Table Of Content

Mathematical Methods for Finance TheFrankJ.FabozziSeries FixedIncomeSecurities,SecondEditionbyFrankJ.Fabozzi FocusonValue:ACorporateandInvestorGuidetoWealthCreationbyJamesL.GrantandJamesA.Abate HandbookofGlobalFixedIncomeCalculationsbyDragomirKrgin ManagingaCorporateBondPortfoliobyLelandE.CrabbeandFrankJ.Fabozzi RealOptionsandOption-EmbeddedSecuritiesbyWilliamT.Moore CapitalBudgeting:TheoryandPracticebyPamelaP.PetersonandFrankJ.Fabozzi TheExchange-TradedFundsManualbyGaryL.Gastineau ProfessionalPerspectivesonFixedIncomePortfolioManagement,Volume3editedbyFrankJ.Fabozzi InvestinginEmergingFixedIncomeMarketseditedbyFrankJ.FabozziandEfstathiaPilarinu HandbookofAlternativeAssetsbyMarkJ.P.Anson TheGlobalMoneyMarketsbyFrankJ.Fabozzi,StevenV.Mann,andMooradChoudhry TheHandbookofFinancialInstrumentseditedbyFrankJ.Fabozzi InterestRate,TermStructure,andValuationModelingeditedbyFrankJ.Fabozzi InvestmentPerformanceMeasurementbyBruceJ.Feibel TheHandbookofEquityStyleManagementeditedbyT.DanielCogginandFrankJ.Fabozzi TheTheoryandPracticeofInvestmentManagementeditedbyFrankJ.FabozziandHarryM.Markowitz FoundationsofEconomicValueAdded,SecondEditionbyJamesL.Grant FinancialManagementandAnalysis,SecondEditionbyFrankJ.FabozziandPamelaP.Peterson MeasuringandControllingInterestRateandCreditRisk,SecondEditionbyFrankJ.Fabozzi,StevenV.Mann, andMooradChoudhry ProfessionalPerspectivesonFixedIncomePortfolioManagement,Volume4editedbyFrankJ.Fabozzi TheHandbookofEuropeanFixedIncomeSecuritieseditedbyFrankJ.FabozziandMooradChoudhry TheHandbookofEuropeanStructuredFinancialProductseditedbyFrankJ.FabozziandMooradChoudhry TheMathematicsofFinancialModelingandInvestmentManagementbySergioM.FocardiandFrankJ.Fabozzi ShortSelling:Strategies,Risks,andRewardseditedbyFrankJ.Fabozzi TheRealEstateInvestmentHandbookbyG.TimothyHaightandDanielSinger MarketNeutralStrategieseditedbyBruceI.JacobsandKennethN.Levy SecuritiesFinance:SecuritiesLendingandRepurchaseAgreementseditedbyFrankJ.FabozziandStevenV.Mann Fat-TailedandSkewedAssetReturnDistributionsbySvetlozarT.Rachev,ChristianMenn,andFrankJ.Fabozzi FinancialModelingoftheEquityMarket:FromCAPMtoCointegrationbyFrankJ.Fabozzi,SergioM.Focardi, andPetterN.Kolm AdvancedBondPortfolioManagement:BestPracticesinModelingandStrategieseditedbyFrankJ.Fabozzi, LionelMartellini,andPhilippePriaulet AnalysisofFinancialStatements,SecondEditionbyPamelaP.PetersonandFrankJ.Fabozzi CollateralizedDebtObligations:StructuresandAnalysis,SecondEditionbyDouglasJ.Lucas,LaurieS.Goodman, andFrankJ.Fabozzi HandbookofAlternativeAssets,SecondEditionbyMarkJ.P.Anson IntroductiontoStructuredFinancebyFrankJ.Fabozzi,HenryA.Davis,andMooradChoudhry FinancialEconometricsbySvetlozarT.Rachev,StefanMittnik,FrankJ.Fabozzi,SergioM.Focardi,andTeoJasic DevelopmentsinCollateralizedDebtObligations:NewProductsandInsightsbyDouglasJ.Lucas, LaurieS.Goodman,FrankJ.Fabozzi,andRebeccaJ.Manning RobustPortfolioOptimizationandManagementbyFrankJ.Fabozzi,PeterN.Kolm,DessislavaA.Pachamanova, andSergioM.Focardi AdvancedStochasticModels,RiskAssessment,andPortfolioOptimizationsbySvetlozarT.Rachev, StoganV.Stoyanov,andFrankJ.Fabozzi HowtoSelectInvestmentManagersandEvaluatePerformancebyG.TimothyHaight,StephenO.Morrell,and GlennE.Ross BayesianMethodsinFinancebySvetlozarT.Rachev,JohnS.J.Hsu,BilianaS.Bagasheva,andFrankJ.Fabozzi TheHandbookofMunicipalBondseditedbySylvanG.FeldsteinandFrankJ.Fabozzi SubprimeMortgageCreditDerivativesbyLaurieS.Goodman,ShuminLi,DouglasJ.Lucas, ThomasAZimmerman,andFrankJ.Fabozzi IntroductiontoSecuritizationbyFrankJ.FabozziandVinodKothari StructuredProductsandRelatedCreditDerivativeseditedbyBrianP.Lancaster,GlennM.Schultz,and FrankJ.Fabozzi HandbookofFinance:VolumeI:FinancialMarketsandInstrumentseditedbyFrankJ.Fabozzi HandbookofFinance:VolumeII:FinancialManagementandAssetManagementeditedbyFrankJ.Fabozzi HandbookofFinance:VolumeIII:Valuation,FinancialModeling,andQuantitativeToolseditedby FrankJ.Fabozzi Finance:CapitalMarkets,FinancialManagement,andInvestmentManagementbyFrankJ.Fabozziand PamelaPeterson-Drake ActivePrivateEquityRealEstateStrategyeditedbyDavidJ.Lynn FoundationsandApplicationsoftheTimeValueofMoneybyPamelaPeterson-DrakeandFrankJ.Fabozzi LeveragedFinance:Concepts,Methods,andTradingofHigh-YieldBonds,Loans,andDerivativesby StephenAntczak,DouglasLucas,andFrankJ.Fabozzi ModernFinancialSystems:TheoryandApplicationsbyEdwinNeave InstitutionalInvestmentManagement:EquityandBondPortfolioStrategiesandApplicationsbyFrankJ.Fabozzi Mathematical Methods for Finance Tools for Asset and Risk Management SERGIO M. FOCARDI FRANK J. FABOZZI TURAN G. BALI Coverimage:(cid:2)C Brownstock/Alamy Coverdesign:Wiley Copyright(cid:2)C 2013byJohnWiley&Sons,Inc.Allrightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin anyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,or otherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyright Act,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthrough paymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222 RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)646-8600,orontheWeb atwww.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothe PermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030, (201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbest effortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespecttothe accuracyorcompletenessofthecontentsofthisbookandspecificallydisclaimanyimplied warrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreated orextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceandstrategies containedhereinmaynotbesuitableforyoursituation.Youshouldconsultwitha professionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanyloss ofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental, consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,please contactourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outside theUnitedStatesat(317)572-3993orfax(317)572-4002. Wileypublishesinavarietyofprintandelectronicformatsandbyprint-on-demand.Some materialincludedwithstandardprintversionsofthisbookmaynotbeincludedine-booksor inprint-on-demand.IfthisbookreferstomediasuchasaCDorDVDthatisnotincludedin theversionyoupurchased,youmaydownloadthismaterialathttp://booksupport.wiley.com. FormoreinformationaboutWileyproducts,visitwww.wiley.com. ISBN978-1-118-31263-6(Hardcover) ISBN978-1-118-42008-9(ePDF) ISBN978-1-118-42149-9(ePub) PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 To the memory of my parents SMF To my wife, Donna, and my children, Patricia, Karly, and Francesco FJF To my wife, Mehtap, and my son, Kaan TGB Contents Preface xi AbouttheAuthors xvii CHAPTER1 BasicConcepts:Sets,Functions,andVariables 1 Introduction 2 SetsandSetOperations 2 DistancesandQuantities 6 Functions 10 Variables 10 KeyPoints 11 CHAPTER2 DifferentialCalculus 13 Introduction 14 Limits 15 Continuity 17 TotalVariation 19 TheNotionofDifferentiation 19 CommonlyUsedRulesforComputingDerivatives 21 Higher-OrderDerivatives 26 TaylorSeriesExpansion 34 CalculusinMoreThanOneVariable 40 KeyPoints 41 CHAPTER3 IntegralCalculus 43 Introduction 44 RiemannIntegrals 44 Lebesgue-StieltjesIntegrals 47 IndefiniteandImproperIntegrals 48 TheFundamentalTheoremofCalculus 51 vii viii CONTENTS IntegralTransforms 52 CalculusinMoreThanOneVariable 57 KeyPoints 57 CHAPTER4 MatrixAlgebra 59 Introduction 60 VectorsandMatricesDefined 61 SquareMatrices 63 Determinants 66 SystemsofLinearEquations 68 LinearIndependenceandRank 69 HankelMatrix 70 VectorandMatrixOperations 72 FinanceApplication 78 EigenvaluesandEigenvectors 81 DiagonalizationandSimilarity 82 SingularValueDecomposition 83 KeyPoints 83 CHAPTER5 Probability:BasicConcepts 85 Introduction 86 RepresentingUncertaintywithMathematics 87 ProbabilityinaNutshell 89 OutcomesandEvents 91 Probability 92 Measure 93 RandomVariables 93 Integrals 94 DistributionsandDistributionFunctions 96 RandomVectors 97 StochasticProcesses 100 ProbabilisticRepresentationofFinancialMarkets 102 InformationStructures 103 Filtration 104 KeyPoints 106 CHAPTER6 Probability:RandomVariablesandExpectations 107 Introduction 109 ConditionalProbabilityandConditionalExpectation 110