Handbook of Modeling High-Frequency Data in Finance Published Wiley Handbooks in Financial Engineering and Econometrics Viens, Mariani, and Florescu · HandbookofModelingHigh-FrequencyDatain Finance ForthcomingWileyHandbooksinFinancialEngineeringandEconometrics Bali and Engle · HandbookofAssetPricing Bauwens, Hafner, and Laurent · HandbookofVolatility ModelsandTheir Applications Brandimarte · HandbookofMonte CarloSimulation Chan and Wong · HandbookofFinancialRiskManagement Cruz, Peters, and Shevchenko · HandbookofOperationalRisk Sarno, James, and Marsh · HandbookofExchangeRates Szylar · HandbookofMarketRisk Handbook of Modeling High-Frequency Data in Finance Edited by Frederi G. Viens Maria C. Mariani Ionut¸ Florescu A JOHNWILEY& SONS, INC., PUBLICATION Copyright©2012JohnWiley&Sons,Inc.Allrightsreserved. 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HG106.V542011 332.01(cid:2)5193–dc23 2011038022 PrintedintheUnitedStatesofAmerica 10987654321 Contents Preface xi Contributors xiii part One Analysis of Empirical Data 1 1 Estimation of NIG and VG Models for High Frequency Financial Data 3 Jos´eE.Figueroa-Lo´pez,StevenR.Lancette,KiseopLee,and YanhuiMi 1.1 Introduction, 3 1.2 TheStatisticalModels, 6 1.3 ParametricEstimationMethods, 9 1.4 Finite-SamplePerformanceviaSimulations, 14 1.5 EmpiricalResults, 18 1.6 Conclusion, 22 References, 24 2 A Study of Persistence of Price Movement using High Frequency Financial Data 27 DragosBozdog,Ionu¸tFlorescu,KhaldounKhashanah, andJimWang 2.1 Introduction, 27 2.2 Methodology, 29 2.3 Results, 35 v vi Contents 2.4 RareEventsDistribution, 41 2.5 Conclusions, 44 References, 45 3 Using Boosting for Financial Analysis and Trading 47 Germa´nCreamer 3.1 Introduction, 47 3.2 Methods, 48 3.3 PerformanceEvaluation, 53 3.4 EarningsPredictionandAlgorithmicTrading, 60 3.5 FinalCommentsandConclusions, 66 References, 69 4 Impact of Correlation Fluctuations on Securitized structures 75 EricHillebrand,AmbarN.Sengupta,andJunyueXu 4.1 Introduction, 75 4.2 DescriptionoftheProductsandModels, 77 4.3 ImpactofDynamicsofDefaultCorrelationon Low-FrequencyTranches, 79 4.4 ImpactofDynamicsofDefaultCorrelationon High-FrequencyTranches, 87 4.5 Conclusion, 92 References, 94 5 Construction of Volatility Indices Using A Multinomial Tree Approximation Method 97 DragosBozdog,Ionu¸tFlorescu,KhaldounKhashanah, andHongweiQiu 5.1 Introduction, 97 5.2 NewMethodology, 99 5.3 ResultsandDiscussions, 101 5.4 SummaryandConclusion, 110 References, 115 Contents vii part Two Long Range Dependence Models 117 6 Long Correlations Applied to the Study of Memory Effects in High Frequency (TICK) Data, the Dow Jones Index, and International Indices 119 ErnestBaranyandMariaPiaBeccarVarela 6.1 Introduction, 119 6.2 MethodsUsedforDataAnalysis, 122 6.3 Data, 128 6.4 ResultsandDiscussions, 132 6.5 Conclusion, 150 References, 160 7 Risk Forecasting with GARCH, Skewed Distributions, and Multiple t Timescales 163 AlecN.KerchevalandYangLiu 7.1 Introduction, 163 7.2 TheSkewedt Distributions, 165 7.3 RiskForecastsonaFixedTimescale, 176 7.4 MultipleTimescaleForecasts, 185 7.5 Backtesting, 188 7.6 FurtherAnalysis:Long-TermGARCHandComparisons usingSimulatedData, 203 7.7 Conclusion, 216 References, 217 8 Parameter Estimation and Calibration for Long-Memory Stochastic Volatility Models 219 AlexandraChronopoulou 8.1 Introduction, 219 8.2 StatisticalInferenceUndertheLMSVModel, 222 8.3 SimulationResults, 227 8.4 ApplicationtotheS&PIndex, 228 viii Contents 8.5 Conclusion, 229 References, 230 part Three Analytical Results 233 9 A Market Microstructure Model of Ultra High Frequency Trading 235 CarlosA.UlibarriandPeterC.Anselmo 9.1 Introduction, 235 9.2 MicrostructuralModel, 237 9.3 StaticComparisons, 239 9.4 QuestionsforFutureResearch, 241 References, 242 10 Multivariate Volatility Estimation with High Frequency Data Using Fourier Method 243 MariaElviraMancinoandSimonaSanfelici 10.1 Introduction, 243 10.2 FourierEstimatorofMultivariateSpotVolatility, 246 10.3 FourierEstimatorofIntegratedVolatilityinthePresenceof MicrostructureNoise, 252 10.4 FourierEstimatorofIntegratedCovarianceinthePresence ofMicrostructureNoise, 263 10.5 ForecastingPropertiesofFourierEstimator, 272 10.6 Application:AssetAllocation, 286 References, 290 11 The ‘‘Retirement’’ Problem 295 CristianPasarica 11.1 Introduction, 295 11.2 TheMarketModel, 296 11.3 PortfolioandWealthProcesses, 297 11.4 UtilityFunction, 299 11.5 TheOptimizationProblemintheCaseπ(τ,T] ≡0, 299 11.6 DualityApproach, 300 11.7 InfiniteHorizonCase, 305 References, 324 Contents ix 12 Stochastic Differential Equations and Levy Models with Applications to High Frequency Data 327 ErnestBaranyandMariaPiaBeccarVarela 12.1 SolutionstoStochasticDifferentialEquations, 327 12.2 StableDistributions, 334 12.3 TheLevyFlightModels, 336 12.4 NumericalSimulationsandLevyModels:Applicationsto ModelsArisinginFinancialIndicesandHighFrequency Data, 340 12.5 DiscussionandConclusions, 345 References, 346 13 Solutions to Integro-Differential Parabolic Problem Arising on Financial Mathematics 347 MariaC.Mariani,MarcSalas,andIndranilSenGupta 13.1 Introduction, 347 13.2 MethodofUpperandLowerSolutions, 351 13.3 AnotherIterativeMethod, 364 13.4 Integro-DifferentialEquationsinaLe´vyMarket, 375 References, 380 14 Existence of Solutions for Financial Models with Transaction Costs and Stochastic Volatility 383 MariaC.Mariani,EmmanuelK.Ncheuguim,andIndranil SenGupta 14.1 ModelwithTransactionCosts, 383 14.2 ReviewofFunctionalAnalysis, 386 14.3 SolutionoftheProblem(14.2)and(14.3)inSobolev Spaces, 391 14.4 ModelwithTransactionCostsandStochasticVolatility, 400 14.5 TheAnalysisoftheResultingPartialDifferential Equation, 408 References, 418 Index 421 Preface This handbook is a collection of articles that describe current empirical and analyticalworkondatasampledwithhighfrequencyinthefinancialindustry. Intoday’sworld,manyfieldsareconfrontedwithincreasinglylargeamounts of data. Financial data sampled with high frequency is no exception. These staggering amounts of data pose special challenges to the world of finance, as traditional models and information technology tools can be poorly suited to grapplewiththeirsizeandcomplexity.Probabilisticmodelingandstatisticaldata analysisattempttodiscoverorderfromapparentdisorder;thisvolumemayserve as a guide to various new systematic approaches on how to implement these quantitativeactivitieswithhigh-frequencyfinancialdata. The volume is split into three distinct parts. The first part is dedicated to empirical work with high frequency data. Starting the handbook this way is consistent with the first type of activity that is typically undertaken when faced with data: to look for its stylized features. The book’s second part is a transitionbetweenempiricalandtheoreticaltopicsandfocusesonpropertiesof longmemory,alsoknownaslongrangedependence.Modelsforstockandindex datawiththistypeofdependenceatthelevelofsquaredreturns,forinstance,are comingintothemainstream;inhighfrequencyfinance,therangeofdependence canbeexacerbated,makinglongmemoryanimportantsubjectofinvestigation. The third and last part of the volume presents new analytical and simulation results proposed to make rigorous sense of some of the difficult modeling questions posed by high frequency data in finance. Sophisticated mathematical tools are used, including stochastic calculus, control theory, Fourier analysis, jumpprocesses,andintegro-differentialmethods. The editors express their deepest gratitude to all the contributors for their talent and labor in bringing together this handbook, to the many anonymous refereeswhohelpedthecontributorsperfecttheirworks,andtoWileyformaking thepublicationareality. FrederiViens MariaC.Mariani Ionut¸ Florescu Washington,DC,ElPaso,TX,andHoboken,NJ April1,2011 xi