CFA三级知识点必备：Derivatives and Currency Management_打印版.docx

CFA直）栗笺亩答BobHong1-272-27CoveredcallstrategyAninvestorcreatescoveredcallpositionbysellingacalloptiononastockthatisownedbytheoptionwriter.YieldenhancementThemostcommonmotivation.BywritinganOTMcalloption.Cashgenerationinanticipationoflimitedupsidemoves.ReducingapositionatafavorablepriceCoveredcallsmightbewritten,whenaninvestorholdsapositioninastockandintendstoreducethatholdinginthenearfuture.(TMcalloption)TargetpricerealizationHybridoftheprevioustwo.Callsarewrittenwithastrikepricejustabovethecurrentmarketprice.(OTMcalloption)CoveredcallstrategyCoveredcall:Inthisstrategy,someonewhoalreadyownssharessellsacalloptiongivingsomeoneelsetherighttobuytheirsharesattheexerciseprice.STSmax0,STX+CConclusion:WhenSTXrwehavemaximumgain5丁Sqmax0,STX+C=(&-$)*X+C=X金+CWhenS干0,wehavemaximumlossST-So-maxO,Sr-X+C=(O-)-O+C=C-SoBreakevenpointST=SLC4-27ProtectiveputstrategyAprotectiveput(alsocalledportfolioinsuranceorahedgedportfolio)isconstructedbyholdingalongpositionintheunderlyingsecurityandbuyingaputoption.Youcanuseaprotectiveputlimitthedownsideriskatthecostoftheputpremium,P0.Youwillseebythediagramthattheinvestorwillstillbeabletobenefitfromincreasesinthestock,sprice,butitwillbelowerbytheamountpaidfortheput,P0.Noticethatthecombinedstrategylooksverymuchlikeacalloption.5-27ProtectiveputstrategyProtectiveput:Someonesimultaneouslyholdsalongpositioninanassetandalongpositioninaputoptiononthatasset.Conclusion:WhenSX,theprofitisunlimited(STS°)+mx0,XSTPWhenSf,wehavemaximumloss(ST-SO)+max0,X-S一P=O-S+X-P=X-S-PooBreakevenpoint:Si=S计PVolatilitySmileWhatisvolatilitysmile?Volatilitysmileisaplotoftheimpliedvolatilityofanoptionasafunctionofitsstrikeprice.Thischapterdescribesthevolatilitysmilesthattradersuseinequityandforeigncurrencymarkets.827VolatilitySmileBasedontheput-callparitysoPmkt+SoqT=Cmkt+e-rT2Conclusions.ThedollarpricingerrorwhentheBlack-ScholesmodelisusedtopriceaEuropeanputoptionshouldbeexactlythesameasthedollarpricingerrorwhenitisusedtopricingaEuropeancalloptionwiththesamestrikepriceandtimetomaturity.TheimpliedvolatilityofaEuropeancalloptionisalwaysthesameastheimpliedvolatilityofaEuropeanputoptionwhenthetwohavethesamestrikepriceandmaturitydate.VolatilitySmileforForeignCurrencyOptionsTheimpliedvolatilityisrelativelylowforat-the-moneyoptions.Itbecomesprogressivelyhigherasanoptionmoveseitherintothemoneyoroutofthemoney.ImpliedvolatilityVolatilityincreasesasoptionsbecomesincreasinglyinthemoneyoroutofthemoney.OutoftheMoneyCallsOutoftheMoneyPutsstrikepriceAtteMoneyOptions10-27ReasonsforSmileinForeignCurrencyOptionsWhyareexchangeratenotIognormallydistributed?TwooftheContidionsforanassetpricetohavealognormaldistributionare:Thevolatilityoftheassetisconstant.Thepriceoftheassetchangessmoothlywithnojumps.Inpractice,neitheroftheseconditionsissatisfiedforanexchangerate.Thevolatilityofanexchangerateisfarfromconstant,andexchangeratesfrequentlyexhibitjumps(sometimesthejumpsareinresponsetotheactionsofcentralbanks).11-27VolatilitySmiles(skew)forEquityOptionsThevolatilityusedtopricealow-strike-priceoption(i.e.,adeepoutofthemoneyputoradeepinthemoneycall)issignificantlyhigherthanthatusedtopriceahigh-strike-priceoption(ie,adeepinthemoneyputoradeepoutofthemoneycall).ImpliedvolatilityOutoftheMoneyCallsOutoftheMoneyPutsstrikepriceAttheMoneyOptionsReasonsfortheSmileinEquityOptions1.everage(equitypriceTvolatility)Asacompany,sequitydeclinesinvalue,thecompanyzsleverageincreases.Thismeansthattheequitybecomesmoreriskyanditsvolatilityincreases.VolatilityFeedbackEffect(volatilityTequityprice)Asvolatilityincreases(decreases)becauseofexternalfactors,investorsrequireahigher(lower)returnandasaresultthestockpricedeclines(increases).Crashophobia(expectedequitypriceTimpliedvolatility)1987stockmarketcrash:higherpremiumsforputpriceswhenthestrikepriceslower.13-27StrategyRelatedtoVolatilitySkewAlongriskreversalcombineslongcallandshortputonthesameunderlyingwithsameexpiration.ForexampleIfatraderbelievesthatputimpliedvolatilityisrelativelytoohigh,comparedtothatforcalls,alongriskreversalcouldbecreatedbybuyingtheOTMcall(underpriced)andsellingtheOTMput(overpriced)forthesameexpiration.However,thiswouldcreatealongexposuretotheunderlying,whichcouldbeproblematic.14-27VolatilitySmileAlternativewaysofcharacterizingthevolatilitysmileThevolatilitysmileisoftencalculatedastherelationshipbetweentheimpliedvolatilityandKS0ratherthanastherelationshipbetweentheimpliedvolatilityandK.ArefinementofthisistocalculatethevolatilitysmileastherelationshipbetweentheimpliedvolatilityandKF0,whereFCistheforwardpirceoftheassetforacontractmaturingatthesametimeastheoptionsthatareconsidered.Anotherapproachtodefiningthevolatilitysmileisastherelationshipbetweentheimpliedvolatilityandthedeltaoftheoption.VolatilitySmileTradersallowtheimpliedvolatilitytodependontimetomaturityaswellasstrikeprice.Volatilitysurfacescombine