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NicholasBucheleresSeptember26,2011

ModelingHigh-FrequencyFinancialEngineering:

Ithinkthatitwouldbereasonableforustomodelthreedisparate,algorithmic,blackboxtradingmodels.AsIexplainedatourmeetingon9/26,thefollowingis

thestructureoftheprojecthatIamproposing.Structure:Ibelievethatourfundamentalquestionshouldfocusonstatisticalmarketcorrelationsasafunctionofmarketvolatility.AsIstated,Ibelieveitwouldbeappropriatetochoosethreediametricallyopposedinstancesofmarketvolatilityoveragivenperiodoftime.Inordertotakefulladvantageofyearly,quarterly,monthly,weekly,anddailyseasonalityofpricemovementcorrelations,Ithinkthatthreetwoyeartimeserieswouldbeappropriate.Forequities,the$VIXindexwillbeourvolatilitybenchmark.Ifwechosetomodelrates,futures,oroptions,wemaywanttocalculateourownvolatilityfeaturesthroughastochasticorregressionmodel(i.e.GARCH).Thebreakdownisasfollows:

Twoyearperiodofincreasingmarketvolatility:o BlackBox#1o BlackBox#2o BlackBox#3

Twoyearperiodofdecreasingmarketvolatility:

o BlackBox#1o BlackBox#2o BlackBox#3

Twoyearperiodofsteady(small,ifany,netchange)marketvolatility:

o BlackBox#1o BlackBox#2o BlackBox#3

Wewillparseourtimeseriesintotwopieces.Giventhefirstpiece(firstyear),wewillgeneticallyevolveeachBlackBoxtooptimizehistoricalreturnsforthepastyear,remainingconsciousofprevailingvolatilityeffectsthatwenoticeforeach

volatilitytimeseriesontheperformanceofouralgorithms.

Hello,thesis.OncewehaveoptimizedeachBlackBoxovertime[-1,0),wewillthentreatt=0asthepresent,andactasif(0,1]isoneyearintothefuture.Wewanttoavoidpurebacktesting,especiallywithgeneticalgorithmicevolution(artificialintelligencefeatures),becauseourresultswillsimplyreflectourabilitytofitalgorithmstohistoricaldataandwillnotnecessarilyhaveanypredictivecapability.

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BlackBoxfeatures:

IntermsofhowwewilldesignourBlackBoxalgorithms,wehaveavarietyoffeaturesthatwecanamalgamateintoeachBlackBox.EachBoxwillconsistofthreetimeseries,orthreeriskprofiles.Possiblesetsfollow:

BlackBox#1:MovingAverageAnalysiso Shortterm-1,5,&20dayexponentiallyweightedmovingaverage

cross-over,firstderivative,andsecondderivateanalysiso Mediumterm-20,45,&100dayexponentiallyweightedmoving

averagecross-over,firstderivative,andsecondderivativeanalysiso Longterm-100,150,&200dayexponentiallyweightedmoving

averagecross-over,firstderivative,andsecondderivateanalysis

BlackBox#2:MeanReversion,Coefficient/SpreadAnalysiso Shortterm-StandardDeviation/Spreadbandsconstructedaboutthe

correlationcoefficient(orstandardizedspread)ofprice-movement-relatedassets.Signalsgeneratedfromcoefficientcrossingverynarrowbands;lessthanonestandarddeviation(z-score1)

o Mediumterm-StandardDeviation/Spreadbandsconstructedaboutthecorrelationcoefficient(orstandardizedspread)ofprice-movement-relatedassets.Signalsgeneratedfromcoefficientcrossinglargerbands;betweenoneandtwostandarddeviations(1z-score2)

o Longterm-StandardDeviation/Spreadbandsconstructedaboutthecorrelationcoefficient(orstandardizedspread)ofprice-movement-relatedassets.Signalsgeneratedfromcoefficientcrossingsignificantlydeviatedbands;greaterthantwostandarddeviations(z-score2)

BlackBox#3:Volatility,Liquidity,Volume,&TimeCorrelations,Miscellaneous

o Shortterm-Intra-dayseasonalitycorrelations(autocorrelation)betweenvolatility,liquidity,volume,timeandpricemovement

o Mediumterm-Intra-weekseasonalitycorrelations(autocorrelation)betweenvolatility,liquidity,volume,timeandpricemovement

o Longterm-Monthlyandquarterlyvolatility,liquidity,volume,andtimeseasonalitypatterns(autocorrelations).

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Process:Wewillcrossanalyzeeachtimehorizon,andBlackBoxsignalgenerationswillbecomprisedofshort,medium,andlongtermsignalgenerationsthatmeetourvalue-at-risk,andexpectedreturnthresholds,whichwillultimatelybedependanton(aswewillsee)prevailingmarketvolatility.

Signalgenerationwillbeabottom-upprocess.Thatis,givenourrisktolerance,wewillwaitforalonger-termsignaltobegeneratedthatalertsusofanattractivepositiontoenter,andthenwewillwaittoseeifashorter-termsignalisgenerated.Ifgenerated,theshorter-termsignalwillallowusthemostattractiveentranceintothelonger-termtrend.Wewillridesaidtrenduntilacountersignalisgenerated.Weareabletopredictthefollowing,andtheyshouldbeconsideredbeforeenteredanyposition:

Absolutesizeoffuturereturns:Calculatedusingarealizedvolatility

equation.Underthiscondition,wewillbeabletoevaluatetheriskofholdinganyposition.

Futurereturnovertheforecastperiod:CalculatedthroughexpectedreturnE(R)=Sum:probability(inscenarioi)*thereturn(inscenarioi)

Fullprobabilitydistributionfunctionoffuturereturns:Calculatedusingthe

continuousprobabilitydistributionequationPr[axb]=abf(x)dxAprofitablealgorithmic(BlackBox)systemwillalwayskeepinmindthebottomline,thatistheprofit&loss,value-at-risk,expectedreturn,andultimatelytheperformanceoftheportfolioasameasureofallfuturedecisions.