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

《CFA三级知识点必备：Derivatives and Currency Management_打印版.docx》由会员分享，可在线阅读，更多相关《CFA三级知识点必备：Derivatives and Currency Management_打印版.docx（9页珍藏版）》请在三一办公上搜索。

1、CFA直）栗笺亩答BobHong1-272-27CoveredcallstrategyAninvestorcreatescoveredcallpositionbysellingacalloptiononastockthatisownedbytheoptionwriter.YieldenhancementThemostcommonmotivation.BywritinganOTMcalloption.Cashgenerationinanticipationoflimitedupsidemoves.ReducingapositionatafavorablepriceCoveredcallsmigh

2、tbewritten,whenaninvestorholdsapositioninastockandintendstoreducethatholdinginthenearfuture.(TMcalloption)TargetpricerealizationHybridoftheprevioustwo.Callsarewrittenwithastrikepricejustabovethecurrentmarketprice.(OTMcalloption)CoveredcallstrategyCoveredcall:Inthisstrategy,someonewhoalreadyownsshare

3、ssellsacalloptiongivingsomeoneelsetherighttobuytheirsharesattheexerciseprice.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(alsocalledportfolioinsuranceo

4、rahedgedportfolio)isconstructedbyholdingalongpositionintheunderlyingsecurityandbuyingaputoption.Youcanuseaprotectiveputlimitthedownsideriskatthecostoftheputpremium,P0.Youwillseebythediagramthattheinvestorwillstillbeabletobenefitfromincreasesinthestock,sprice,butitwillbelowerbytheamountpaidfortheput,

5、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-PooBr

6、eakevenpoint:Si=S计PVolatilitySmileWhatisvolatilitysmile?Volatilitysmileisaplotoftheimpliedvolatilityofanoptionasafunctionofitsstrikeprice.Thischapterdescribesthevolatilitysmilesthattradersuseinequityandforeigncurrencymarkets.827VolatilitySmileBasedontheput-callparitysoPmkt+SoqT=Cmkt+e-rT2Conclusions

7、.ThedollarpricingerrorwhentheBlack-ScholesmodelisusedtopriceaEuropeanputoptionshouldbeexactlythesameasthedollarpricingerrorwhenitisusedtopricingaEuropeancalloptionwiththesamestrikepriceandtimetomaturity.TheimpliedvolatilityofaEuropeancalloptionisalwaysthesameastheimpliedvolatilityofaEuropeanputoptio

8、nwhenthetwohavethesamestrikepriceandmaturitydate.VolatilitySmileforForeignCurrencyOptionsTheimpliedvolatilityisrelativelylowforat-the-moneyoptions.Itbecomesprogressivelyhigherasanoptionmoveseitherintothemoneyoroutofthemoney.ImpliedvolatilityVolatilityincreasesasoptionsbecomesincreasinglyinthemoneyor

9、outofthemoney.OutoftheMoneyCallsOutoftheMoneyPutsstrikepriceAtteMoneyOptions10-27ReasonsforSmileinForeignCurrencyOptionsWhyareexchangeratenotIognormallydistributed?TwooftheContidionsforanassetpricetohavealognormaldistributionare:Thevolatilityoftheassetisconstant.Thepriceoftheassetchangessmoothlywith

10、nojumps.Inpractice,neitheroftheseconditionsissatisfiedforanexchangerate.Thevolatilityofanexchangerateisfarfromconstant,andexchangeratesfrequentlyexhibitjumps(sometimesthejumpsareinresponsetotheactionsofcentralbanks).11-27VolatilitySmiles(skew)forEquityOptionsThevolatilityusedtopricealow-strike-price

11、option(i.e.,adeepoutofthemoneyputoradeepinthemoneycall)issignificantlyhigherthanthatusedtopriceahigh-strike-priceoption(ie,adeepinthemoneyputoradeepoutofthemoneycall).ImpliedvolatilityOutoftheMoneyCallsOutoftheMoneyPutsstrikepriceAttheMoneyOptionsReasonsfortheSmileinEquityOptions1.everage(equitypric

12、eTvolatility)Asacompany,sequitydeclinesinvalue,thecompanyzsleverageincreases.Thismeansthattheequitybecomesmoreriskyanditsvolatilityincreases.VolatilityFeedbackEffect(volatilityTequityprice)Asvolatilityincreases(decreases)becauseofexternalfactors,investorsrequireahigher(lower)returnandasaresultthesto

13、ckpricedeclines(increases).Crashophobia(expectedequitypriceTimpliedvolatility)1987stockmarketcrash:higherpremiumsforputpriceswhenthestrikepriceslower.13-27StrategyRelatedtoVolatilitySkewAlongriskreversalcombineslongcallandshortputonthesameunderlyingwithsameexpiration.ForexampleIfatraderbelievesthatp

14、utimpliedvolatilityisrelativelytoohigh,comparedtothatforcalls,alongriskreversalcouldbecreatedbybuyingtheOTMcall(underpriced)andsellingtheOTMput(overpriced)forthesameexpiration.However,thiswouldcreatealongexposuretotheunderlying,whichcouldbeproblematic.14-27VolatilitySmileAlternativewaysofcharacteriz

15、ingthevolatilitysmileThevolatilitysmileisoftencalculatedastherelationshipbetweentheimpliedvolatilityandKS0ratherthanastherelationshipbetweentheimpliedvolatilityandK.ArefinementofthisistocalculatethevolatilitysmileastherelationshipbetweentheimpliedvolatilityandKF0,whereFCistheforwardpirceoftheassetfo

16、racontractmaturingatthesametimeastheoptionsthatareconsidered.Anotherapproachtodefiningthevolatilitysmileisastherelationshipbetweentheimpliedvolatilityandthedeltaoftheoption.VolatilitySmileTradersallowtheimpliedvolatilitytodependontimetomaturityaswellasstrikeprice.Volatilitysurfacescombinevolatilitys

17、mileswiththetimetomaturityandK%Impliedvolatilitytendstobeanincreasingfunctionofmaturitywhenshort-datedvolatilitiesarehistoricallylow.Volatilitytendstobeadecreasingfunctionofmaturitywhenshort-datedvolatilitiesarehistoricallyhigh.16-27VolatilityTermStructureandVolatilitySurfaceImpliedvolatilityonthez-

18、axis;maturity(x-axis);andKS0(y-ais).17-27UsingDerivativestoAlteringAssetAllocationAlteringassetallocationbetweenequityanddebtwithfuturesStep1:CalculatethereallocatingamountStep2:Toreallocateanamountfromequitytobonds:Removeallsystematicriskfromtheposition(beta=O)byshortingequityfutures.Adddurationtot

19、heposition(BPVO)bygoinglongbondfutures.Step3:Toreallocateanamountfrombondstoequity:Removealldurationfromtheposition(BVP=O)byshortingbondfutures.Addsystematicrisktotheposition(betaO)bygoinglongequityfutures.equityCashBeta=OBPV=Obonds19-27UsingDerivativestoAlteringAssetAllocationAmendingportfoliobeta&

20、SyntheticstockpositionsNumberofcontractsJalg“PPfPmultiplierEquity/EquityMid-capequityB；：ToSmalMapEquityequityEquity/DebtCashBeta=ObondsBPV=O20-27VarianceSwapVarianceswapspayoffsarebasedonvarianceratherthanvolatility(standarddeviation).Theseproductsaretermedswapsastheyhavetwocounterparties,onemakinga

21、fixedpaymentandtheothermakingavariablepaymentThefixedpaymentistypicallybasedonimpliedvolatility2(impliedvariance)overtheperiodandisknownattheinitiationoftheswap,thisisreferredtoasthevariancestrikeThevariablepaymentisunknownatswapinitiationandisonlyknownatswapmaturity.Itistheactualvarianceoftheunderl

22、yingassetoverthelifeoftheswapandisreferredtoasrealizedvariance.22-27VarianceSwapThefeaturesofvarianceswapnoexchangeofnotionalprincipalandnointerimsettlementperiods.Withavarianceswap,thereisasinglepaymentattheexpirationoftheswapbasedonthedifferencebetweenactualandimpliedvarianceoverthelifeOftheswaptn

23、oumaInemelttesgnolnotionalvariance(2-Ktnoumatnemelttesgnol=notionalD萌，%(notionalvega=notionalvarianceK223-27VarianceSwapTheMark-to-MarketvalueofvarianceswapThevalueofavarianceswapiszeroatinitiation,butovertime,theswapwilleithergainorlosevalueasrealizedandimpliedvolatilitydiverge.Consideraone-yearswa

24、pwherethreemonthshaveelapsedsinceinception,theMtMvalueoftheswapcanbecalculatedasfollow:VarianceSwapTheMark*to-MarketvalueofvarianceswapConsideraone-yearswapwherethreemonthshaveelapsedsinceinception,theMtMvalueoftheswapcanbecalculatedasfollow:Step1:Computeexpectedvarianceatmaturity(thetime-weightedav

25、erageofrealizedvarianceandimpliedvarianceovertheremainderoftheswapslife).tyituramtoecnairavdetceExp=dK(?TxTLr)Step2:Computeexpectedpayoffatswapmaturity:ffyoaPdetceExp=lanoiotnecnairav(tyituramtoecnairavdetcexpe-Step#flAPc)payoffatmaturitybacktothevaluationdate.25-27Example1.ukeAmos,anequityfundmanag

26、er,haspurchasedaone-yearvarianceswapontheS&P500withveganotionalof$100,000andastrikeof20%.NinemonthshavepassedandtheS&Phasrealizedavolatilityof21%.Thestrikepriceforathree-monthvarianceswapatthistimeisquotedat22%,andthethree-monthinterestrateis2%.Computethecurrentvalueoftheswap.2627ExampleCorrectAnswe

27、rStep1:Computetheexpectedvarianceatmaturity:932izx+222C=330.75+121=451.751212Step2:Computetheexpectedpayoffatmaturity:Variancenotional=Vega犬ional=$1欺00=Expectedpayoffatmaturity=(2-K2)variancenotional,whereK2=202=400expectedpayoffatmaturity=(451.75-400)$2,500=$129,375Step3:Discountexpectedpayofffrommaturitytothevaluationdate(3months):Unannualizetheinterestrate=2%312v=0.5%Currentvalueofswap=$/客=$128,731Thisisagaintothepurchaser(long)andalosstotheseller(short).