Table of 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
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 Ionuţ 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 Ionuţ 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
MariaElviraMancinoandSimonaSanfelici
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 (τT ] ≡ 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
