Handbook of Modeling High–Frequency Data in Finance

CUTTING–EDGE DEVELOPMENTS IN HIGH–FREQUENCY FINANCIAL ECONOMETRICS

In recent years, the availability of high–frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High–Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data.

A one–stop compilation of empirical and analytical research, this handbook explores data sampled with high–frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real–world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high–frequency finance, such as:

Designing new methodology to discover elasticity and plasticity of price evolution

Constructing microstructure simulation models

Calculation of option prices in the presence of jumps and transaction costs

Using boosting for financial analysis and trading

The handbook motivates practitioners to apply high–frequency finance to real–world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi–period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods.

Handbook of Modeling High–Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high–frequency data in their everyday work. It also serves as a supplement for risk management and high–frequency finance courses at the upper–undergraduate and graduate levels.

Preface xi

Contributors xiii

Part One Analysis of Empirical Data 1

1 Estimation of NIG and VG Models for High FrequencyFinancial Data 3
José E. Figueroa–López, Steven R. Lancette, KiseopLee, and Yanhui Mi

1.1 Introduction, 3

1.2 The Statistical Models, 6

1.3 Parametric Estimation Methods, 9

1.4 Finite–Sample Performance via Simulations, 14

1.5 Empirical Results, 18

1.6 Conclusion, 22

References, 24

2 A Study of Persistence of Price Movement using HighFrequency Financial Data 27
Dragos Bozdog, Ionut¸ Florescu, Khaldoun Khashanah, and JimWang

2.1 Introduction, 27

2.2 Methodology, 29

2.3 Results, 35

2.4 Rare Events Distribution, 41

2.5 Conclusions, 44

References, 45

3 Using Boosting for Financial Analysis and Trading47
Germán Creamer

3.1 Introduction, 47

3.2 Methods, 48

3.3 Performance Evaluation, 53

3.4 Earnings Prediction and Algorithmic Trading, 60

3.5 Final Comments and Conclusions, 66

References, 69

4 Impact of Correlation Fluctuations on Securitizedstructures 75
Eric Hillebrand, Ambar N. Sengupta, and Junyue Xu

4.1 Introduction, 75

4.2 Description of the Products and Models, 77

4.3 Impact of Dynamics of Default Correlation on

Low–Frequency Tranches, 79

4.4 Impact of Dynamics of Default Correlation on High–FrequencyTranches, 87

4.5 Conclusion, 92

References, 94

5 Construction of Volatility Indices Using A MultinomialTree Approximation Method 97
Dragos Bozdog, Ionut¸ Florescu, Khaldoun Khashanah, andHongwei Qiu

5.1 Introduction, 97

5.2 New Methodology, 99

5.3 Results and Discussions, 101

5.4 Summary and Conclusion, 110

References, 115

Part Two Long Range Dependence Models 117

6 Long Correlations Applied to the Study of Memory Effects inHigh Frequency (TICK) Data, the Dow Jones Index, and InternationalIndices 119
Ernest Barany and Maria Pia Beccar Varela

6.1 Introduction, 119

6.2 Methods Used for Data Analysis, 122

6.3 Data, 128

6.4 Results and Discussions, 132

6.5 Conclusion, 150

References, 160

7 Risk Forecasting with GARCH, Skewed t Distributions,and Multiple Timescales 163
Alec N. Kercheval and Yang Liu

7.1 Introduction, 163

7.2 The Skewed t Distributions, 165

7.3 Risk Forecasts on a Fixed Timescale, 176

7.4 Multiple Timescale Forecasts, 185

7.5 Backtesting, 188

7.6 Further Analysis: Long–Term GARCH and Comparisons usingSimulated Data, 203

7.7 Conclusion, 216

References, 217

8 Parameter Estimation and Calibration for Long–MemoryStochastic Volatility Models 219
Alexandra Chronopoulou

8.1 Introduction, 219

8.2 Statistical Inference Under the LMSV Model, 222

8.3 Simulation Results, 227

8.4 Application to the S&P Index, 228

8.5 Conclusion, 229

References, 230

Part Three Analytical Results 233

9 A Market Microstructure Model of Ultra High FrequencyTrading 235
Carlos A. Ulibarri and Peter C. Anselmo

9.1 Introduction, 235

9.2 Microstructural Model, 237

9.3 Static Comparisons, 239

9.4 Questions for Future Research, 241

References, 242

10 Multivariate Volatility Estimation with High FrequencyData Using Fourier Method 243
Maria Elvira Mancino and Simona Sanfelici

10.1 Introduction, 243

10.2 Fourier Estimator of Multivariate Spot Volatility, 246

10.3 Fourier Estimator of Integrated Volatility in the Presenceof Microstructure Noise, 252

10.4 Fourier Estimator of Integrated Covariance in the Presenceof Microstructure Noise, 263

10.5 Forecasting Properties of Fourier Estimator, 272

10.6 Application: Asset Allocation, 286

References, 290

11 The "Retirement" Problem 295
Cristian Pasarica

11.1 Introduction, 295

11.2 The Market Model, 296

11.3 Portfolio and Wealth Processes, 297

11.4 Utility Function, 299

11.5 The Optimization Problem in the Case (t,T]  0, 299

11.6 Duality Approach, 300

11.7 Infinite Horizon Case, 305

References, 324

12 Stochastic Differential Equations and Levy Models withApplications to High Frequency Data 327
Ernest Barany and Maria Pia Beccar Varela

12.1 Solutions to Stochastic Differential Equations, 327

12.2 Stable Distributions, 334

12.3 The Levy Flight Models, 336

12.4 Numerical Simulations and Levy Models: Applications toModels Arising in Financial Indices and High Frequency Data,340

12.5 Discussion and Conclusions, 345

References, 346

13 Solutions to Integro–Differential Parabolic ProblemArising on Financial Mathematics 347
Maria C. Mariani, Marc Salas, and Indranil SenGupta

13.1 Introduction, 347

13.2 Method of Upper and Lower Solutions, 351

13.3 Another Iterative Method, 364

13.4 Integro–Differential Equations in a Lévy Market,375

References, 380

14 Existence of Solutions for Financial Models withTransaction Costs and Stochastic Volatility 383
Maria C. Mariani, Emmanuel K. Ncheuguim, and IndranilSenGupta

14.1 Model with Transaction Costs, 383

14.2 Review of Functional Analysis, 386

14.3 Solution of the Problem (14.2) and (14.3) in SobolevSpaces, 391

14.4 Model with Transaction Costs and Stochastic Volatility,400

14.5 The Analysis of the Resulting Partial DifferentialEquation, 408

References, 418

Index 421

Frederi G. Viens, PhD, is Director and Coordinator of theComputational Finance Program at Purdue University, where he alsoserves as Professor of Statistics and Mathematics. He has publishedextensively in the areas of mathematical finance, probabilitytheory, and stochastic processes. Dr. Viens is co–organizer of theannual Conference on Modeling High–Frequency Data in Finance.

Maria C. Mariani, PhD, is Pro–fessor and Chair in theDepartment of Mathematical Sciences at The University of Texas atEl Paso. She currently focuses her research on mathematicalfinance, applied mathematics, and numerical methods. Dr. Mariani isco–organizer of the annual Conference on Modeling High–FrequencyData in Finance.

Ionut Florescu, PhD, is Assistant Professor ofMathematics at Stevens Institute of Technology. He has published inresearch areas including stochastic volatility, stochastic partialdifferential equations, Monte Carlo methods, and numerical methodsfor stochastic processes. Dr. Florescu is lead organizer of theannual Conference on Modeling High–Frequency Data in Finance.