FRM一级百题巅峰班培训课件：估值与风险模型（打印版）

2021FRMPartI百题巅峰班估值与风险模型2021年3月4. ValuationandRiskModelsBondReplication重要知识点Lawofoneprice:absentconfoundingfactors(e.g.,liquidity,financing,taxes,creditrisk),identicalsetsofcashflowsshouldsellforthesameprice.Whilethe lawofonepriceisintuitivelyreasonable,itsjustificationrestsonastrongerfoundation.Itturnsoutthatadeviationfromthelawofonepriceimpliesthe existenceofanarbitrageopportunity,thatis,atradethatgeneratesprofitswithoutanychanceoflosingmoney.基础题Q-1.YouhavebeenaskedtocheckforarbitrageopportunitiesintheTreasurybondmarketbygehflowsofeledbondshehflowsofbinationsofotherbonds.Ifa1-yearnbondispricedtD96.12da1-yearbondpayinga10%nem-annualyispricedtD106.20,tdbeepriceofa1-yearTreasurybondthatpaysacouponof8%semiannually?USD98.10B. USD101.23C. USD103.35D. USD104.18CouponPrice27/894.4041/2？61/4101.30.efoowingablegiveseprisofooutofeSynotesfortont30,2008.lenoteswilelyoneyearleronAugust30,2009.Assumesemi-annuaCouponPrice27/894.4041/2？61/4101.30ApproxielytuIdbeeprieofe41/2Synote?A. 99.20B. 99.40C. 97.71D. 100.20YTM重要知识点YieldtoMaturity► TheYTMofabondisthe singlediscountrateatwhichallcashflowsofthebondarediscountedandsummeduptothemarketpriceCouponEffect► Upard-sloping,eyeldoyfalssenr► Downward-slopingtrend,theyieldtomaturityrisesasthecouponrises.基础题Q-3. Aneight(8)-yearbondwithacurrentpriceof$975.00anannualcouponof6.0%.tisebond'sield-to-maturity()?A. B. 6C. 6.89%D. . hofefolowingsnecesarilyEtabond'sield-to-maturity()EXCEPAbondthatsellsatapremiumtoparhasayield(YTM)thatislessthanitscouponrateAondtstadistoparhasayield(YM)tisgreaternisrateTheyield(YTM)ofazero-couponbondequalsthe spot(zero)rateofthebond'smaturityIfthesametermstructureofspotratesappliestotwobondswithidenticalmaturities,thebondwiththehigheryield(YTM)isasuperiorinvestmentDuionandDVOl重要知识点Duration► MacaulayDuration ModifiedDurationDVOl&DD► DVOl"'lbps► DV01=DDX0.0001PortfolioDuration► Dportfolio忆XD;基础题Q-5.Atradingportfolioconsistsoftwobonds,AandB.Bothhavemodifieddurationof3sandfacevalueofUSO1000,butAisazero-couponbondanditscurrentpriceisUSO900,andbondBpaysannualcouponsandispricedatpar.WhatdoyouexpectwillhappentothemarketpricesofAandBiftherisk-freeyieldcurvemovesupby1basispoint?Bothbondpriceswillmoveupbyroughlythesameamount.Bothbondpriceswillmoveup,butbondBwillgainmorethanbondA.Bothbondpriceswillmovedownbyroughlyequalamounts.Bothbondpriceswillmovedown,butbondBwilllosemorethanbondA.Q-6. WhichofthefollowingassumptionsaremadewhenusingDVOlasameasureofinterestraterisk?一xuebajun888sChangesintheinterestratesaresmall.Theyieldcurveisflat.Ill. Changestotheyieldcurveareparallel.IV.Theyieldcurveisdownwardsloping.IandIllIandIIIandIVIIandIllBondValue(USD)ModifiedDuration14,000,0007.522,000,0001.633,000,0006.041,000BondValue(USD)ModifiedDuration14,000,0007.522,000,0001.633,000,0006.041,000,0001.3A. USD-41,000B. USD-52,500C. USD-410,000USD-525,000PriceApproximation,EffectofConvexity重要知识点Theactual,exactpricep=f(y。+tiy)Thedurationestimate:P=yThedurationandconvexityestimate:P=—。 1 (y+-CB2飞OO

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WhichofthefollowingisTRUE?RiIfaconsol(perpetual)bondwitha$100facevaluepaysa3.0%couponinperpetuityandtheyieldistheconsol'spriceis$60anditsmodifieddurationis20RiSinceaBARBELLbondportfoliohasgreaterconvexitythanaBULLET,thebarbellalwaysoutperformsDuration,convexityandDVOlareall(each)increasingwithmaturityPortfoliodurationisweightedaverageofindividual(component)durationsbutportfolioconvexityisnotaweightedaverageofindividualconvexitiesQ-10.BondsissuedbytheXYZCorp.arecurrentlycallableatparvalueandtradeclosetopaThebondsmaturein8yearsandhaveacouponof8%.Theyieldonthe双Zbondsis175basispointsover8-yearSuryrit,derurytieldhsanormal,risingshape.IfeieldonbondsarableotheXYZbonddecasharpl,eZbondswiltikelyhibit:NegativeconvexityIncreasingmodifieddurationIncreasingeffectivedurationPositiveconvexityEffectiveDuration&EffectiveConvexity重要知识点EffectiveDuration2XP► 2XPEffectiveConvexityX/'J.y► EffectConvexity=P_凡-2X/'J.y4.5.2. 基础题Q-11. An8-year5%couponbondwithatparvalueof100iscurrentlytradingatapriceof94.65.Thepriceofthisbondrisesto96.35wheninterestratesfallby30basispointsandfallsto92.75wheninterestratesriseby30basispoints.Theeffectivedurationofthisbondisclosestto:A. B. 6.34C. 6.69D. . AportfolioruseshervaluationlotiethevalueofabondportfolioatUSD125.482million.Thetermstructureisflat.Usingthesamemodel,she estimatesthatthevalueoftheportfoliowouldincreasetoUSO127.723millionifallinterestratesfellby30basispointsandwoulddecreasetoUSO122.164millionifallinterestratesroseby30basispoints.Usingtheseestimates,theeffectivedurationofthebondportfolioisclosestto:A. 7.38B. 8.38C. 14.77D. 16.76ValueinUSDperUSD100facevalueInterestRateLevelCallableBondCallOption4.98%102.078482.08715.00%101.611582.05015.02%100.921892.0131Q-13.Ariskmanagerisevaluatingthepricesensitivityofaninvestment-gradecallablebondusingthefirm'svaluationsystem.ThetablebelowpresentsiValueinUSDperUSD100facevalueInterestRateLevelCallableBondCallOption4.98%102.078482.08715.00%101.611582.05015.02%100.921892.0131Theconvexityofthecallablebondcanbeestimatedas:A. -55698B. -54814C. -5.5698D. -5.4814BulletversusBarbellPortfolio重要知识点Barbellbenefitsmorefrominterestratevolatilitythandoesthebulletportfolio.Thebarbellhasgreaterconvexitythanthebulletbecausedurationlinearlywithmaturitywhileconvexityincreaseswiththesquareofmaturity.基础题Q-14.Afixed-incomeportfoliomanagercurrentlyholdsabullet7-yearUSTreasurypositionwithUSO60millionfacevalue.Themanagerwouldliketocreateacostmatchingbarbellportfoliobypurchasingacombinationofa2-yearTreasuryanda15-yearTreasurythatwouldhavethesamedurationasthe7-yearUSTreasuryposition.ThedataforthethreeUSTreasuriesarelistedbelow:MaturityPriceDuration2Years100.9721.9387Years106.4436.27215Years122.17511.687BACDWeightof2-YearTreasuryWeightof15-YearTreasury14.22%85.78%44.46%55.54%55.54%44.46%85.78%14.22%WhichofthefollBACDWeightof2-YearTreasuryWeightof15-YearTreasury14.22%85.78%44.46%55.54%55.54%44.46%85.78%14.22%Q-15.Assumetwobondportfolioswithidenticalyieldsof5.0%.Oneisabulletportfoliowithdurationequalto9;theotherisabarbellportfoliowithdurationalsoequalto9.Howdotheirconvexitiescompare?Barbellconvexityislessthan(<)bullet'sconvexityBarbelxityisgreatern)bul'sxityConvexitsesimilarNeedmoreinformation. IfeisaEparaelshiftneyieldcurve,howdoestheirperformancecompare?BarbelloutperformsbulletBulletoutperformsbarbelleorsimilarNeedmoreinformationKeyRate重要知识点Thekeyrateshifttechniqueisanapproachtononparallelshiftsintheyieldcurve,whichisallowsforchangesinallratestobedeterminedbychangesfromselectedkeyrates.erateofagivenysdolelybyistkey-rShiftsinthekey-ratesaredeclinelinearly.基础题Q-17.Youareusingkeyrateshiftstoanalyzetheeffectofspotratechangesonbondprices.Supposethe10-yearspotratehasincreasedby10basispointsandthisshockdecreaseslinearlytozeroforthe20-yearspotrate.Whatistheeffectofthisshockonthe14-yearspotrate?IncreaseofObasispointsIncreaseof4basispointsIncreaseof6basispointsIncreaseof10basispointsQ-18. Usingkeyratesof2-year,5-yea7-yeaand20-yearexposuresassumesallofthefoowingttthe:2-yearratewillaffectthe5-yearrate7-yearratewillaffectthe20-yearrate5-yearratewillaffectthe7-yearrate2-yearratewillaffectthe20-yearrateUsethefollowinginformationtoanswerthefollowingtwoquestions:ValueInitialvalue25.115842-yearshift25.116815-yearshift25.1198410-yearshift25.1398430-yearshift25.01254efoowingbleprovideseinitialpriceofaC-stripdispresentvaluerappValueInitialvalue25.115842-yearshift25.116815-yearshift25.1198410-yearshift25.1398430-yearshift25.01254Q-19. Whatisthekeyrate'01fora30-yearshift?A. -0.058B. 0C. 0.1030.158Q-20. Whatisthekey-ratedurationfora30-yearshift?A. -4.57B. 15.80C. 38.60D. 41.13ValueOptionUsingaBinomialTree重要知识点f=e-rt[pfu+(1—p)fctl!.ert>t_d!.p=— u=顽 d=u-d ushdividendsdk:replacetwth-q)twhereqsthedividendyieldofastockorstockindex.基础题Commontextforfollowingtwoquestions:AriskmanagerforBankXYZ,Markisconsideringwritinga6monthAmericanputoptiononanon-dividendpayingstockABC.ThecurrentstockpriceisUSO50andthestrikepriceoftheoptionisUSO52.Inordertofindtheno-arbitragepriceoftheoption.Markusesatwo-stepbinomialtree.Thekpriengoupordownby20%hperiod.ark'svewisekpriehasn80%probabityofgoingupherodda20%probabiliyofgoingdown.eannualri-frees1%wthontinuousmpounding.. tiserisk-neutralprobabiltyofekpriegoingupinaeA. 34.5%B. 57.6%C. 65.5%80.0%Q-22.Marthausedathree-stepbinomialmodeltovaluea(long-term)putoptionwiththreeyearstomaturity;i.e.,eachtimestepisoneyear.Whiletherisk-freerateis4.0%,theunderlyingasset'svolatilityis28.480%.Usingtheseassumptions,shewaspleasantlysurprisedtoseethattherisk-neutralprobabilityofupmovementinhermodelas50.0i.e.,p=d=0.50.However,sheforgottoincludetheassumptionthattheassetwillpayacontinuousdividendof2.0%perannum.Byhowmuchwillthisassumptionchangehermodel'srisk-neutralprobab山tyofadown(d)movement?Decreaseprobabilityofdownmovement,(d),byaboutpercentagepointsDecreaseprobabilityofdownmovement,(d),byaboutpercentagepointsIncreaseprobatyofdownmovement,(d),byabout3.57%percentagepointsIncreaseprobabilityofdownmovement,(d),byabout10.79%percentagepointsQ-23.Thecurrentpriceofastockis$10,anditisknownthatattheendofthreemonthsthestock'spricewillbeeither$13or$7.Therisk-freerateis4%perannum.Whatistheipliednoarbitragepriceofah(T=0.25)nloptiononstockwithastrikepriceof$10?(Note:thisdoesnotincludeanassumptionaboutthestock'svolatility).A. $0.97B. $1.28C. $1.53D. $1.65Q-24. AtraderhasanAmericanputoptionwithstrikepriceof$50.Theunderlyingassetiskwithatprieof$40.singnone-stepbinomialeoevaluateeoption.eekprielgoupordownby$8in6,eri-freerateis6.,whatisthevalueofthisAmericanput?USD8.19USD8.45USD10.00USD10.32.Akwithatprieof$32dvoltlityof15%paysadiidendof2.0%perm(htinuous).eriksrateis2.0%.euseatelepbinomiallopriennputoptionwithoneyearoexpiration;i.e.,stepisonemonth.Whatistherisk-neutralprobatyofadownmovement(1-p)?A. 0.4646B. 0.4962C. 0.5108D. 0.5375Q-26.Whatistherisk-neutralprobabilityofanupmovement(p)inatwo-stepbinomialmodelusedovaluenrerian-styeputoptiononakhavolatilityof38%whentherisk-freerateis4.0%;i.e.,eachstepisoneyear?A. 0.411B. 0.459C. 0.503D. 0.548Q-27. Astockwitha(continuous)dividendyieldof1.0%hasacurrentpriceof$30andvoltliyof22%.euseapbinomiallovaluearnylecalloptiononthestock;i.e.,eachtimestepisoneyear.Therisk-freerateis3.0%.Inthebinomial,tsekpricetenodehelotkpriA. $14.78B. $19.32C. $22.49D. $25.25. etprieofanon-dividendpayingkis$75.eannualvoltlityofks18.25,dettinuouslydriskfreeinterestrateis5%.A3-yearEuropeancalloptionexiststhathasastrikepriceof$90.Assumingthatthepriceofthestockwillriseorfallbyaproportionalamounteachyear,andthattheprobabilitythatthestockwillriseinanyoneyearis60%,whatisthevalueofthenalloption?A. $22.16B. $12.91C. $3.24D. $7.36. e0kindexisy,300.0dhasavoltityof40.0%dadividendyeldof1.0%.erikfreerateis3.%.IfeeployapbinomialwhichisnearesttothevalueofaEuropean6-monthcalloptionwithastrikepriceof7,500.0;i.e.,thecallisout-of-the-moneybyexactly200?A. $714.77B. $734.20C. $756.93D. $777.51Black-Scholes-MertonModel重要知识点Black-Scholes-Mertonmodelonanon-dividend-payingstockc=N(—TN(d2),Ap=TNN),AlnS/K)+(r+u2/d1= 叭厅屯=d1—对平Black-Scholes-Mertonmodelonadividend-payingstock► c=STN()—TNd刃RulesforExercisingAmericanOption► Itsneveroptialoenericanalonanon-dividend-payingbeforeitsexpirationdate.► Americanputscanbeoptimallyexercisedearlyiftheyaresufficientlyin-the-money.► AnAmericancallonadividend-payingstockmaybeexercisedearlyifthedividendexceedstheamountofforgoneinterest.基础题. hihofefoowingsistttheyeofericanoptions?Itisalsoptialoexercenerianaloptiononanon-dividend-payingbeforetheexpirationdate.ItcanbeoptimaltoexerciseanAmericanputoptiononanon-dividend-payingstockarl.ItcanbeoptimaltoexerciseanAmericancalloptiononanon-dividend-payingstockearly.ItisneveroptimaltoexerciseanAmericanputoptiononanon-dividend-payingstockbeforetheexpirationdate.. hofefolowingisnot n mptionofeBlck-Shols optionspricimodel?Thepriceoftheunderlyingmovesinacontinuousfashion.Theinterestratechangesrandomlyovertime.Theinstantaneousvarianceofthereturnoftheunderlyingisconstant.arsepefect,.e.talse aloed,therearenonsoraxes,andmarketsoperatecontinuously.Q-32. Thecurrentpriceofastockis$25.Aputoptionwitha$20strikepricethatexpiresinsixmonthsisavailable.N(d1)=0.9737andN(d2)=0.9651.lftheunderlyingstockexhibitsanannualstandarddeviationof25%,andthecurrentcontinuouslycompoundedrisk-freerateis4.25%,theBlack-Scholes-Mertonvalueoftheputisclosestto:A. $0.01B. $0.03C. $0.33D. $0.36Q-33.AEuropeancalloptionhasatimetomaturityofsixmonthsonastockwitha2%dividendyield.Thecurrentstockandstrikepricesareboth$50.Thevolatilityofthestockis18%perannum.Theriskfreerateis4%.Whatisthepriceofthecalloption?A. $2.00B. $2.75C. $3.08D. $3.16Q-34.Aone-yearEuropeancalloptionontheEurohasanexercisepriceof$1.40whenthecurrentexchangerateisEUR/USO$1.34.Therisk-freerateintheUnitedStatesis4%andtheEurozonerisk-freerateis3%.Thevolatilityofthespotexchangerateis30%perannum.Whatisthepriceofthecalloption?A. $0.136B. $0.297C. $0.355D. $0.425Q-35.WhatisthepriceofathreemonthEuropeanputoptiononanon-dividend-payingstockwithastrikepriceof$50whenthecurrentstockpriceistherisk-freeinterestrateis10%perannum,andthevolatilityis30%perannum.A. 2.37B. 2.48C. 2.25D. 2.63Q-36.EachofthefollowingisanunderlyingassumptionofthebasicBlack-ScholesoptionpricingmodelEXCEPT:ThestockpricefollowsageometricBrownianmotion(GBM)whichisacontinuousprocesswithout一：xuebajun888sThecontinuouslycompoundedrateofreturnonthestockisnormallydistributed,suchthatthedistributionofthefuturestockpriceislognormalTheexpectedrateofreturnonthestock(u)andvolatility(sigma)areconstantTheexpectedreal-world(risky)rateofreturnonthestockisknownandthevalueoftheoptionisanincreasingfunctionofthisrateofreturnQ-37. TheCFOatanon-dividend-payingfirmasksafinancialanalysttoevaluateaplanbythefirmtograntstockoptionstoitsemployees.Thefirmhas60millionsharesoutstanding.Undertheproposal,thefirmwouldissue3millionemployeestockoptions,witheachoptiontheholdertherighttobuyoneshareofthefirm'sstockatastrikepriceofUSD70.Theemployeestockoptionswouldexpirein4years.Afour-yearcalloptiononthestockwiththesamestrikepriceiscurrentlyvaluedatSGD4.39usingtheBlack-Scholes-Mertonmodel.Whichofthefollowingisthebestestimateofthepriceofoneemployeestockoptionassumingthatthecalloptioniscorrectlypriced?SGD3.97SGD4.18SGD4.39SGD4.45GreekLetters互要知识点1001垃1001垃釭百,.1tIO，纽I四竺匹竺九窃严 碗肛九次函沁巧aJ

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110► Deltaofanat-the-moneycalloptioniscloseto0.5.Deltamovestolasthecallgoesdeepinthemoney.Itmovestozeroasthecallgoesdeepoutofthemoney.► Gammaishighestforshort-termat-the-moneyoptions.► Vegaishighestforlong-termat-the-moneyoptions.► RhoissimilartoDelta.► asevaritionnoptonvaluedueoepassageof.ssotimedecay.Unlikeotherfactors,however,themovementinremainingmaturityisperfectlypredictable.Timeisnotariskfactor.基础题Q-38. Ifriskisdefinedasapotentialforunexpectedloss,whichfactorscontributetotheriskofashortcalloptionposition?DeltVega,RhoVega,RhoDeltVega,Gamma,RhoDeltVega,Gamma,Theta,RhoQ-39. Youaregiventhefollowinginformationaboutacalloption:Timetomaturity=2yearsContinuousrisk-freerate=4%Continuousdividendyield=1%N(d1)=0.64alculeedeltaofthisoption.A. -0.64B. 0.36C. 0.63D. 0.64Q-40. Mr.BlackhasbeenaskedbyaclienttowritealargeputoptionontheS&P500index.eoptionhasnerciepriedaturitytisnotailabeforoptionsonexchanges.He,therefore,hastohedgethepositiondynamically.WhichofthefoowingsteriskofhispositionenotenehisportfoiodeltaneutralbyhortingindexfutureseisatpositioninnP500futuresttlehisportfioinsensitivetobothsmallandlargemovesintheS&P500.AgpositioninadoptiononeP500wilhelphedgeevoltlityriskoftheoptionhehaswritten.oehishedgedportfoiogammaneutral,heneedsoepositionsinoptionswellasfutures.Q-41.PortfoliomanagerSallyhasapositionin100optioncontractswiththefollowingpositionGreeks:theta=+25,000;vega=+330,000andgamma=-200;ie.,positivetheta,positivevegaandnegativegamma.Whichofthefollowingadd巾onaltrades,utilizinggenerallyat-the-money(ATM)options,willneutralize(hedge)theportfoliowithrespecttotheta,vegaandgamma?Sellshort-termoptions+selllong-termoptions(allroughlyat-the-money)lmoptions+buylong-termoptions')yort-termoptions+llong-termoptions(')yort-termoptions+buymoptions()Q-42. Whichofthefollngstatementsiscorrect?Therhoofacalloptionchangeswiththepassageoftimeandtendstoapproachosexpiration,butthisisnoteforerhoofputoptions.aisalsnegativeforgalsdlongputsdpositivefortalsshortputs.Ionly.IIonlyIandIINeitherQ-43. WhichofthefollowingstatementsistrueingoptionsGreeks?Thetatendstobelargeandpositivewhenbuyingat-the-moneyoptions.Gammaisgreatestforin-the-moneyoptionswithlongmaturities.Vegaisgreatestforat-the-moneyoptionswithlongmaturities.Deltaofdeepin-the-moneyputoptionstendstoward+1.Q-44. Whichpositionismostrisky?Gamma-negative,delta-neutralGamma-positive,delta-positiveGamma-negative,delta-positiveGamma-positive,delta-neutralQ-45.AportfolioofstockAandoptionsonstockAiscurrentlydeltaneutral,buthasapositivema.Whichofthefollowingactionswillmaketheportfoliobothaandgammaneutral?BuycalloptionsonstockAandsellstockASellcalloptionsonstockAandsellstockABuyputoptionsonstockAandbuystockASellputoptionsonstockAandsellstockAQ-46.WhichofthefollowingchoiceswilleffectivelyhedgeashortcalloptionpositionthatexhibitsadeltaofO.5?Selltwosharesoftheunderlyingforeachoptionsold.Buytwosharesoftheunderlyingforeachoptionsold.Sellthenumberofsharesoftheunderlyingequaltoone-halftheoptionssold.Buythenumberofsharesoftheunderlyingequaltoone-halftheoptionssold.Q-47.ThecurrentstockpriceofacompanyisUSO80.ArimanaismonitoringcallandputoptionsonthestockwithexercisepricesofUSO50and5daystomaturity.WhichofthesescenariosismostlikelytooccurifthestockpricefallsbyUSO1?ScenarioCallValuePutValueADecreasebyUSO0.94IncreasebyUSO0.08BDecreasebyUSO0.94IncreasebyUSO0.89CDecreasebyUSO0.07IncreasebyUSO0.89DDecreasebyUSO0.07IncreasebyUSO0.08ScenarioAScenarioBScenarioCScenarioDQ-48.WandaZheng(FRM)isresponsiblefortheoptionsdeskinaLondonbank.engisconcernedabouttheimpactofdividendsontheoptionsheldbytheoptionsdesk.easksyoutoassesswhichoptionsarethemostsensitivetodividendpayments.WhatwouldbeyouranswerifthevalueoftheoptionsisfoundbyusingtheBlack-Scholesmodeladjustedfordividends?Everythingelseequal,out-of-the-moneycalloptionsexperiencealargerdecreaseinvaluethanin-the-moneycalloptionsasexpecteddividendsincrease.Theincreaseinthevalueofin-the-moneyputoptionscausedbyanincreaseinexpecteddividendsisalwayslargerthanthedecreaseinvalueofin-the-moneycalloptions.Keepingthetypeofoptionconstant,in-the-moneyoptionsexperiencethegreatestabsolutechangeinvalueandout-of-the-moneyoptionsthesmallestabsolutechangeinvalueasexpecteddividendsincrease.Keepingthetypeofoptionconstant,at-the-moneyoptionsexperiencethelargestabsolutechangeinvalueandoutof-the-moneyoptionsthesmallestabsolutechangeinvalueasaresultofdividendpayment.DeltaHedging重要知识点Apositionwithadeltaofzeroiscalledadeltaneutralposition.Apositionisdeltaneutralonlyinstantaneously(foraveryshortperiodoftime).Tomaintainadeltaneutralposition,thetradermustre-balancetheportfolio.基础题Q-49. AbankhassoldUSO300,000ofcalloptionson100,000equities.Theequitiestradeat50,theoptionstrikepriceis49,thematurityisin3months,volatilityis20%,andtheinterestrateis5%.Howdoesitthebankdeltahedge?(roundtothenearestthousandshare)Buy65,000sharesBuy100,000sharesBuy21,000sharesSell100,000sharesGammaandVegaHedging至要知识点asusedotehedgingrcidhdelteutralpositionsbyprovidingdprotectiontlargesineunderlyingt'spri.Ifgammashighlynegativeorhighlypositive,deltasveryensitiveopriceoftheunderlyingasset.al:hedgetlersnkpriVegaistherateofchangeofthevalueoftheoptionwithrespecttothevolatilityoftheunderlyingasset.基础题.noptionportfoloexhibishighunfavorableensitivtyoincasnipledvoltiltydhileexperiencingsignifiantdailyloswithepassageofti.huldetrertlikelyeployohedgehisportflltdatedoptionsdbuylongdatedoptionsBuyshortdatedoptionsandselllongdatedoptionsltdatedoptionsdlgdatedoptionsytdatedoptionsdbuygdatedoptionsMarketRisk重要知识点ValueatRisk► CalculatingandApplyingVaRVaR=ZaXoVaRT-days=VaR1-daysx,/fVaRi=VaRf+VaR多+ 2pXVaR1XVaR2a(d)=I—PIXa(dy)VaR(df)=l!ilXVaR(dS)(dP)=I—*PIX(d)—(1/2)(CX)X(dy)2VaR(df)=l!ilXVaR(dS)—(1/2)fxVaR(dS)2RiskMeasurement. 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c斗血廿顷基础题Q-51. AriskmanagerstatesthattheVaRoftheportfolioat95%confidenceintervaland1-dayholdingperods$1.hichofefollowingtsThedailylossontheportfoliowillexceed$1million95%oftime.Thedailylossontheportfoliowillnotexceed$1million95%oftime.Themaximumlossthattheportfoliocanincuris$1millionatanypointintime.95%ofriskmanagerswillagreethatthemaximumlossontheportfoliowillbe$1million.Q-52. HugoNelsonispreparingapresentationontheattributesofvalueatrisk.WhichofNelson'sfollowingstatementsisnotcorrect?Rntforediversifiedholdingsofafinancialinsttuton,reducingapitalrequirements.VaR(10%)=$0indicatesapositivedollarreturnislikelytoo