Handbook of High-Frequency Trading and Modeling in Finance

Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley.Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences.Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.

• Notes on Contributors xiiiPreface xv1 Trends and Trades 1Michael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos1.1 Introduction 11.2 A trend-based trading strategy 31.2.1 Signaling and trends 31.2.2 Gain over a subperiod 51.3 CUSUM timing 71.3.1 Cusum process and stopping time 71.3.2 A CUSUM timing scheme 101.3.3 US treasury notes, CUSUM timing 111.4 Example: Random walk on ticks 121.4.1 Random walk expected gain over a subperiod 151.4.2 Simple random walk, CUSUM timing 181.4.3 Lazy simple random walk, cusum timing 211.5 CUSUM strategy Monte Carlo 241.6 The effect of the threshold parameter 271.7 Conclusions and future work 39Appendix: Tables 40References 472 Gaussian Inequalities and Tranche Sensitivities 51Claas Becker and Ambar N. Sengupta2.1 Introduction 512.2 The tranche loss function 522.3 A sensitivity identity 542.4 Correlation sensitivities 55Acknowledgment 58References 583 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61Germán G. Creamer and Bernardo Creamer3.1 Introduction 613.1.1 Causality analysis 623.2 Data 643.3 Estimation techniques 643.4 Results 653.5 Discussion 673.6 Conclusions 69Acknowledgments 69References 704 Portfolio Optimization: Applications in Quantum Computing 73Michael Marzec4.1 Introduction 734.2 Background 754.2.1 Portfolios and optimization 764.2.2 Algorithmic complexity 774.2.3 Performance 784.2.4 Ising model 794.2.5 Adiabatic quantum computing 794.3 The models 804.3.1 Financial model 814.3.2 Graph-theoretic combinatorial optimization models 824.3.3 Ising and Qubo models 834.3.4 Mixed models 844.4 Methods 844.4.1 Model implementation 854.4.2 Input data 854.4.3 Mean-variance calculations 854.4.4 Implementing the risk measure 864.4.5 Implementation mapping 864.5 Results 884.5.1 The simple correlation model 884.5.2 The restricted minimum-risk model 914.5.3 The WMIS minimum-risk, max return model 944.6 Discussion 954.6.1 Hardware limitations 974.6.2 Model limitations 974.6.3 Implementation limitations 984.6.4 Future research 984.7 Conclusion 100Acknowledgments 100Appendix 4.A: WMIS Matlab Code 100References 1035 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107Ionut Florescu and Forrest Levin5.1 Introduction 1075.1.1 The original motivation 1085.1.2 The model and the problem 1085.1.3 A brief historical note 1095.2 The methodology 1105.2.1 Obtaining filtered empirical distributions at t1,…, tT 1105.2.2 Obtaining the parameters of the Markov chain 1125.3 Results obtained applying the model to real data 1135.3.1 Part i: financial applications 1135.3.2 Part ii: physical data application. temperature data 1195.3.3 Part iii: analysis of seismometer readings during an earthquake 1215.3.4 Analysis of the earthquake signal: beginning 1235.3.5 Analysis: during the earthquake 1255.3.6 Analysis: end of the earthquake signal, aftershocks 1275.4 Conclusion 1275.A Theoretical results and empirical testing 1285.A.1 How does the particle filter work? 1285.A.2 Theoretical results about convergence and parameter estimates 1295.A.3 Markov chain parameter estimates 1315.A.4 Empirical testing 1325.A.5 A list of supplementary documents 133References 1336 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137Ping-Chen Tsai and Mark B. Shackleton6.1 Introduction 1376.2 Review on the intraday jump tests 1406.2.1 Realized volatility measure and the BNS tests 1406.2.2 The ABD and LM tests 1426.3 A data-driven testing procedure 1466.3.1 Spy data and microstructure noise 1466.3.2 A generalized testing procedure 1496.4 Simulation study 1536.4.1 Model specification 1536.4.2 Simulation results 1586.5 Empirical results 1616.5.1 Results on the backward-looking test 1626.5.2 Results on the interpolated test 1656.6 Conclusion 165Acknowledgments 166Appendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167Appendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168Appendix 6.C: Minimized loss function loss(𝜌1, 𝜌2) for SV2FJ_2𝜌 model, SPY 169Appendix 6.D.1: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.08 170Appendix 6.D.2: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.40 171Appendix 6.D.3: Calibration of 𝜉 under SV2FJ_2𝜌 model at 5-min frequency, E[Nt] = 0.08 172Appendix 6.D.4: Calibration of 𝜉 under SV2FJ_2𝜌 Model at 5-min frequency, E[Nt] = 0.40 173Appendix 6.D.5: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.08 174Appendix 6.D.6: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.40 175References 1757 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183Baron Law and Frederi G. Viens7.1 Introduction 1837.2 Point processes 1847.3 Hawkes processes 1867.3.1 Branching structure representation 1887.3.2 Stationarity 1887.3.3 Convergence 1897.4 Statistical inference of Hawkes processes 1917.4.1 Simulation 1917.4.2 Estimation 1947.4.3 Hypothesis testing 1977.5 Applications of Hawkes processes 1987.5.1 Modeling order arrivals 1997.5.2 Modeling price jumps 2007.5.3 Modeling jump-diffusion 2057.5.4 Measuring endogeneity (Reflexivity) 205Appendix 7.A: Point Processes 2077.A.1 Definition 2077.A.2 Moments 2087.A.3 Marked point processes 2097.A.4 Stochastic intensity 2097.A.5 Random time change 211Appendix 7.B: A Brief History of Hawkes processes 211References 2128 Multifractal Random Walk Driven by a Hermite Process 221Alexis Fauth and Ciprian A. Tudor8.1 Introduction 2218.2 Preliminaries 2248.2.1 Fractional brownian motion and hermite processes 2248.2.2 Wiener integrals with respect to the hermite process 2268.2.3 Infinitely divisible cascading noise 2298.3 Multifractal random walk driven by a Hermite process 2318.3.1 Definition and existence 2318.3.2 Properties of the hermite multifractal random walk 2338.4 Financial applications 2348.4.1 Simulation of the Hmrw 2358.4.2 Financial statistics 2418.5 Concluding remarks 243References 2479 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251K. Basu and Maria C. Mariani9.1 Introduction 2519.2 Nonparametric regression models 2539.2.1 Local polynomial regression 2559.2.2 Lowess/loess method 2579.2.3 Numerical applications 2599.3 Interpolation methods 2719.3.1 Nearest-neighbor interpolation 2719.3.2 Bilinear interpolation 2729.3.3 Bicubic interpolation 2769.3.4 Biharmonic interpolation 2779.3.5 Thin plate splines 2829.3.6 Numerical applications 2859.4 Conclusion 287Acknowledgments 292References 29210 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295Maria C. Mariani, F. Biney, and I. SenGupta10.1 Introduction 29510.2 Short memory models 29710.2.1 ARMA(p,q) model 29710.2.2 GARCH(p,q) model 29710.2.3 IGARCH(1,1) model 29810.3 Long memory models 29810.3.1 ARFIMA(p,d,q) model 29910.3.2 ARFIMA(p,d,q)-GARCH(r,s) 29910.3.3 Intermediate memory process 30010.3.4 Figarch model 30010.4 Detection and estimation of long memory 30210.4.1 Augmented dickey–fuller test(ADF test) 30210.4.2 KPSS test 30310.4.3 Whittle method 30410.5 Data collection, analysis, and result 30610.5.1 Analysis on dow Jones index (DJIA) returns 30610.5.2 Model selection and specification: conditional mean 30610.5.3 Conditional mean model (returns) 30910.5.4 Model diagnostics: ARMA(2, 2) 30910.5.5 Test for ARCH effect 31110.5.6 Model selection and specification: Conditional variance 31310.5.7 Standardized residuals test 31410.5.8 Model diagnostics 31410.5.9 Returns and variance equation 31510.5.10 standardized residuals test 31710.5.11 Model diagnostic of conditional returns with conditional variance 31810.5.12 One-step ahead prediction of last 10 observations 33010.5.13 Analysis on high-frequency, earthquake, and explosives series 33010.6 Discussion and conclusion 335References 33711 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341M. P. Beccar-Varela, Ionut Florescu, and I. SenGupta11.1 Introduction 34111.2 Governing equations for the deterministic model 34211.2.1 Application to geophysical (earthquake data) 34311.2.2 Results 34411.3 L´evy flights and application to geophysics 34511.3.1 Truncated L´evy flight distribution 35311.3.2 Results 35611.4 Application to the high-frequency market data 36011.4.1 Methodology 36011.4.2 Results 36111.5 Brief program code description 36211.6 Conclusion 36411.A Appendix 36611.A.1 Stable distributions 36611.A.2 Characterization of stable distributions 367References 36812 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371M. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek12.1 Introduction 37112.2 Statistical preliminaries and results 37312.2.1 Sum of exponential random variables with different parameters 37412.3 Statistical and numerical analysis 37712.4 Analysis with Lévy distribution 38012.4.1 Characterization of Stable Distributions 38312.4.2 Truncated Lévy flight (TLF) distribution 38412.4.3 Data analysis with TLF distribution 38912.4.4 Sum of Lévy random variables with different parameters 39012.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 39412.6 Results and discussion 409Acknowledgments 42112.A Appendix A—Big ‘O’ notation 421References 422Index 425