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1、Chapter21 ValueatRiskOptions,Futures,andOtherDerivatives,8thEdition,Copyright?JohnC.Hull20121TheQuestionBeingAskedinVaR“WhatlosslevelissuchthatweareX%confidentitwillnotbeexceededinNbusinessdays?”O(jiān)ptions,Futures,andOtherDerivatives,8thEdition,Copyright?JohnC.Hull20122VaRvs.ExpectedShor
2、tfallVaRisthelosslevelthatwillnotbeexceededwithaspecifiedprobabilityExpectedShortfall(orC-VaR)istheexpectedlossgiventhatthelossisgreaterthantheVaRlevelAlthoughexpectedshortfallistheoreticallymoreappealing,itisVaRthatisusedbyregulatorsinsettingbankcapitalrequirementsOptions,Futures,and
3、OtherDerivatives,8thEdition,Copyright?JohnC.Hull20123AdvantagesofVaRItcapturesanimportantaspectofriskinasinglenumberItiseasytounderstandItasksthesimplequestion:“Howbadcanthingsget?”O(jiān)ptions,Futures,andOtherDerivatives,8thEdition,Copyright?JohnC.Hull20124HistoricalSimulationtoCalculatet
4、heOne-DayVaRCreateadatabaseofthedailymovementsinallmarketvariables.ThefirstsimulationtrialassumesthatthepercentagechangesinallmarketvariablesareasonthefirstdayThesecondsimulationtrialassumesthatthepercentagechangesinallmarketvariablesareasontheseconddayandsoonOptions,Futures,andOtherD
5、erivatives,8thEdition,Copyright?JohnC.Hull20125HistoricalSimulationcontinuedSupposeweuse501daysofhistoricaldata(Day0toDay500)LetvibethevalueofavariableondayiThereare500simulationtrialsTheithtrialassumesthatthevalueofthemarketvariabletomorrowisOptions,Futures,andOtherDerivatives,8thEdi
6、tion,Copyright?JohnC.Hull20126Example:Calculationof1-day,99%VaRforaPortfolioonSept25,2008(Table21.1,page475)Options,Futures,andOtherDerivatives,8thEdition,Copyright?JohnC.Hull20127IndexValue($000s)DJIA4,000FTSE1003,000CAC401,000Nikkei2252,000DataAfterAdjustingforExchangeRates(Table21.
7、2,page475)Options,Futures,andOtherDerivatives,8thEdition,Copyright?JohnC.Hull20128DayDateDJIAFTSE100CAC40Nikkei2250Aug7,200611,219.386,026.334,345.0814,023.441Aug8,200611,173.596,007.084,347.9914,300.912Aug9,200611,076.186,055.304,413.3514,467.093Aug10,200611,124.375,964.904,333.9014,
8、413.3
