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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues PDF

351 Pages·2013·6.45 MB·English
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Mathematics of Financial Markets ForothertitlesintheWileyFinanceseries pleaseseewww.wiley.com/finance Mathematics of Financial Markets Financial Instruments and Derivatives Modeling, Valuation and Risk Issues Alain Ruttiens A John Wiley & Sons, Ltd., Publication Thiseditionfirstpublished2013 Copyright(cid:2)C 2013AlainRuttiens Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,in anyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbythe UKCopyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher. Wileypublishesinavarietyofprintandelectronicformatsandbyprint-on-demand.Somematerialincludedwith standardprintversionsofthisbookmaynotbeincludedine-booksorinprint-on-demand.Ifthisbookrefersto mediasuchasaCDorDVDthatisnotincludedintheversionyoupurchased,youmaydownloadthismaterialat http://booksupport.wiley.com.FormoreinformationaboutWileyproducts,visitwww.wiley.com. Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing thisbook,theymakenorepresentationsorwarrantieswiththerespecttotheaccuracyorcompletenessofthe contentsofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticular purpose.Itissoldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesand neitherthepublishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorother expertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. LibraryofCongressCataloging-in-PublicationDatatofollow AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN978-1-118-51345-3(hardback)ISBN978-1-118-51347-7(ebk) ISBN978-1-118-51348-4(ebk)ISBN978-1-118-51349-1(ebk) Setin10/12ptTimesbyAptara,Inc.,NewDelhi,India PrintedinGreatBritainbyCPIGroup(UK)Ltd,Croydon,CR04YY ToProf.DidierMarteau, withoutwhomthisbookwouldnotexist Contents ForewordbyA.G.MALLIARIS,LoyolaUniversity,Chicago xi MainNotations xiii Introduction xv PARTI THEDETERMINISTICENVIRONMENT 1 PriortotheYieldCurve:SpotandForwardRates 3 1.1 InterestRates,PresentandFutureValues,InterestCompounding 3 1.2 DiscountFactors 5 1.3 ContinuousCompoundingandContinuousRates 6 1.4 ForwardRates 8 1.5 TheNoArbitrageCondition 11 FurtherReading 12 2 TheTermStructureorYieldCurve 13 2.1 IntroductiontotheYieldCurve 13 2.2 TheYieldCurveComponents 15 2.3 BuildingaYieldCurve:Methodology 17 2.4 AnExampleofYieldCurvePointsDetermination 21 2.5 InterpolationsonaYieldCurve 21 FurtherReading 22 3 SpotInstruments 23 3.1 Short-TermRates 23 3.2 Bonds 24 3.3 Currencies 43 FurtherReading 45 4 EquitiesandStockIndexes 47 4.1 StocksValuation 47 4.2 StockIndexes 51 viii Contents 4.3 ThePortfolioTheory 52 FurtherReading 73 5 ForwardInstruments 75 5.1 TheForwardForeignExchange 75 5.2 FRAs 84 5.3 OtherForwardContracts 86 5.4 ContractsforDifference(CFD) 88 FurtherReading 89 6 Swaps 91 6.1 DefinitionsandFirstExamples 91 6.2 PriortoanIRSSwapPricingMethod 94 6.3 PricingofanIRSSwap 99 6.4 (Re)ValuationofanIRSSwap 102 6.5 TheSwap(Rates)Market 103 6.6 PricingofaCRSSwap 105 6.7 PricingofSecond-GenerationSwaps 108 FurtherReading 118 7 Futures 119 7.1 IntroductiontoFutures 119 7.2 FuturesPricing 123 7.3 FuturesonEquitiesandStockIndexes 127 7.4 FuturesonShort-TermInterestRates 130 7.5 FuturesonBonds 132 7.6 FuturesonCurrencies 138 7.7 Futureson(Non-Financial)Commodities 139 FurtherReading 144 PARTII THEPROBABILISTICENVIRONMENT 8 TheBasisofStochasticCalculus 147 8.1 StochasticProcesses 147 8.2 TheStandardWienerProcess,orBrownianMotion 150 8.3 TheGeneralWienerProcess 152 8.4 TheItoˆ Process 152 8.5 ApplicationoftheGeneralWienerProcess 153 8.6 TheItoˆ Lemma 155 8.7 ApplicationoftheItoˆ Lemma 156 8.8 NotionofRiskNeutralProbability 158 8.9 NotionofMartingale 159 Annex8.1: ProofsofthePropertiesofdZ(t) 161 Annex8.2: ProofoftheItoˆ Lemma 163 FurtherReading 164

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