Handbook of Modeling High-Frequency Data in Finance

443 Pages·2011·4.028 MB·English

by  Frederi G. Viens, Maria C. Mariani, Ionut Florescu

Handbook of
Modeling
High-Frequency
Data in Finance
Published Wiley Handbooks in Financial Engineering and Econometrics
Viens, Mariani, and Florescu · HandbookofModelingHigh-FrequencyDatain
Finance
ForthcomingWileyHandbooksinFinancialEngineeringandEconometrics
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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
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LibraryofCongressCataloging-in-PublicationData:
Viens,FrederiG.,1969–
Handbookofmodelinghigh-frequencydatainfinance/FrederiG.Viens,MariaC.
Mariani,Ionu¸tFlorescu.—1
p.cm.—(Wileyhandbooksinfinancialengineeringandeconometrics;4)
Includesindex.
ISBN978-0-470-87688-6(hardback)
1.Finance–Econometricmodels.I.Mariani,MariaC.II.Florescu,Ionu¸t,
1973–III.Title.
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