Title Details

Maria C. Mariani, PhD, is Pro-fessor and Chair in the Department of Mathematical Sciences at The University of Texas at El Paso. She currently focuses her research on mathematical finance, applied mathematics, and numerical methods. Dr. Mariani is co-organizer of the annual Conference on Modeling High-Frequency Data in Finance.

Ionut Florescu, PhD, is Assistant Professor of Mathematics at Stevens Institute of Technology. He has published in research areas including stochastic volatility, stochastic partial differential equations, Monte Carlo methods, and numerical methods for stochastic processes. Dr. Florescu is lead organizer of the annual Conference on Modeling High-Frequency Data in Finance.

Contributors xiii

Part One Analysis of Empirical Data 1

1 Estimation of NIG and VG Models for High Frequency Financial Data 3
José E. Figueroa-López, Steven R. Lancette, Kiseop Lee, 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 High Frequency Financial Data 27
Dragos Bozdog, Ionut¸ Florescu, Khaldoun Khashanah, and Jim Wang

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 Trading 47
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 Securitized structures 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-Frequency Tranches, 87

4.5 Conclusion, 92

References, 94

5 Construction of Volatility Indices Using A Multinomial Tree Approximation Method 97
Dragos Bozdog, Ionut¸ Florescu, Khaldoun Khashanah, and Hongwei 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 in High Frequency (TICK) Data, the Dow Jones Index, and International Indices 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 using Simulated Data, 203

7.7 Conclusion, 216

References, 217

8 Parameter Estimation and Calibration for Long-Memory Stochastic 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 Frequency Trading 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 Frequency Data 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 Presence of Microstructure Noise, 252

10.4 Fourier Estimator of Integrated Covariance in the Presence of 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 π(_{t ,T}] ≡ 0, 299

11.6 Duality Approach, 300

11.7 Infinite Horizon Case, 305

References, 324

12 Stochastic Differential Equations and Levy Models with Applications 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 to Models Arising in Financial Indices and High Frequency Data, 340

12.5 Discussion and Conclusions, 345

References, 346

13 Solutions to Integro-Differential Parabolic Problem Arising 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 with Transaction Costs and Stochastic Volatility 383
Maria C. Mariani, Emmanuel K. Ncheuguim, and Indranil SenGupta

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 Sobolev Spaces, 391

14.4 Model with Transaction Costs and Stochastic Volatility, 400

14.5 The Analysis of the Resulting Partial Differential Equation, 408

References, 418

Index 421