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时间:2018-02-10
《empirical analysis of volatility》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、CHAPTER53empiricalanalysisofvolatilityInthisChapter...•howtoanalyzevolatilitydatatodeterminethemostsuitabletime-independentstochasticmodel•howtodeterminetheprobabilitythatthevolatilitywillstaywithinanyspecifiedrange•howtoassignadegreeofconfidencetoyouruncertainvolatilitymodelprice53.1
2、INTRODUCTIONInthischapterweexaminerealdatainordertomodelthebehaviorofvolatility.Ourprincipalaiminthisistoderiveagoodstochasticvolatilitymodel.Thisvolatilitymodelcanthenbeusedinanumberofways:Inatwo-factoroption-pricingmodel;Toexaminethetimeevolutionofvolatilityfromaninitialknownvalue
3、todayto,inthelongrun,asteady-statedistribution;Toestimatetheprobabilityofouruncertainvolatilitymodelpricebeingcorrect.Theapproachweadoptmustbecontrastedwiththetraditionalapproachtostochasticvolatilitywhichseemstobetowritedownsomethingniceandtractableandthenfittheparameters.53.2STOCHA
4、STICVOLATILITYANDUNCERTAINPARAMETERSREVISITEDTheclassicalwayofdealingwithrandomvariablesistomodelthemstochastically.Thiswedohereforvolatility,derivingastochasticmodelsuchthatdriftandvariance,andthesteady-statemeananddispersionofvolatilityarecompatiblewithhistoricaldata.Wecanthen,amo
5、ngotherthings,determinetheevolutionofvolatilityfromtheknownvaluetodaytothesteady-statedistributioninthelongterm.Recallalso,theapproachofAvellaneda,Levy,ParasandLyonsformodelingvolatility.In´theirmodeltheyallowvolatilitytodojustaboutanythingaslongasitdoesn’tmoveoutsidesomegivenrange.
6、Withthismodelitisnaturaltocalculatenotasingleoptionvaluebutaworstpriceandabestpricefortheoption.Thisresultsinanon-linearpartialdifferential882PartFiveadvancedtopicsequation.Thisprocedureyieldsa‘certaintyinterval’forthepriceoftheoption,drivenbytheinputvolatilityband.Henceweknowthat,f
7、orexample,ifwecouldaccesstheoptioninthemarketbelowourworstpricethenwithinthelimitsofourcertaintybandassumptions,weareguaranteedaprofit.Butwhatifwearenotonehundredpercentsureaboutthevolatilityrange?Canweuseourstochasticvolatilitymodeltoseehowlikelyvolatilityistostayintherange?53.3DERI
8、VINGANEMPIRICALSTOC
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