期權期貨與其他衍生產品第九版課后習題與答案

1、CHAPTER22ValueatRiskPracticeQuestionsProblem22.1.Considerapositionconsistingofa$100000investmentinassetAa$100000investmentinassetB.Assumethatthedailyvolatilitiesofbothassetsare1%thatthecoefficientofcrelationbetweentheirr

2、eturnsis0.3.Whatisthe5day99%VaRftheptfolioThestarddeviationofthedailychangeintheinvestmentineachassetis$1000.Thevarianceoftheptfolio’sdailychangeis2210001000203100010002600000?????????????Thestarddeviationoftheptfolio’sd

3、ailychangeisthesquarerootofthis$1612.45.Thestarddeviationofthe5daychangeis1612455$360555??????BecauseN1(0.01)=2.3261%ofanmaldistributionliesmethan2.326starddeviationsbelowthemean.The5day99percentvalueatriskistherefe2.326

4、3605.55=$8388.Problem22.2.DescribethreewaysofhlinginterestratedependentinstrumentswhenthemodelbuildingapproachisusedtocalculateVaR.HowwouldyouhleinterestratedependentinstrumentswhenhisticalsimulationisusedtocalculateVaRT

5、hethreealternativeproceduresmentionedinthechapterfhlinginterestrateswhenthemodelbuildingapproachisusedtocalculateVaRinvolve(a)theuseofthedurationmodel(b)theuseofcashflowmapping(c)theuseofprincipalcomponentsanalysis.Whenh

6、isticalsimulationisusedweneedtoassumethatthechangeinthezerocouponyieldcurvebetweenDaymDay1m?isthesameasthatbetweenDayiDay1i?fdifferentvaluesofi.InthecaseofaLIBthezerocurveisusuallycalculatedfromdepositratesEurodollarfutu

7、resquotesswaprates.WecanassumethatthepercentagechangeineachofthesebetweenDaymDay1m?isthesameasthatbetweenDayiDay1i?.InthecaseofaTreasurycurveitisusuallycalculatedfromtheyieldsonTreasuryinstruments.Againwecanassumethatthe

8、percentagechangeineachofthesebetweenDaymDay1m?isthesameasthatbetweenDayiDay1i?.Problem22.3.AfinancialinstitutionownsaptfolioofoptionsontheU.S.dollar–sterlingexchangerate.Thedeltaoftheptfoliois56.0.Thecurrentexchangeratei

9、s1.5000.Deriveanapproximatelinearrelationshipbetweenthechangeintheptfoliovaluethepercentagechangeintheexchangerate.Ifthedailyvolatilityoftheexchangerateis0.7%estimatethe10day99%VaR.Theapproximaterelationshipbetweenthedai

10、lychangeintheptfoliovalueP?thedailychangeintheexchangerateS?is56PS???Whenafinalexchangeofprincipalisaddedinthefloatingsideisequivalentazerocouponbondwithamaturitydateequaltothedateofthenextpayment.Thefixedsideisacouponbe

11、aringbondwhichisequivalenttoaptfolioofzerocouponbonds.Theswapcantherefebemappedintoaptfolioofzerocouponbondswithmaturitydatescrespondingtothepaymentdates.Eachofthezerocouponbondscanthenbemappedintopositionsintheadjacents

12、tardmaturityzerocouponbonds.Problem22.8.ExplainthedifferencebetweenValueatRiskExpectedShtfall.Valueatriskisthelossthatisexpectedtobeexceeded(100)X%?ofthetimeinNdaysfspecifiedparametervaluesXN.Expectedshtfallistheexpected

13、lossconditionalthatthelossisgreaterthantheValueatRisk.Problem22.9.ExplainwhythelinearmodelcanprovideonlyapproximateestimatesofVaRfaptfoliocontainingoptions.Thechangeinthevalueofanoptionisnotlinearlyrelatedtothechangeinth

14、evalueoftheunderlyingvariables.Whenthechangeinthevaluesofunderlyingvariablesisnmalthechangeinthevalueoftheoptionisnonnmal.Thelinearmodelassumesthatitisnmalistherefeonlyanapproximation.Problem22.10.Sometimeagoacompanyhase

15、nteredintoafwardcontracttobuy￡1millionf$1.5million.Thecontractnowhassixmonthstomaturity.Thedailyvolatilityofasixmonthzerocouponsterlingbond(whenitspriceistranslatedtodollars)is0.06%thedailyvolatilityofasixmonthzerocoupon

16、dollarbondis0.05%.Thecrelationbetweenreturnsfromthetwobondsis0.8.Thecurrentexchangerateis1.53.Calculatethestarddeviationofthechangeinthedollarvalueofthefwardcontractinoneday.Whatisthe10day99%VaRAssumethatthesixmonthinter

17、estrateinbothsterlingdollarsis5%perannumwithcontinuouscompounding.Thecontractisalongpositioninasterlingbondcombinedwithashtpositioninadollarbond.Thevalueofthesterlingbondis00505153e?????$1.492million.Thevalueofthedollarb

18、ondis0050515e?????$1.463million.Thevarianceofthechangeinthevalueofthecontractinonedayis2222149200006146300005208149200006146300005??????????????????0000000288??Thestarddeviationistherefe$0.000537million.The10day99%VaRis0