JohnHull《期货、期权和衍生证券》13章习题解答.doc

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1、CHAPTER13WienerProcessesandItô’sLemmaPracticeQuestionsProblem13.1.WhatwoulditmeantoassertthatthetemperatureatacertainplacefollowsaMarkovprocess?Doyouthinkthattemperaturesdo,infact,followaMarkovprocess?Imaginethatyouhavetoforecastthefuturetemperaturefroma)thecurrenttemperature,b)thehistoryofthetemp

2、eratureinthelastweek,andc)aknowledgeofseasonalaveragesandseasonaltrends.IftemperaturefollowedaMarkovprocess,thehistoryofthetemperatureinthelastweekwouldbeirrelevant.ToanswerthesecondpartofthequestionyoumightliketoconsiderthefollowingscenarioforthefirstweekinMay:(i)MondaytoThursdayarewarmdays;today

3、,Friday,isaverycoldday.(ii)MondaytoFridayareallverycolddays.Whatisyourforecastfortheweekend?Ifyouaremorepessimisticinthecaseofthesecondscenario,temperaturesdonotfollowaMarkovprocess.Problem13.2.Canatradingrulebasedonthepasthistoryofastock’spriceeverproducereturnsthatareconsistentlyaboveaverage?Dis

4、cuss.Thefirstpointtomakeisthatanytradingstrategycan,justbecauseofgoodluck,produceaboveaveragereturns.Thekeyquestioniswhetheratradingstrategyconsistentlyoutperformsthemarketwhenadjustmentsaremadeforrisk.Itiscertainlypossiblethatatradingstrategycoulddothis.However,whenenoughinvestorsknowaboutthestra

5、tegyandtradeonthebasisofthestrategy,theprofitwilldisappear.Asanillustrationofthis,consideraphenomenonknownasthesmallfirmeffect.Portfoliosofstocksinsmallfirmsappeartohaveoutperformedportfoliosofstocksinlargefirmswhenappropriateadjustmentsaremadeforrisk.Researchwaspublishedaboutthisintheearly1980san

6、dmutualfundsweresetuptotakeadvantageofthephenomenon.Thereissomeevidencethatthishasresultedinthephenomenondisappearing.Problem13.3.Acompany’scashposition,measuredinmillionsofdollars,followsageneralizedWienerprocesswithadriftrateof0.5perquarterandavariancerateof4.0perquarter.Howhighdoesthecompany’si

7、nitialcashpositionhavetobeforthecompanytohavealessthan5%chanceofanegativecashpositionbytheendofoneyear?Supposethatthecompany’sinitialcashpositionis.Theprobabilitydistributionofthecashpositionattheendofoneyeariswh