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, 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
