Handbook of Modeling High-Frequency Data in Finance

Preface xi Contributors xiii Part One Analysis of Empirical Data 1 1 Estimation of NIG and VG Models for High Frequency Financial Data 3 Jose E. Figueroa-Lopez, 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, IonutC 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 German 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, IonutC 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 pi( 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 Levy 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