The price of market volatility risk

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1、ThepriceofmarketvolatilityriskJeffersonDuarte∗andChristopherS.Jones†October28,2007AbstractWeanalyzethevolatilityriskpremiumbyapplyingamodifiedtwo-passFama-MacBethproceduretothereturnsofalargecrosssectionofthereturnsofoptionsonindividualequities.Ourresultsprovidestrongevi

2、denceofavolatilityriskpremiumthatisincreasinginthelevelofoverallmarketvolatility.Thisriskpremiumprovidescompensationforriskstemmingbothfromthecharacteristicsoftheoptioncontractandtheriskinessoftheunderlyingequity.WealsoshowwithalargescaleMonteCarlosimulationthatmeasure

3、menterrorinoptionpricesandviolationsofarbitrageboundsinducehighlyeconomicallysignificantbiasesinthemeanreturnsofoptions.Infact,oursimulationresultsdemonstratethatbiasescanbeuptoseveralpercentagepointsperday.Theselargebiasescanleadresearcherstofaultyconclusionswithrespec

4、ttoboththemagnitudeofthevolatilityriskpremiumandthesignofexpectedoptionreturns.∗UniversityofWashington.E-mail:jduarte@u.washington.edu†UniversityofSouthernCalifornia.E-mail:christopher.jones@marshall.usc.edu11IntroductionThereisnodoubtthatstockmarketvolatilitychangesov

5、ertime,butwhetherornotvolatilityrepresentsapricedriskfactorremainslesscertain.Theoretically,astochasticvolatilityfactorseemsaprimecandidateforanonzeroriskpremiumbecause,intheframeworkofMerton’s(1973)ICAPM,itrepresentsavariablethatdrivestheinvestmentopportunityset.Empir

6、ically,supportforanonzerovolatilityriskpremiumisvaried,withsomestudiesfindinglargevaluesandsomefindingnone.Theprimarygoalofthispaperistoaddressthisquestionusinganempiricalmethodandadatasetthattogethershouldofferamuchcleareranswerthanhaspreviouswork.Determiningwhethervolat

7、ilityispricedhasimportantconsequencesforoptionpricing,interpretingimpliedvolatilities,andunderstandinginvestorpreferences.Stochasticvolatilitymodelsarethenormintheoptionpricingliterature,andnumerouspapershavedemonstratedthatanonzeropriceofvolatilityriskcanimprovemodelfi

8、tsubstantially.Avolatilityriskpremiumalsomeansthatimpliedvolatilities,whethertheyarefromtheBlack-Scholes(1973)modelor