the relation between implied and realised volatility in the dax index options market

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1、TherelationbetweenimpliedandrealisedvolatilityintheDAXindexoptionsmarketSilviaMuzzioliAbstract.Theaimofthispaperistoinvestigatetherelationbetweenimpliedvolatility,histor-icalvolatilityandrealisedvolatilityintheDAXindexoptionsmarket.Sinceimpliedvolatilityvariesacrossopt

2、iontype(callversusput)werunahorseraceofdifferentimpliedvolatilityestimates:impliedcallandimpliedput.TwohypothesesaretestedintheDAXindexoptionsmarket:unbiasednessandefficiencyofthedifferentvolatilityforecasts.Ourresultssuggestthatbothimpliedvolatilityforecastsareunbiased

3、(afteraconstantadjustment)andefficientforecastsoffuturerealisedvolatilityinthattheysubsumealltheinformationcontainedinhistoricalvolatility.Keywords:volatilityforecasting,Black-ScholesImpliedvolatility,put-callparity1IntroductionVolatilityisakeyvariableinoptionpricingmod

4、elsandriskmanagementtechniquesandhasdrawntheattentionofmanytheoreticalandempiricalstudiesaimedatassess-ingthebestwaytoforecastit.Amongthevariousmodelsproposedintheliteratureinordertoforecastvolatility,wedistinguishbetweenoption-basedvolatilityforecastsandtimeseriesvola

5、tilitymodels.Theformermodelsusepricesoftradedoptionsinordertounlockvolatilityexpectationswhilethelattermodelsusehistoricalin-formationinordertopredictfuturevolatility(following[17],inthissetwegrouppredictionsbasedonpaststandarddeviation,ARCHconditionalvolatilitymodelsa

6、ndstochasticvolatilitymodels).Manyempiricalstudieshavetestedtheforecastingpowerofimpliedvolatilityversusatimeseriesvolatilitymodel.Someearlycontributionsfindevidencethatimpliedvolatility(IV)isabiasedandinefficientforecastoffuturerealisedvolatility(seee.g.,[2,6,14]).Altho

7、ughtheresultsofsomeofthesestudies(e.g.,[6,14])areaffectedbyoverlappingsamples,asrecalledby[4],ormismatchingmaturitiesbetweentheoptionandthevolatilityfore-casthorizon,theyconstituteearlyevidenceagainsttheunbiasednessandinformationefficiencyofIV.Morerecently,severalpapers

8、analysetheempiricalperformanceofIVinvariousoptionmarkets,rangingfromindexes,futuresorindividualstocksandfindthatIVisun