5-UML_面向对象技术PPT

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1、Chapter5Hedging§1.DeltaHedgingi.e.HedgingisameansofminimizingriskHedgingRule:Tohedgethesaleofoneoption,buysharesofstockConstructaportfolio:selloneoption,buysharesofstock,andaddjustenoughcashordebttomakethenetamountequaltozero1.1Hedging,DynamicProgramming,andaProofth

2、atBlack-ScholesReallyWorksinanIdealizedWorldProblem:Ifyouselloneoption,howdoyouhedgeit?ThevalueoftheportfolioisWewouldliketochosesothatd=0.ButtheBlack-ScholesequationstatesthatCiscashordebtanditsdifferentialisRecallourexpressionfordVfromChapter4:sowegetThenBychoosin

3、g,weseethatBut=0initially,sod=0,andt=0forallt0.Thus,nomatterthevalueofthestock,ST,attimeT,ourstockandcashpositionmustbalanceoutagainsttheoptionposition,whichtellsusthattheBlack-ScholespricemustbetheuniquecorrectpricefortheoptioninaworldwhereweknowStevolvesasageome

4、tricBrownianmotion,andwecanadjust(t)instantbyinstant.1.2WhytheForegoingArgumentDoesnotHoldintheRealWorldNotethatthestrategyweemployedrequiresustomakeaninfinitesimaladjustmentateveryinstantintime.ItrequiresthatweknowS(t0)attimet0andsimultaneouslyadjust(t0)bybuyingors

5、ellingstock.Wedonotbuyorselladiscreteamountofstock.Webuyorsellsharesofstockataratewhichisconstantlychanging.Itclearlyisnotpossibletotradeinthisfashionintherealworld.Second,notethatwedonotpayanyspreadortransactioncostswithourportfolioapproach.HedgingRule:Tohedgethesale

6、ofoneoption,buysharesofstockLetuslookatthisruleinaction.First,weneedawaytocompute.Fortunately,thatiseasyforthecaseofaEuropeancalloption.BydifferentiatingtheBlack-Scholesformula,onefindsthat=(d1).Notethatahedgeisnota“set-it-and-forget-it”hedge.Itmustbeconstantlyre

7、adjusted.ExampleSellcalloptionson1000sharesofstockABCwhereS0=50,X=40,r=0.05,=0.3,and=1year.ThusHence,Therefore,tohedgeoursaleofoptionson1,000sharesofstock,weshouldpurchase855sharesofstockABC.TimetoexpirationinweeksStockpricevalued1=(d1)NumberofsharesofstockChange

8、ofsharesofstock525011.0600.85548558555151.551/521.1640.877887823504950/521.00040.8413841-374950.549/521.10780.8660866254849.