Handbook of Modeling High-Frequency Data in Finance

Frederi G. Viens, PhD, is Director and Coordinator of the Computational Finance Program at Purdue University, where he also serves as Professor of Statistics and Mathematics. He has published extensively in the areas of mathematical finance, probability theory, and stochastic processes. Dr. Viens is co-organizer of the annual Conference on Modeling High-Frequency Data in Finance. 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.

• Preface xiContributors xiiiPart One Analysis of Empirical Data 11 Estimation of NIG and VG Models for High Frequency Financial Data 3José E. Figueroa-López Steven R. Lancette Kiseop Lee and Yanhui mi1.1 Introduction 31.2 The Statistical Models 61.3 Parametric Estimation Methods 91.4 Finite-Sample Performance via Simulations 141.5 Empirical Results 181.6 Conclusion 22References 242 A Study of Persistence of Price Movement using High Frequency Financial Data 27Dragos Bozdog Ionuţ Florescu Khaldoun Khashanah and Jim Wang2.1 Introduction 272.2 Methodology 292.3 Results 352.4 Rare Events Distribution 412.5 Conclusions 44References 453 Using Boosting for Financial Analysis and Trading 47Germán Creamer3.1 Introduction 473.2 Methods 483.3 Performance Evaluation 533.4 Earnings Prediction and Algorithmic Trading 603.5 Final Comments and Conclusions 66References 694 Impact of Correlation Fluctuations on Securitized structures 75Eric Hillebrand Ambar N. Sengupta and Junyue Xu4.1 Introduction 754.2 Description of the Products and Models 774.3 Impact of Dynamics of Default Correlation on Low-Frequency Tranches 794.4 Impact of Dynamics of Default Correlation on High-Frequency Tranches 874.5 Conclusion 92References 945 Construction of Volatility Indices Using A Multinomial Tree Approximation Method 97Dragos Bozdog Ionuţ Florescu Khaldoun Khashanah and Hongwei Qiu5.1 Introduction 975.2 New Methodology 995.3 Results and Discussions 1015.4 Summary and Conclusion 110References 115Part Two Long Range Dependence Models 1176 Long Correlations Applied to the Study of Memory Effects in High Frequency (TICK) Data the Dow Jones Index and International Indices 119Ernest Barany and Maria Pia Beccar Varela6.1 Introduction 1196.2 Methods Used for Data Analysis 1226.3 Data 1286.4 Results and Discussions 1326.5 Conclusion 150References 1607 Risk Forecasting with GARCH Skewed t Distributions and Multiple Timescales 163Alec N. Kercheval and Yang Liu7.1 Introduction 1637.2 The Skewed t Distributions 1657.3 Risk Forecasts on a Fixed Timescale 1767.4 Multiple Timescale Forecasts 1857.5 Backtesting 1887.6 Further Analysis: Long-Term GARCH and Comparisons using Simulated Data 2037.7 Conclusion 216References 2178 Parameter Estimation and Calibration for Long-Memory Stochastic Volatility Models 219Alexandra Chronopoulou8.1 Introduction 2198.2 Statistical Inference Under the LMSV Model 2228.3 Simulation Results 2278.4 Application to the S&P Index 2288.5 Conclusion 229References 230Part Three Analytical Results 2339 A Market Microstructure Model of Ultra High Frequency Trading 235Carlos A. Ulibarri and Peter C. Anselmo9.1 Introduction 2359.2 Microstructural Model 2379.3 Static Comparisons 2399.4 Questions for Future Research 241References 24210 Multivariate Volatility Estimation with High Frequency Data Using Fourier Method 243MariaElviraMancinoandSimonaSanfelici10.1 Introduction 24310.2 Fourier Estimator of Multivariate Spot Volatility 24610.3 Fourier Estimator of Integrated Volatility in the Presence of Microstructure Noise 25210.4 Fourier Estimator of Integrated Covariance in the Presence of Microstructure Noise 26310.5 Forecasting Properties of Fourier Estimator 27210.6 Application: Asset Allocation 286References 29011 The ‘‘Retirement’’ Problem 295Cristian Pasarica11.1 Introduction 29511.2 The Market Model 29611.3 Portfolio and Wealth Processes 29711.4 Utility Function 29911.5 The Optimization Problem in the Case π (τT ] ≡ 0 29911.6 Duality Approach 30011.7 Infinite Horizon Case 305References 32412 Stochastic Differential Equations and Levy Models with Applications to High Frequency Data 327Ernest Barany and Maria Pia Beccar Varela12.1 Solutions to Stochastic Differential Equations 32712.2 Stable Distributions 33412.3 The Levy Flight Models 33612.4 Numerical Simulations and Levy Models: Applications to Models Arising in Financial Indices and High Frequency Data 34012.5 Discussion and Conclusions 345References 34613 Solutions to Integro-Differential Parabolic Problem Arising on Financial Mathematics 347Maria C. Mariani Marc Salas and Indranil SenGupta13.1 Introduction 34713.2 Method of Upper and Lower Solutions 35113.3 Another Iterative Method 36413.4 Integro-Differential Equations in a Lévy Market 375References 38014 Existence of Solutions for Financial Models with Transaction Costs and Stochastic Volatility 383Maria C. Mariani Emmanuel K. Ncheuguim and Indranil SenGupta14.1 Model with Transaction Costs 38314.2 Review of Functional Analysis 38614.3 Solution of the Problem (14.2) and (14.3) in Sobolev Spaces 39114.4 Model with Transaction Costs and Stochastic Volatility 40014.5 The Analysis of the Resulting Partial Differential Equation 408References 418Index 421