期权期货与其他衍生产品第九版课后习题与答案Chapter (22).pdf

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1、CHAPTER22ValueatRiskPracticeQuestionsProblem22.1.Considerapositionconsistingofa$100,000investmentinassetAanda$100,000investmentinassetB.Assumethatthedailyvolatilitiesofbothassetsare1%andthatthecoefficientofcorrelationbetweentheirreturnsis0.3.Whatisthe5-day99%VaRforthepo

2、rtfolio?Thestandarddeviationofthedailychangeintheinvestmentineachassetis$1,000.Thevarianceoftheportfolio’sdailychangeis2210001000203100010002600000Thestandarddeviationoftheportfolio’sdailychangeisthesquarerootofthisor$1,612.45.Thestandarddeviationofthe5-day

3、changeis1612455$360555BecauseN-1(0.01)=2.3261%ofanormaldistributionliesmorethan2.326standarddeviationsbelowthemean.The5-day99percentvalueatriskistherefore2.326×3605.55=$8388.Problem22.2.Describethreewaysofhandlinginterest-rate-dependentinstrumentswhenthemodelbuild

4、ingapproachisusedtocalculateVaR.Howwouldyouhandleinterest-rate-dependentinstrumentswhenhistoricalsimulationisusedtocalculateVaR?ThethreealternativeproceduresmentionedinthechapterforhandlinginterestrateswhenthemodelbuildingapproachisusedtocalculateVaRinvolve(a)theuseofth

5、edurationmodel,(b)theuseofcashflowmapping,and(c)theuseofprincipalcomponentsanalysis.Whenhistoricalsimulationisusedweneedtoassumethatthechangeinthezero-couponyieldcurvebetweenDaymandDaym1isthesameasthatbetweenDayiandDayi1fordifferentvaluesofi.InthecaseofaLIBOR,thezeroc

6、urveisusuallycalculatedfromdepositrates,Eurodollarfuturesquotes,andswaprates.WecanassumethatthepercentagechangeineachofthesebetweenDaymandDaym1isthesameasthatbetweenDayiandDayi1.InthecaseofaTreasurycurveitisusuallycalculatedfromtheyieldsonTreasuryinstruments.Againweca

7、nassumethatthepercentagechangeineachofthesebetweenDaymandDaym1isthesameasthatbetweenDayiandDayi1.Problem22.3.AfinancialinstitutionownsaportfolioofoptionsontheU.S.dollar–sterlingexchangerate.Thedeltaoftheportfoliois56.0.Thecurrentexchangerateis1.5000.Deriveanapproximat

8、elinearrelationshipbetweenthechangeintheportfoliovalueandthepercentagechangeintheexchangerate.Ifthedailyvolati