Table Of ContentHigh Frequency Financial Econometrics
Recent Developments
.
Luc Bauwens Wi nfried Pohlmeier
David Veredas (Eds.)
High Frequency
Financial
Econometrics
Recent Developments
With57Figuresand64Tables
Physica-Verlag
ASpringerCompany
Prof.LucBauwens Prof.Winfried Pohlmeier
CORE Department of Economics
Voie du Roman Pays University of Konstanz
1348 Louvain-la-Neuve 78457 Konstanz
Belgium Germany
[email protected] [email protected]
Prof.David Veredas
ECARES
Universite´ Libre des Bruxelles
30, Avenue Roosevelt
1050 Brussels
Belgium
[email protected]
Parts of the papers have been first published in
“Empirical Economic s,“Vol. 30, No. 4, 2006
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Contents
Editor’sintroduction:recentdevelopments
inhighfrequencyfinancialeconometrics ........................... 1
L.Bauwens,W.PohlmeierandD.Veredas
Exchangeratevolatilityandthemixtureofdistributionhypothesis.... 7
L.Bauwens,D.RimeandG.Sucarrat
Amultivariateintegercounthurdlemodel:
theoryandapplicationtoexchangeratedynamics................... 31
K.Bien,I.NolteandW.Pohlmeier
Asymmetriesinbidandaskresponsestoinnovations
inthetradingprocess ............................................ 49
A.EscribanoandR.Pascual
Liquiditysupplyandadverseselection
inapurelimitorderbookmarket ................................. 83
S.FreyandJ.Grammig
Howlargeisliquidityriskinanautomatedauctionmarket? ......... 111
P.GiotandJ.Grammig
Orderaggressivenessandorderbookdynamics..................... 133
A.D.HallandN.Hautsch
Modellingfinancialtransactionpricemovements:
adynamicintegercountdatamodel ............................... 167
R.Liesenfeld,I.NolteandW.Pohlmeier
Theperformanceanalysisofchartpatterns:
MonteCarlosimulationandevidence
fromtheeuro/dollarforeignexchangemarket ...................... 199
W.B.OmraneandH.VanOppens
Semiparametricestimationforfinancialdurations .................. 225
J.M.Rodríguez-Poo,D.VeredasandA.Espasa
vi Contents
Intradaystockprices,volume,andduration:
anonparametricconditionaldensityanalysis ....................... 253
A.S.TayandC.Ting
Macroeconomicsurprisesandshort-termbehaviour
inbondfutures.................................................. 269
D.Veredas
Dynamicmodellingoflarge-dimensionalcovariancematrices ........ 293
V.Voev
LucBauwens·WinfriedPohlmeier·DavidVeredas
Editor’s introduction: recent developments
in high frequency financial econometrics
“But there are several aspects of the quantitative approach to finance,
andnosingleoneoftheseaspects,takenbyitself,shouldbeconfounded
with financial econometrics. Thus, financial econometrics is by no
means the same as finance statistics. Nor is it identical with what we
callgeneral financial theory…Notshouldbefinancialeconometricsa
synonymouswiththeapplicationofmathematicstofinance.Experience
hasshownthateachofthesethreeview-points,thatofstatistics, finan-
cialtheory,andmathematics,isanecessary,butnotsufficient,condition
for a real understanding of the quantitative relations of modern finan-
ciallife.Itistheunificationofallthethreethatispowerful.Anditisthis
unificationthatconstitutesfinancialeconometrics.”
Thisparagraphisavirtualcopyoftheoneinp.2ofFrisch’sEditorNoteon
EconometricaVol.1,No.1.Theonlydifferenceisthateconomicshasbeenreplaced
byfinance,economicbyfinancial,econometricsbyfinancialeconometrics.
Itwaswritten74yearsagobutitfullyreflectsthespiritofthisspecialissue.
High frequency finance is an archetypical example of Ragnar Frisch’s words.
Itrepresentsaunificationof(1)financialtheory,inparticularmarketmicrostruc-
ture,(2)mathematicalfinance,exemplifiedinderivativemarkets,and(3)statistics,
forinstancethetheoryofpointprocesses.Itistheintersectionofthesethreecompo-
nentsthatyieldsanincrediblyactiveresearcharea,withcontributionsthatenhance
theunderstandingoftoday’scomplexintra-dailyfinancialworld.
“Theory,informulatingitsabstractquantitativenotions,mustbeinspired
toalargerextentbythetechniqueofobservations.Andfreshstatistical
and other factual studies must be the healthy element of disturbance
thatconstantlythreatensanddisquietstheoristsandpreventsthemfrom
comingtorestonsomeinherited,obsoletesetofassumptions.”
Here again high frequency finance is fully reflected in Ragnar Frisch’s
words.Its modusvivendi isaperfectcombinationofobservedrealfacts,market
microstructure theory, and statistics and they all form a system in which each
2 L.Bauwensetal.
component nicely dovetails with the others. Market microstructure theory deals
withmodelsexplainingpriceandagent’sbehaviorinamarketgovernedbycertain
rules.Thesemarketshavedifferentwaystooperate(with/withoutmarketmakers,
with/withoutorderbooks),openingandclosinghours,maximumpricevariations,
minimum traded volume, etc. On the other hand, empirical analysis deals with
thestudyofmarketbehaviorusingrealdata.Forexample,whataretherelations
betweentradedvolume,pricevariations,andliquidity?Whatarethepotentialprob-
lems?Last,statisticallyspeaking,highfrequencydataarerealizationsofso-called
pointprocesses,thatis,thearrivaloftheobservationsisrandom.This,jointlywith
the fact that financial data has pathological and unique features (long memory,
strong skewness, and kurtosis) implies that new methods and new econometric
modelsareneeded.
The econometric analysis of high frequency data permits us to answer to
questions that are of great interest for policy markers. For instance, how much
informationshouldregulatorsdisclosetomarketparticipants?Or,howdoextreme
movements in the book affect market liquidity? Or is a market maker really
necessary?
On the other side, the practitioners, the traders that participate in the market
everyday,alsohaveagrowinginterestintheunderstandingoffinancialmarkets
that operate at high frequency. For instance, trading rules may be constructed
based on the markets conditions that, in turn, may be explained with financial
econometrics.
Thisvolumepresentssomeadvancedresearchinthisarea.Inordertodocument
the potential of high frequency finance, it is our goal to select a wide range of
papers,includingstudiesoftheorderbookdynamics,theroleofnewsevents,and
the measurement of market risks as well as new econometric approaches to the
analysisofmarketmicrostructures.
Bauwens, Rime, and Sucarrat shed new light on the mixture of distribution
hypothesis by means of a study of the weekly exchange rate volatility of the
Norwegian krone. They find that the impact of information arrival on exchange
ratevolatilityispositiveandstatisticallysignificant,andthatthehypothesisthatan
increaseinthenumberoftradersreducesexchangeratevolatilityisnotsupported.
Moreover,theydocumentthatthepositiveimpactofinformationarrivalonvolatil-
ityisrelativelystableacrossthreedifferentexchangerateregimes,andinthatthe
impactisrelativelysimilarforbothweeklyvolatilityandweeklyrealisedvolatility.
Despite its rather weak theoretical and statistical foundation, chart analysis
isstillafrequentlyusedtoolamongfinancialanalysts.OmraneandvanOppens
investigate the existence of chart patterns in the Euro/Dollar intra-daily foreign
exchangemarketatthehighfrequencylevel.Checking12typesofchartpatterns,
theystudythedetectedpatternsthroughtwocriteria:predictabilityandprofitability
andfindanapparentexistenceofsomechartpatternsinthecurrencymarket.More
thanonehalfofdetectedchartspresentasignificantpredictability.Butonlytwo
chartpatternsimplyasignificantprofitabilitywhichis,however,toosmalltocover
thetransactioncosts.
Tickdatais,bymarketstructure,discrete.Pricesmovebymultiplesofthetick,
theminimumpricevariation.Twoapproachescanbetakentoaccountforpricedis-
creteness.One,whichstemsfromtherealizedvarianceliterature,istoconsidertick
changesasmarketmicrostructurenoise.Theotheristoconsiderpricediscreteness
as structural information. Bien, Nolte, and Pohlmeier pursue this second line of
Editor’sintroduction: recentdevelopmentsinhighfrequencyfinancialeconometrics 3
research and propose a model for multivariate discrete variables. Econometric
modelsforunivariatediscretepriceprocesseshavebeensuggestedrecentlybuta
multivariateversionofitwasstillmissing.Themultivariateintegercounthurdle
model(MICH)proposedbyBien,Nolte,andPohlmeiercanbeviewedasacom-
binationofthecopulaapproachbyCameronetal.(2004)withtheintegercount
hurdle(ICH)modelofLiesenfeld,Nolteand,Pohlmeier(2006),whichallowsthe
dynamicspecificationofaunivariateconditionaldistributionwithdiscretesupport.
Theyillustratetheusefulnessofthemodelforestimatingthejointdistributionof
theEUR/GBPandtheEUR/USDexchangeratechangesatthe1-minlevel.Their
approach leaves the door open to other applications such as the measurement of
multivariate conditional volatilities, the quantification of intradaily liquidity and
value-at-risk applications, and the joint analysis of several marks of the trading
process(volumes,priceandvolumedurations,discretequotechanges).
EscribanoandPascualproposeanewapproachofjointlymodelingthetrading
processandtherevisionsofmarketquotes.Thismethodaccommodatesasymme-
triesinthedynamicsofaskandbidquotesaftertrade-relatedshocks.Theempirical
specificationisavectorerrorcorrection(VEC)modelforaskandbidquotes,with
thespreadastheco-integratingvector,andwithanendogenoustradingprocess.
Contrary to some hypothesis implied from market microstructure theory, they
provide evidence against several symmetry assumptions and report asymmetric
adjustmentsofaskandbidpricestotrade-relatedshocks,andasymmetricimpacts
of buyer and seller-initiated trades. In general, buys are more informative than
sells.
Frey and Grammig analyze adverse selection costs and liquidity supply in a
pure open limit order book market using the Glosten/Sandas modeling frame-
work.RelaxingsomeassumptionsofSandas’(2001)basicmodel,theyshowthat
theirrevisedmethodologydeliversimprovedempiricalresults.1Theyfindempir-
icalsupportforoneofthemainhypothesisputforthbythetheoryoflimitorder
book markets, which states that liquidity supply and adverse selection costs are
inverselyrelated.Furthermore,adverseselectioncostestimatesbasedonthestruc-
tural model and those obtained using popular model-free methods are strongly
correlated.
In the mid-1990s, financial institutions started implementing VaR type mea-
sures to meet the 1988 and 1996 Basel Accords’capital requirements to cover
theirmarketrisk.Basedonaninternalmodel,theycomputethe“Value-at-Risk,”
whichrepresentsthelosstheycanincurover10tradingdaysata1%confidence
level.However,mostofthesemodelsdonotaccountfortheliquidityriskthathas
beenwidelydocumentedinthemicrostructureliterature.Duetothepriceimpact
oftrades,whichreliesontradesize,theremayindeedbeadifferencebetweenthe
marketvalueofaportfolio,computedover“no-tradereturns,”anditsliquidation
value. Giot and Grammig propose an original way to shed light on the liquidity
discount that should be part of the evaluation of market risk borne by financial
institutions. They quantify the liquidity risk premiums over different time hori-
zons,forportfoliosofdifferentsizes,composedofthreestockstradedonXetra.
Thispaperthusnotonlycontributestotheexistingliteratureonmarketliquidity,
1Sandås,P.(2001),“AdverseSelectionandCompetitiveMarketMaking:EmpiricalEvidence
fromaLimitOrderMarket”,ReviewofFinancialStudies,14,705–734.
4 L.Bauwensetal.
butprovidesalsoananswertopractitioners’concernsrelativetothemeasurement
ofmarketrisk.
HallandHautschstudythedeterminantsoforderaggressivenessandtraders’
ordersubmissionstrategyinanopenlimitorderbookmarket.Applyinganorder
classificationscheme,theymodelthemostaggressivemarketorders,limitorders
aswellascancellationsonbothsidesofthemarketemployingasix-dimensional
autoregressiveconditionalintensitymodel.UsingorderbookdatafromtheAus-
tralianStockExchange,theyfindthatmarketdepth,thequeuedvolume,thebid-ask
spread,recentvolatility,aswellasrecentchangesinboththeorderflowandthe
price play an important role in explaining the determinants of order aggressive-
ness. Overall, their empirical results broadly confirm theoretical predictions on
limitorderbooktrading.
Liesenfeld,Nolte,andPohlmeierdevelopadynamicmodeltocapturethefun-
damental properties of financial prices at the transaction level.They decompose
thepriceindiscretecomponents—directionandsizeofpricechanges—and,using
autoregressivemultinomialmodels,theyshowthatthemodeliswellsuitedtotest
sometheoreticalimplicationsofmarketmicrostructuretheoryontherelationship
betweenpricemovementsandothermarksofthetradingprocess.
Intradaily financial data is characterized by its dynamic behavior as well by
deterministic seasonal patterns that are due to the market structure. Volatility is
known to be larger at the opening and closing than during the lunch time. Simi-
larlyforfinancialdurations:theyareshorterattheopeningandclosing,indicating
higher activity at these times of the day.Any econometric model should there-
fore incorporate these features. Rodriguez-Poo, Veredas, and Espasa propose a
semiparametricmodelforfinancialdurations.Thedynamicsarespecifiedparamet-
rically,withanACDtypeofmodel,whileseasonalityisleftunspecifiedandhence
nonparametric. Estimation rests on generalized profile likelihood, which allows
forjointestimationoftheparametric—anACDtypeofmodel—andnonparamet-
riccomponents,providingconsistentandasymptoticallynormalestimators.Itis
possible to derive the explicit form for the nonparametric estimator, simplifying
estimationtoastandardmaximumlikelihoodproblem.
TayandTingcarryoutanempiricalanalysisusinghighfrequencydataandmore
specificallyestimatethedistributionofpricechangesconditionalontradevolume
anddurationbetweentrades.Theirmainempiricalfindingisthatevenwhencon-
trollingforthetradevolumelevel,durationhasaneffectonthedistributionofprice
changes, and the higher the conditioning volume level, the higher the impact of
durationonpricechanges.Theauthorsfindsignificantpositive(negative)skewness
inthedistributionofpricechangesinbuyer(respectivelyseller)—initiatedtrades,
andseethisfindingassupportoftheDiamondandVerrecchia(1987)analysisofthe
probabilityoflargepricefallswithhighlevelsofduration.2Theanalysisiscarried
out using up-to-date techniques for the nonparametric estimation of conditional
distributions,andoutlinesadescriptiveprocedurethatcanbeusefulinchoosing
the specification of the relationship between duration, volume, and prices when
performingaparametricinvestigation.
2Diamond,D.W.andVerrecchia,R.E.(1987),“ConstraintsonShort-SellingandAssetPrice
AdjustmenttoPrivateInformation”,JournalofFinancialEconomics,18,277–311.
Editor’sintroduction: recentdevelopmentsinhighfrequencyfinancialeconometrics 5
News is the driving force of price movements in financial markets. Veredas
analyses the effect of macroeconomic news on the price of the USA 10-year
treasury bond future. Considering 15 fundamentals, he investigates the effect of
theirforecastingerrorsconditionalupontheirsignandthemomentumofthebusi-
ness cycle.The results show that traders react when the forecasting error differs
fromzero.Thereactiontoapositiveornegativeforecastingerrorisdifferentand,
mostimportantly,thereactionvariessignificantlydependingonthemomentumof
the economic cycle. Moreover, the time of the release matters: the closer it is to
thecoveringperiod,themoreeffectithasonthebondfuture.
Modelingandforecastingthecovarianceofalargenumberoffinancialreturn
serieshasalwaysbeenachallengeduetotheso-called“curseofdimensionality.”
For example, the multivariate GARCH models are heavily parameterized or the
dynamicsofconditionalvariancesandcovariancesmustberestrictedtoreducethe
numberofparameters,e.g.,throughfactorstructures.Asanalternative,thesample
covariancematrixhasoftenbeenused,basedonrollingwindows,e.g.,amonthly
covarianceisestimatedfrommonthlyreturnsofthelast5years.Voevcomparethis
approach,andvariantsofit,withothersthatusehigherfrequencydata(dailydata),
theso-calledrealizedcovariancematrix.Ineachapproach,therearedifferentways
todefineforecasts.Forexample,therealizedcovariancematrixformontht may
servetopredictthecovariancematrixofnextmonth.Amoresophisticatedforecast
isobtainedbytakingaconvexcombinationoftherealizedcovarianceofmontht
andanequicorrelatedcovariancematrix,atechniqueknownas“shrinkage.”The
previous forecasts are static.Another method consists in modeling the different
elementsoftherealizedcovariancematrixbyusingseparateunivariatetimeseries
modelstoconstructforecasts.Thisraisesthedifficultytoobtainalwaysapositive
definiteforecast.Voevmeasuresthedeviationoftheforecastasamatrixfromits
targetbyusingtheFrobeniusnorm,wherethetargetor“true”covariancematrix
istherealizedcovariancematrix(observedexpost),andbyDiebold–Marianosta-
tisticaltests.Hismainconclusionisthatthedynamicmodelsresultinthesmallest
errorsinthecovariancematrixforecastsformostoftheanalyzeddataseries.
