johnhull《期货期权和衍生证券》章习题解答

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1、CHAPTER13WienerProcessesandItô’sLemmaPracticeQuestionsProblem13.1.WhatwoulditmeantoassertthatthetemperatureatacertainplacefollowsaMarkovprocess?Doyouthinkthattemperaturesdo,infact,followaMarkovprocess?Imaginethatyouhavetoforecastthefuturetemperaturefroma)thecurrenttemperature,b)t

2、hehistoryofthetemperatureinthelastweek,andc)aknowledgeofseasonalaveragesandseasonaltrends.IftemperaturefollowedaMarkovprocess,thehistoryofthetemperatureinthelastweekwouldbeirrelevant.ToanswerthesecondpartofthequestionyoumightliketoconsiderthefollowingscenarioforthefirstweekinMay:

3、(i)MondaytoThursdayarewarmdays;today,Friday,isaverycoldday.(ii)MondaytoFridayareallverycolddays.Whatisyourforecastfortheweekend?Ifyouaremorepessimisticinthecaseofthesecondscenario,temperaturesdonotfollowaMarkovprocess.Problem13.2.Canatradingrulebasedonthepasthistoryofastock’spric

4、eeverproducereturnsthatareconsistentlyaboveaverage?Discuss.Thefirstpointtomakeisthatanytradingstrategycan,justbecauseofgoodluck,produceaboveaveragereturns.Thekeyquestioniswhetheratradingstrategyconsistentlyoutperformsthemarketwhenadjustmentsaremadeforrisk.Itiscertainlypossibletha

5、tatradingstrategycoulddothis.However,whenenoughinvestorsknowaboutthestrategyandtradeonthebasisofthestrategy,theprofitwilldisappear.Asanillustrationofthis,consideraphenomenonknownasthesmallfirmeffect.Portfoliosofstocksinsmallfirmsappeartohaveoutperformedportfoliosofstocksinlargefi

6、rmswhenappropriateadjustmentsaremadeforrisk.Researchwaspublishedaboutthisintheearly1980sandmutualfundsweresetuptotakeadvantageofthephenomenon.Thereissomeevidencethatthishasresultedinthephenomenondisappearing.Problem13.3.Acompany’scashposition,measuredinmillionsofdollars,followsag

7、eneralizedWienerprocesswithadriftrateof0.5perquarterandavariancerateof4.0perquarter.Howhighdoesthecompany’sinitialcashpositionhavetobeforthecompanytohavealessthan5%chanceofanegativecashpositionbytheendofoneyear?Supposethatthecompany’sinitialcashpositionis.Theprobabilitydistributi

8、onofthecashpositionattheendofoneyeariswh