermudan Callable Fixed Bond SetupAnalysisIncluding 120 bp OASAnalysisCMS 10Y vs. Euribor 6M SwaptionAnalysisGSR Calibration for Float SwaptionAnalysisMarkov Functional ModelAnalysisSummaryVisualizationKey ObservationsFinancial InsightVisualizationKey ObservationsFinancial InsightsContextVisualizationKey ObservationsFinancial InsightsContext10.4 Conclusion
11. Valuing Bermudan Swaptions with LSMC, LMM, and QuantLib Implementation Using Short-Rate Models (G2++, Hull–White, BK)
11.1 Overview11.2 Bermudan Swaptions11.3 Practical Implementation11.4 Pricing Bermudan Swaptions11.5 Key Characteristics11.6 Bermudan Swaption Valuation Using the LSMC Method, LMM, Hull–White Model, and Eigen/Dense LibraryImplementationCode AnalysisKey ConceptsIncludesInitial Setup and ParametersVolatility and CorrelationMain Simulation LoopSwap Value ComputationLongstaff–Schwartz RegressionEarly Exercise DecisionPrice CalculationOutput to CSVLibraries and UtilitiesOutputAnalysis of the OutputMatrix Dimensions ReviewForward Simulation OutputBackward Regression (LSMC) OutputBermudan Swaption PriceUnderstand the Bermudan Swaption ParametersTenor StructureCompare Prices11.7 Bermudan Multi-asset Asian–Barrier–Lookback–StochVol Call Option Price Using Monte Carlo Simulation and the Longstaff–Schwartz Model (LSM) and Eigen/Dense LibraryMain ObjectiveWhat the Code IntegratesImplementationCode AnalysisMonte Carlo SimulationStock and Variance EvolutionLongstaff–Schwartz Method (LSM)The Eigen/Dense LibraryKey Roles of Eigen/Dense in Our CodePath Matrix Storage and ManipulationLongstaff–Schwartz RegressionEigen/DenseVectorized Logic for Early ExerciseOutputAnalysis of the OutputMatrix DimensionsRegression LoopMidpoint DiagnosticsFinal OutputSummary11.8 Bermudan Swaption Valuation with Different Models: G2++, Hull–White, and Black–Karasinski (Analytical and Numerical Prices) Using QuantLib and Boost LibrariesKey ComponentsKey FeaturesImplementationCode AnalysisKey ConceptsIncludes and Using NamespaceGlobal Variables for the Calibration GridCalibration Function: calibrateModelMain FunctionSetup: Dates, Yield Curve, and SwapSwaption Helpers for CalibrationDefine and Calibrate ModelsBermudan Swaption Setup and PricingLambda FunctionCleanup and Error HandlingVanilla Swap (VanillaSwap Struct)Swaption Helper (SwaptionHelper Struct)Pricing Engine (PricingEngine and DiscountingSwapEngine)Calibration Model (CalibrationModel Struct)Calibration Function (calibrate)ApplicationsCode StrengthsSummaryOutputAnalysis of the OutputCalibration ResultsGeneral Structure of Calibration OutputG2++ CalibrationHull–White (Analytic) CalibrationHull–White (Numerical) CalibrationBlack–Karasinski CalibrationBermudan Swaption PricingKey ObservationsCalibration QualityModel ComparisonPricing EnginesSwaption TypesFinancial ContextSummarySuggestions for Advanced ImplementationVisualization11.9 Conclusion
12. Range Notes Using a Heath–Jarrow–Morton (HJM) Tree, CDS, Quanto, and Currency Swaps
12.1 Range Notes Valuation Using a Heath–Jarrow–Morton (HJM) TreeDefinition of a Range NoteHJM Tree Model OverviewWhat the Code IncludesBasic ImplementationCode AnalysisWhat Is a Range Note?Core Financial Concepts in Our CodeForward Curve Initialization (calibrateForwardCurve)Simulation Loop (simulatePrice)Initialize Stochastic FactorsSimulate Interest Rates (HJM Dynamics)Range Note LogicFinal PricingKey FeaturesOutputAnalysis of the Output12.2 HJM Range Note Using the Eigen/Dense Library and Three Approaches—Two-Factor HJM Tree, Two-Factor HJM Monte Carlo, and Three-Factor HJM Monte Carlo: Advanced ImplementationRange NoteHJM ModelVolatility TermAdvanced ImplementationCode Analysisstruct FactorClass HJMTree2FactorKey FieldsKey MethodscalibrateForwardCurve()drift(t,T)buildRateTree()priceNote()getPrice()monteCarloHJMRangeNotePrice(...)Cholesky DecompositionSimulate PathsScenariosLibraries and FeaturesSummaryOutputAnalysis of the OutputAdding a Third Factor → Further Price DropInterpretationConclusionVisualizationAnalysis12.3 Implementing a Vanilla Credit Default Swap (CDS) and Quanto CDSWhat Is a Vanilla CDS?Use Case of a Vanilla CDSWhat Is a Quanto CDS?Use Case of a Quanto CDSHow to Value Vanilla and Quanto CDSs?Vanilla CDS ValuationDiscounted Cash FlowsQuanto CDS ValuationWhat Is the Best Way to Value Them?Vanilla CDSQuanto CDSWhat’s the Use of CDS?ImplementationCode AnalysisClass CreditDefaultSwapConstructorKey Methodsmain() FunctionVanilla CDSQuanto CDSAnalysisSummaryOutputAnalysis of the OutputAnalysisSummary12.4 Implementing the Garman–Kohlhagen Model for Pricing Foreign Exchange (FX) Options and Its GreeksStandard Normal CDFAdvantages of the Garman–Kohlhagen ModelUses of the Garman–Kohlhagen ModelImplementationCode AnalysisNormal CDFBlack–Scholes d1 and d2 (Adjusted for FX)Analytical Price: Garman–Kohlhagen FormulaGreeksDeltaGammaVegaThetaRhoMonte Carlo Simulation for FX OptionMain FunctionOutputAnalysis of the OutputVisualizationAxesWhat’s a Volatility Smile?ObservationsAxesKey Observations12.5 Currency SwapFull ImplementationCode AnalysisClass DefinitionPrivate MembersPublic MethodsStatic Utility FunctionsMain FunctionKey Functionality ExplainedSwap Valuation (valueSwap)Forward FX Rate (forwardFXRate)Sensitivity Analysis (sensitivityAnalysis)Cash Flow Schedule (cashFlowSchedule)Forward FX Curve (plotForwardFXCurve)Break-Even Analysis (breakEvenAnalysis)Monte Carlo Simulation (monteCarloSimulation)Risk Metrics (calculateRiskMetrics and riskMetricsAnalysis)Main FunctionKey Features and DesignOutputAnalysis of the OutputSwap ValueForward FX RateSensitivity AnalysisSpot FX RateLeg 1 Rate (USD Fixed Rate)Leg 2 Forward Rate Shift (EUR Floating Rates)USD Yield ShiftEUR Yield ShiftCash Flow ScheduleForward FX CurveBreak-Even AnalysisMonte Carlo SimulationRisk MetricsVisualization12.6 ConclusionWhat We Learned
13. Swap Engineering with Quantitative Models: Index-Amortizing Swap, TRS with Antithetic Variates, and Hull–White Trigger Swaps
13.1 Index-Amortizing SwapOverview of an Index-Amortizing SwapFull ImplementationCode AnalysisCode StructureKey C++23 Features UsedIndexAmortizingSwap ClassPrivate MembersKey MethodsPublic Interfacesensitivity_analysis Functionplot_value_distribution Functionmain FunctionKey Features and AssumptionsOutputAnalysis of the OutputFunctionalityHull–White SimulationRisk MetricsSensitivity AnalysisCustom AmortizationVisualization13.2 Total Return Swap (TRS) Using Boost and Eigen/Dense Libraries and Antithetic VariatesWhat Is a Total Return Swap (TRS)?Full ImplementationCode AnalysisLibrariesPreprocessor DirectivesSOFRCurve ClassTotalReturnSwap ClassKey Methodsvalidate_inputs()simulate_path_pair()calculate_npv()Monte Carlo SimulationFunding LegStatisticsNPVMain FunctionFinancial and Mathematical ConceptsTotal Return Swap MechanicsMonte Carlo SimulationAntithetic VariatesSOFR CurveVariance and Standard ErrorHow Antithetic Variates WorkUse of Boost and Eigen/Dense LibrariesBoostEigenSummaryOutputAnalysis of the OutputKey InsightsSummary13.3 Trigger Swap with the Calibrated Hull–White ModelKey Features of a Trigger SwapValuation of a Trigger SwapModel the TriggerValue the Underlying SwapIncorporate the Trigger ProbabilityAdjust for RiskNumerical MethodsImplementationAssumptionsTrigger Swap Code ImplementationKey ParametersFull ImplementationCode AnalysisData StructuresYieldCurveHullWhiteTriggerSwapRiskMetricsValidation (validateParams)Hull–White Path Simulation (simulateHullWhitePath)Precompute Discount Factors (precomputeDiscountFactors)Single Path Valuation (valueSinglePath)Cash Flow Schedule (cashFlowSchedule)Risk Metrics (calculateRiskMetrics)Trigger Swap Valuation (valueTriggerSwap)Sensitivity Analysis (sensitivityAnalysis)Value Distribution Histogram (plotValueDistribution)Main FunctionC++23 FeaturesNumerical StabilitySummaryOutput (Short Version)Analysis of the OutputOverview of the Trigger Swap and Hull–White ModelCash Flow SchedulesObservations from Cash Flow SchedulesNet Cash FlowRisk MetricsAnalysisKey ObservationsSensitivity AnalysisSwap Value DistributionHull–White Model ContextKey AspectsPractical ApplicationsC++23 Implementation NotesVisualizing Net Cash FlowsSummary13.4 Conclusion
14. Cross-Currency Swap (CCS) and Advanced Option Models: From Monte Carlo to QuantLib Implementations
14.1 Cross-Currency Swap (CCS) with Boost and Eigen/Dense LibrariesWhat Is a CCS?ImplementationDay Count ConventionsDayCount (Abstract)Act360 and Thirty360Yield CurveFunctionsBootstrap LogicSwap LegsLeg (Abstract)FixedLegFloatingLegCrossCurrencySwap ClassConstructorcalculate_npv()calculate_rate_sensitivity()summary()Utility: generate_payment_datesMain FunctionOutputAnalysis of the OutputValuation DatePresent Value of LegsFixed Leg PV (Domestic)Floating Leg PV (Foreign)Net Present Value (NPV)Rate Sensitivity Matrix14.2 Implementing a Shout Floor Option Using the Kwok–Dai–Wu (2004) ModelUse Case for Shout Floor OptionsHow Do We Price a Shout Floor Option?ImplementationIncludesNormal Distribution ToolsBlack–Scholes Put PriceBigP FunctionTheta FunctionBisection MethodMain Pricing FunctionOutputAnalysis of the Output14.3 Implementing a Cliquet Option Using Monte Carlo SimulationKey FeaturesPurpose of Cliquet OptionsCliquet Option ValuationFactors Influencing Its ValuationApplicationsMonte Carlo Valuation MethodMonte Carlo Simulation StepsUsage in mainImplementationKey Components of the CodeCliquetOption ClasscalculatePayoff(...)monteCarloValuation(...)Main FunctionStrengthsSummaryOutputAnalysis of the Output14.4 American Call and Put Option Using the Longstaff–Schwartz Least Squares Method (LSM) and Eigen/Dense LibraryImplementationIncludesGBM Path SimulationPayoff FunctionsBasis Function for RegressionRegression Coefficients (Training Phase)Longstaff–Schwartz Pricing (Valuation Phase)MainOutputAnalysis of the Output14.5 Option Pricing Engine Using QuantLib and Boost LibrariesImplementationCode AnalysisCode StructureSummaryKey QuantLib FeaturesOutputAnalysis of the OutputAnalysis of Each Pricing MethodKey InsightsConsistency Across MethodsEarly Exercise PremiumModel DifferencesSome Methods Are N/ASummaryVisualization14.6 Equity Option Pricing Engine Using QuantLib and Boost LibrariesImplementationCode AnalysisCode StructureSummaryKey Differences from the Previous CodeKey QuantLib FeaturesOutputOutput AnalysisAnalysis of Each Pricing MethodKey InsightsSummaryVisualization14.7 Conclusion
15. Credit Derivatives (CLN), Euribor–SOFR Swaption Calibrator, and Bond Curve Fitting with QuantLib
15.1 Credit-Linked Note (CLN) Valuation Using Boost and Eigen/Dense Libraries and Antithetic VariatesImplementationCode AnalysisCode Structure and ComponentsTermStructure ClassgenerateCorrelationMatrix FunctionCLNPricer ClassKey Insightsmain FunctionLibrariesKey ComputationsOutputAnalysis of the OutputSummaryFinal Suggestions for an Advanced ImplementationVisualization15.2 Implementing EuriborSOFRSwaptionCalibrator: Calibration of Models G2++ and Hull–White (Analytical and Numerical Prices) for Both Euribor and SOFR Swaptions, Using QuantLib and Boost LibrariesOverviewImplementationCode AnalysisKey Code ComponentsSwaption Volatility MatrixYield Curve ConstructionSwap DefinitionsModel Calibration (calibrateModel Function)Bermudan Swaption PricingPricing EnginesMain WorkflowSummaryOutputOutput AnalysisSOFR Swaption CalibrationG2 Model (Analytic)Hull–White Model (Analytic)Euribor Swaption CalibrationG2 Model (Analytic)Hull–White Model (Analytic)Bermudan Swaption PricingSOFR Bermudan SwaptionsEuribor 3M Bermudan SwaptionsKey ObservationsSummaryVisualization15.3 Fitted Bond Curve Using QuantLib 1.39 and Boost 1.89Key ConceptsImplementationCode AnalysisKey Functions and HelpersparRate FunctionprintOutput FunctionMain Program StructureOutputOutput AnalysisPractical Uses of the CodeYield Curve Construction and PricingRisk ManagementPortfolio OptimizationMarket Analysis and ForecastingRegulatory and Reporting RequirementsSpecific Applications by UserPotential Enhancements for Broader ApplicationsVisualization ToolsSummaryVisualization15.4 Conclusion
References
Index

Content preview from Advanced Quantitative Finance with Modern C++: Interest Rate Modeling and Advanced Derivatives

A. De La RosaAdvanced Quantitative Finance with Modern C++https://doi.org/10.1007/979-8-8688-2059-5_2

2. Random Number Generation (RNG)

Aaron De La Rosa¹

(1)

La Perla, Estado de México, Mexico

In quantitative finance and computational modeling, random number generation forms the backbone of simulation-based methods such as Monte Carlo pricing, risk analysis, and stochastic process modeling.

This chapter introduces the theory and practical implementation of random and quasi-random sequences in C++23, preparing readers to build high-performance simulation engines for complex financial instruments. Random number generation is a fundamental component in computational finance, underpinning a wide range of simulation techniques, ...

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Advanced Quantitative Finance with Modern C++: Interest Rate Modeling and Advanced Derivatives

by Aaron De La Rosa

2. Random Number Generation (RNG)

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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