Handbook of High-Frequency Trading and Modeling in Finance

Notes on Contributors xiii Preface xv 1 Trends and Trades 1 Michael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos 1.1 Introduction 1 1.2 A trend-based trading strategy 3 1.2.1 Signaling and trends 3 1.2.2 Gain over a subperiod 5 1.3 CUSUM timing 7 1.3.1 Cusum process and stopping time 7 1.3.2 A CUSUM timing scheme 10 1.3.3 US treasury notes, CUSUM timing 11 1.4 Example: Random walk on ticks 12 1.4.1 Random walk expected gain over a subperiod 15 1.4.2 Simple random walk, CUSUM timing 18 1.4.3 Lazy simple random walk, cusum timing 21 1.5 CUSUM strategy Monte Carlo 24 1.6 The effect of the threshold parameter 27 1.7 Conclusions and future work 39 Appendix: Tables 40 References 47 2 Gaussian Inequalities and Tranche Sensitivities 51 Claas Becker and Ambar N. Sengupta 2.1 Introduction 51 2.2 The tranche loss function 52 2.3 A sensitivity identity 54 2.4 Correlation sensitivities 55 Acknowledgment 58 References 58 3 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61 Germán G. Creamer and Bernardo Creamer 3.1 Introduction 61 3.1.1 Causality analysis 62 3.2 Data 64 3.3 Estimation techniques 64 3.4 Results 65 3.5 Discussion 67 3.6 Conclusions 69 Acknowledgments 69 References 70 4 Portfolio Optimization: Applications in Quantum Computing 73 Michael Marzec 4.1 Introduction 73 4.2 Background 75 4.2.1 Portfolios and optimization 76 4.2.2 Algorithmic complexity 77 4.2.3 Performance 78 4.2.4 Ising model 79 4.2.5 Adiabatic quantum computing 79 4.3 The models 80 4.3.1 Financial model 81 4.3.2 Graph-theoretic combinatorial optimization models 82 4.3.3 Ising and Qubo models 83 4.3.4 Mixed models 84 4.4 Methods 84 4.4.1 Model implementation 85 4.4.2 Input data 85 4.4.3 Mean-variance calculations 85 4.4.4 Implementing the risk measure 86 4.4.5 Implementation mapping 86 4.5 Results 88 4.5.1 The simple correlation model 88 4.5.2 The restricted minimum-risk model 91 4.5.3 The WMIS minimum-risk, max return model 94 4.6 Discussion 95 4.6.1 Hardware limitations 97 4.6.2 Model limitations 97 4.6.3 Implementation limitations 98 4.6.4 Future research 98 4.7 Conclusion 100 Acknowledgments 100 Appendix 4.A: WMIS Matlab Code 100 References 103 5 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107 Ionut Florescu and Forrest Levin 5.1 Introduction 107 5.1.1 The original motivation 108 5.1.2 The model and the problem 108 5.1.3 A brief historical note 109 5.2 The methodology 110 5.2.1 Obtaining filtered empirical distributions at t1,..., tT 110 5.2.2 Obtaining the parameters of the Markov chain 112 5.3 Results obtained applying the model to real data 113 5.3.1 Part i: financial applications 113 5.3.2 Part ii: physical data application. temperature data 119 5.3.3 Part iii: analysis of seismometer readings during an earthquake 121 5.3.4 Analysis of the earthquake signal: beginning 123 5.3.5 Analysis: during the earthquake 125 5.3.6 Analysis: end of the earthquake signal, aftershocks 127 5.4 Conclusion 127 5.A Theoretical results and empirical testing 128 5.A.1 How does the particle filter work? 128 5.A.2 Theoretical results about convergence and parameter estimates 129 5.A.3 Markov chain parameter estimates 131 5.A.4 Empirical testing 132 5.A.5 A list of supplementary documents 133 References 133 6 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137 Ping-Chen Tsai and Mark B. Shackleton 6.1 Introduction 137 6.2 Review on the intraday jump tests 140 6.2.1 Realized volatility measure and the BNS tests 140 6.2.2 The ABD and LM tests 142 6.3 A data-driven testing procedure 146 6.3.1 Spy data and microstructure noise 146 6.3.2 A generalized testing procedure 149 6.4 Simulation study 153 6.4.1 Model specification 153 6.4.2 Simulation results 158 6.5 Empirical results 161 6.5.1 Results on the backward-looking test 162 6.5.2 Results on the interpolated test 165 6.6 Conclusion 165 Acknowledgments 166 Appendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167 Appendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168 Appendix 6.C: Minimized loss function loss(rho1, rho2) for SV2FJ_2 rho model, SPY 169 Appendix 6.D.1: Calibration of xi under SV2FJ_2 rho model at 2-min frequency, E[Nt] = 0.08 170 Appendix 6.D.2: Calibration of xi under SV2FJ_2 rho model at 2-min frequency, E[Nt] = 0.40 171 Appendix 6.D.3: Calibration of xi under SV2FJ_2 rho model at 5-min frequency, E[Nt] = 0.08 172 Appendix 6.D.4: Calibration of xi under SV2FJ_2 rho Model at 5-min frequency, E[Nt] = 0.40 173 Appendix 6.D.5: Calibration of xi under SV2FJ_2 rho model at 10-min frequency, E[Nt] = 0.08 174 Appendix 6.D.6: Calibration of xi under SV2FJ_2 rho model at 10-min frequency, E[Nt] = 0.40 175 References 175 7 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183 Baron Law and Frederi G. Viens 7.1 Introduction 183 7.2 Point processes 184 7.3 Hawkes processes 186 7.3.1 Branching structure representation 188 7.3.2 Stationarity 188 7.3.3 Convergence 189 7.4 Statistical inference of Hawkes processes 191 7.4.1 Simulation 191 7.4.2 Estimation 194 7.4.3 Hypothesis testing 197 7.5 Applications of Hawkes processes 198 7.5.1 Modeling order arrivals 199 7.5.2 Modeling price jumps 200 7.5.3 Modeling jump-diffusion 205 7.5.4 Measuring endogeneity (Reflexivity) 205 Appendix 7.A: Point Processes 207 7.A.1 Definition 207 7.A.2 Moments 208 7.A.3 Marked point processes 209 7.A.4 Stochastic intensity 209 7.A.5 Random time change 211 Appendix 7.B: A Brief History of Hawkes processes 211 References 212 8 Multifractal Random Walk Driven by a Hermite Process 221 Alexis Fauth and Ciprian A. Tudor 8.1 Introduction 221 8.2 Preliminaries 224 8.2.1 Fractional brownian motion and hermite processes 224 8.2.2 Wiener integrals with respect to the hermite process 226 8.2.3 Infinitely divisible cascading noise 229 8.3 Multifractal random walk driven by a Hermite process 231 8.3.1 Definition and existence 231 8.3.2 Properties of the hermite multifractal random walk 233 8.4 Financial applications 234 8.4.1 Simulation of the Hmrw 235 8.4.2 Financial statistics 241 8.5 Concluding remarks 243 References 247 9 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251 K. Basu and Maria C. Mariani 9.1 Introduction 251 9.2 Nonparametric regression models 253 9.2.1 Local polynomial regression 255 9.2.2 Lowess/loess method 257 9.2.3 Numerical applications 259 9.3 Interpolation methods 271 9.3.1 Nearest-neighbor interpolation 271 9.3.2 Bilinear interpolation 272 9.3.3 Bicubic interpolation 276 9.3.4 Biharmonic interpolation 277 9.3.5 Thin plate splines 282 9.3.6 Numerical applications 285 9.4 Conclusion 287 Acknowledgments 292 References 292 10 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295 Maria C. Mariani, F. Biney, and I. SenGupta 10.1 Introduction 295 10.2 Short memory models 297 10.2.1 ARMA(p,q) model 297 10.2.2 GARCH(p,q) model 297 10.2.3 IGARCH(1,1) model 298 10.3 Long memory models 298 10.3.1 ARFIMA(p,d,q) model 299 10.3.2 ARFIMA(p,d,q)-GARCH(r,s) 299 10.3.3 Intermediate memory process 300 10.3.4 Figarch model 300 10.4 Detection and estimation of long memory 302 10.4.1 Augmented dickey-fuller test(ADF test) 302 10.4.2 KPSS test 303 10.4.3 Whittle method 304 10.5 Data collection, analysis, and result 306 10.5.1 Analysis on dow Jones index (DJIA) returns 306 10.5.2 Model selection and specification: conditional mean 306 10.5.3 Conditional mean model (returns) 309 10.5.4 Model diagnostics: ARMA(2, 2) 309 10.5.5 Test for ARCH effect 311 10.5.6 Model selection and specification: Conditional variance 313 10.5.7 Standardized residuals test 314 10.5.8 Model diagnostics 314 10.5.9 Returns and variance equation 315 10.5.10 standardized residuals test 317 10.5.11 Model diagnostic of conditional returns with conditional variance 318 10.5.12 One-step ahead prediction of last 10 observations 330 10.5.13 Analysis on high-frequency, earthquake, and explosives series 330 10.6 Discussion and conclusion 335 References 337 11 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341 M. P. Beccar-Varela, Ionut Florescu, and I. SenGupta 11.1 Introduction 341 11.2 Governing equations for the deterministic model 342 11.2.1 Application to geophysical (earthquake data) 343 11.2.2 Results 344 11.3 L´evy flights and application to geophysics 345 11.3.1 Truncated L´evy flight distribution 353 11.3.2 Results 356 11.4 Application to the high-frequency market data 360 11.4.1 Methodology 360 11.4.2 Results 361 11.5 Brief program code description 362 11.6 Conclusion 364 11.A Appendix 366 11.A.1 Stable distributions 366 11.A.2 Characterization of stable distributions 367 References 368 12 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371 M. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek 12.1 Introduction 371 12.2 Statistical preliminaries and results 373 12.2.1 Sum of exponential random variables with different parameters 374 12.3 Statistical and numerical analysis 377 12.4 Analysis with Lévy distribution 380 12.4.1 Characterization of Stable Distributions 383 12.4.2 Truncated Lévy flight (TLF) distribution 384 12.4.3 Data analysis with TLF distribution 389 12.4.4 Sum of Lévy random variables with different parameters 390 12.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 394 12.6 Results and discussion 409 Acknowledgments 421 12.A Appendix A--Big 'O' notation 421 References 422 Index 425