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1、CHAPTER3therandombehaviorofassetsInthisChapter...•Jensen’sinequality•morenotationcommonlyusedinmathematicalfinance•howtoexaminetime-seriesdatatomodelreturns•theWienerprocess,amathematicalmodelofrandomness•asimplemodelforequities,currencies,commoditiesandindices3
2、.1INTRODUCTIONInthischapterIdescribeasimplecontinuous-timemodelforequitiesandotherfinancialinstruments,inspiredbyourearliercoin-tossingexperiment.ThistakesusintotheworldofstochasticcalculusandWienerprocesses.AlthoughthereisagreatdealoftheorybehindtheideasIdescri
3、be,Iamgoingtoexplaineverythinginassimpleandaccessiblemanneraspossible.Wewillbemodelingthebehaviorofequities,currenciesandcommodities,buttheideasareapplicabletothefixed-incomeworldasweshallseeinPartThree.3.2THEPOPULARFORMSOF‘ANALYSIS’Therearethreeformsof‘analysis
4、’commonlyusedinthefinancialworld:•Fundamental•Technical•QuantitativeFundamentalanalysisisallabouttryingtodeterminethe‘correct’worthofacompanybyanin-depthstudyofbalancesheets,managementteams,patentapplications,competitors,lawsuits,etc.Inotherwords,gettingtothehea
5、rtofthefirm,doinglotsofaccountingandprojectionsandwhat-not.Thissoundslikeareallysensiblewaytomodelacompanyandhenceitsstockprice.Well,itisandwewilltalkaboutthislaterinthesubjectofRealOptions.56PartOnemathematicalandfinancialfoundationsHowever,thereareunfortunately
6、twodifficultieswiththisapproach.Firstitisvery,veryhard.Youneedadegreeinaccountingandplentyofpatience.Andeventhenallthemostimportantstuffcanbehidden‘offbalancesheet.’Second,andmoreimportantly,‘Themarketcanstayirrationallongerthanyoucanstaysolvent’(possiblysaidbyK
7、eynes).Inotherwords,evenifyouhavetheperfectmodelforthevalueofafirmitdoesn’tmeanyoucanmakemoney.Youhavetofindsomemispricingandthenhopethattherestoftheworldstartstoseeyourpointofview.Andthismayneverhappen.Iffundamentalanalysisishard,thenthenextformofanalysisistheex
8、actopposite,becauseitissoeasy.Technicalanalysisiswhenyoudon’tcareanythingaboutthecompanyotherthantheinformationcontainedwithinitsstockpricehistory.Youdrawtrendlines,lookfors
