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Irregularly Spaced Intraday Value at Risk ISIVaR Models

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Irregularly Spaced Intraday Value at Risk (ISIVaR) Models Forecasting and Predictive Abilities Gilbert Colletaz, Christophe Hurlin and Sessi Tokpavi LEO, University of Orléans. Rue de Blois. BP 6739. 45067 Orléans Cedex 2. France. Corresponding author: This draft, July 2007 Abstract The objective of this paper is to propose a market risk measure de?ned in price event time and a suitable backtesting procedure for irregularly spaced data. Firstly, we combine Autoregressive Conditional Duration models for price movements and a non parametric quantile estimation to derive a semi-parametric Irregularly Spaced Intraday Value at Risk (ISIVaR) model. This ISIVaR measure gives two information: the expected duration for the next price event and the related VaR. Secondly, we use a GMM approach to develop a backtest and investigate its ?nite sample properties through numerical Monte Carlo simulations. Finally, we propose an application to two NYSE stocks. Key words: Value at Risk, High-frequency data, ACD models, Irregularly spaced market risk models, Backtesting. 1 We would like to thank Pierre Giot and Renaud Beaupain for providing us with NYSE Trades And Quotes (TAQ) data, and the participants at the 14th ?Forecasting Financial Markets (FFM)? Conference in Aix-en-Provence (May, 2007) for their helpful comments.

  • market events

  • irregularly spaced

  • ?xed-time intervals

  • var

  • semi-parametric irregularly

  • intraday-var

  • events-hit-count variable

  • corresponding price


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Language English
IrregularlySpacedIntradayValueatRisk(ISIVaR)ModelsForecastingandPredictiveAbilitiesGilbertColletaz,ChristopheHurlinandSessiTokpaviLEO,UniversityofOrléans.RuedeBlois.BP6739.45067OrléansCedex2.France.Correspondingauthor:sessi.tokpavi@univ-orleans.frThisdraft,July2007AbstractTheobjectiveofthispaperistoproposeamarketriskmeasurede…nedinpriceeventtimeandasuitablebacktestingprocedureforirregularlyspaceddata.Firstly,wecombineAutoregressiveConditionalDurationmodelsforpricemovementsandanonparametricquantileestimationtoderiveasemi-parametricIrregularlySpacedIntradayValueatRisk(ISIVaR)model.ThisISIVaRmeasuregivestwoinformation:theexpecteddurationforthenextpriceeventandtherelatedVaR.Secondly,weuseaGMMapproachtodevelopabacktestandinvestigateits…nitesamplepropertiesthroughnumericalMonteCarlosimulations.Finally,weproposeanapplicationtotwoNYSEstocks.Keywords:ValueatRisk,High-frequencydata,ACDmodels,Irregularlyspacedmarketriskmodels,Backtesting.1WewouldliketothankPierreGiotandRenaudBeaupainforprovidinguswithNYSETradesAndQuotes(TAQ)data,andtheparticipantsatthe14th’ForecastingFinancialMarkets(FFM)’ConferenceinAix-en-Provence(May,2007)fortheirhelpfulcomments.Anyerrorsandinaccuraciesareourowns.
1IntroductionTheavailabilityofhigh-frequency(ortickbytick)data,inducedbytheevo-lutionofthetradingenvironmentonthemajor…nancialplaces,hasledtotheemergenceofanewcategoryofactivemarketparticipants,suchashighfre-quencytraders.Thelatterarecharacterizedbyveryshortinvestmenthorizonsandthenrequirenewmarketriskmethodology:sinceriskmustbeevaluatedonshorterthandailytimeintervals,traditionalriskmeasures,suchasValueatRisk(VaR),mustbeextendedtointradaydatacontext.Thisnewbodyofresearchreceiveslessattentionintherelevantliteraturecomparedtode…nitionandvalidationofday-to-dayriskmeasures.Tothebestofourknowledge,twoattemptstoderiveintradailymarketriskmodelsusingtickbytickdataarethoseofGiot(2005)andDionneetal.(2006).Giot(2005)quanti…esmarketriskatanintradaytimehorizon,usingNormalGARCH,StudentGARCH,RiskMetricsfordeseasonalizedtickbytickdatasampledatequidistanttime.HealsoappliedtheLog-ACDmodelonpricedurationtocomputeirregularlyspacedVaRandthenscalethemtoderive…xed-timeintervalsVaR.TheIntraday-VaR(IVaR)ofDionneetal.(2006)isbasedonarichmodelofpricedynamicsconditionalondurations-knownastheUltra-High-FrequencyGARCH(UHF-GARCH)modelofEngle(2000)-suchthatunequallyspacedVaRcanbeeasilygeneratedinaconvenientway.But,theauthorsinsteadmakeuseofasimulation-basedmethodtoinferVaRatany…xed-timehorizon2.So,inbothapproaches,theunequallyspacednatureofhigh-frequencymarketriskmodelsisforfeited,mainlybecauseofbacktestingprocedure.Thisrestrictionobviouslyimpliesalossofinformation,sincedurationsbe-2ItseemsinthecaseofDionneetal.(2006)paper,asinGiot(2005),thatVaRsarerescaledin…xed-timeintervalsforvalidationpurpose.2
tweenmarketevents3areanessentialdimensionofriskwhendealingwithtickbytickdata.Averyshortdurationforecastthusindicatesinthelineofmicrostructuretheory(EasleyandO’Hara,1992)thattherearemanyin-formedtraders,andthisinformationwiththeleveloftheforecastvalueofVaR,willdeterminethemarketmonitoringoftraders.Besides,thesedura-tionsallowassessingliquidityrisk,withforinstancethede…nitionofTimeatRisk(TaR)measures(Ghyselsetal.,2004).Inthiscontext,ourobjectiveistoproposeamarketriskorVaRmethodologyde…nedinpriceeventstime(andnotincalendartime)andacorrespond-ingbacktestingprocedure.Forthat,wede…neanISIVaR(IrregularlySpacedIntradayValueatRisk)modelwhichconsistsinacoupleoftwomeasures:theforecastofthetimingforthenextpriceevent(ortheexpecteddura-tionbetweentwoconsecutivepricechanges)andthecorrespondinglevelofrisksummarizedbyVaRforecast.ThisVaRcorrespondstothemaximumex-pectedlossthatwillnotbeexceeded(atagivencon…dencelevel)atthenextpriceevent,ifthiseventoccurs.Moreprecisely,theISIVaRisderivedfromanAutoregressiveConditionalDuration(ACD)modelappliedtodeseasonalizedpriceeventdurationsasinGiot(2005).However,contrarytoGiot,wedonotimposeaparticulardistributiononthestandardizedreturnstoderiveVaRmeasurefrompricechangesvolatility.WeuseasemiparametricapproachsimilartothatconsideredbyEngleandManganelli(2001)intheday-to-dayVaRperspective.WealsoproposeabacktestingprocedurethatallowstestingtheaccuracyofourirregularlyspacedVaRforecasts.ThemainadvantageofthisprocedureisthatitdoesnotrequirerescalingISIVaRforecaststo…xed-timeintervals.Asusualinthebacktestingliterature(seeCampbell,2007forasurvey)ourmodel3Marketeventscanbeeithertradesorde…nedusingaparticulartimetransfor-mation(seefore.g.LeFolandMercier,1998).Inthispaper,wewillfocusonpriceevents,i.e.theminimumamountoftimeneededforthepricetohaveasigni…cantchange.3