{"product_id":"handbook-of-highfrequency-trading-and-modeling-in-finance-9781118443989","title":"Handbook of HighFrequency Trading and Modeling in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eReflecting the fast pace and ever-evolving nature of the financial industry, the \u003ci\u003eHandbook of High-Frequency Trading and Modeling in Finance \u003c\/i\u003edetails how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data.\u003c\/p\u003e \u003cp\u003eIntroducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The \u003ci\u003eHandbook of High-Frequency Trading and Modeling in Finance \u003c\/i\u003ealso features:\u003c\/p\u003e \u003cp\u003e Contributions by well-known\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eNotes on Contributors xiii\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Trends and Trades 1\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMichael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 A trend-based trading strategy 3\u003c\/p\u003e \u003cp\u003e1.2.1 Signaling and trends 3\u003c\/p\u003e \u003cp\u003e1.2.2 Gain over a subperiod 5\u003c\/p\u003e \u003cp\u003e1.3 CUSUM timing 7\u003c\/p\u003e \u003cp\u003e1.3.1 Cusum process and stopping time 7\u003c\/p\u003e \u003cp\u003e1.3.2 A CUSUM timing scheme 10\u003c\/p\u003e \u003cp\u003e1.3.3 US treasury notes, CUSUM timing 11\u003c\/p\u003e \u003cp\u003e1.4 Example: Random walk on ticks 12\u003c\/p\u003e \u003cp\u003e1.4.1 Random walk expected gain over a subperiod 15\u003c\/p\u003e \u003cp\u003e1.4.2 Simple random walk, CUSUM timing 18\u003c\/p\u003e \u003cp\u003e1.4.3 Lazy simple random walk, cusum timing 21\u003c\/p\u003e \u003cp\u003e1.5 CUSUM strategy Monte Carlo 24\u003c\/p\u003e \u003cp\u003e1.6 The effect of the threshold parameter 27\u003c\/p\u003e \u003cp\u003e1.7 Conclusions and future work 39\u003c\/p\u003e \u003cp\u003eAppendix: Tables 40\u003c\/p\u003e \u003cp\u003eReferences 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Gaussian Inequalities and Tranche Sensitivities 51\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eClaas Becker and Ambar N. Sengupta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 51\u003c\/p\u003e \u003cp\u003e2.2 The tranche loss function 52\u003c\/p\u003e \u003cp\u003e2.3 A sensitivity identity 54\u003c\/p\u003e \u003cp\u003e2.4 Correlation sensitivities 55\u003c\/p\u003e \u003cp\u003eAcknowledgment 58\u003c\/p\u003e \u003cp\u003eReferences 58\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eGermán G. Creamer and Bernardo Creamer\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 61\u003c\/p\u003e \u003cp\u003e3.1.1 Causality analysis 62\u003c\/p\u003e \u003cp\u003e3.2 Data 64\u003c\/p\u003e \u003cp\u003e3.3 Estimation techniques 64\u003c\/p\u003e \u003cp\u003e3.4 Results 65\u003c\/p\u003e \u003cp\u003e3.5 Discussion 67\u003c\/p\u003e \u003cp\u003e3.6 Conclusions 69\u003c\/p\u003e \u003cp\u003eAcknowledgments 69\u003c\/p\u003e \u003cp\u003eReferences 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Portfolio Optimization: Applications in Quantum Computing 73\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMichael Marzec\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 73\u003c\/p\u003e \u003cp\u003e4.2 Background 75\u003c\/p\u003e \u003cp\u003e4.2.1 Portfolios and optimization 76\u003c\/p\u003e \u003cp\u003e4.2.2 Algorithmic complexity 77\u003c\/p\u003e \u003cp\u003e4.2.3 Performance 78\u003c\/p\u003e \u003cp\u003e4.2.4 Ising model 79\u003c\/p\u003e \u003cp\u003e4.2.5 Adiabatic quantum computing 79\u003c\/p\u003e \u003cp\u003e4.3 The models 80\u003c\/p\u003e \u003cp\u003e4.3.1 Financial model 81\u003c\/p\u003e \u003cp\u003e4.3.2 Graph-theoretic combinatorial optimization models 82\u003c\/p\u003e \u003cp\u003e4.3.3 Ising and Qubo models 83\u003c\/p\u003e \u003cp\u003e4.3.4 Mixed models 84\u003c\/p\u003e \u003cp\u003e4.4 Methods 84\u003c\/p\u003e \u003cp\u003e4.4.1 Model implementation 85\u003c\/p\u003e \u003cp\u003e4.4.2 Input data 85\u003c\/p\u003e \u003cp\u003e4.4.3 Mean-variance calculations 85\u003c\/p\u003e \u003cp\u003e4.4.4 Implementing the risk measure 86\u003c\/p\u003e \u003cp\u003e4.4.5 Implementation mapping 86\u003c\/p\u003e \u003cp\u003e4.5 Results 88\u003c\/p\u003e \u003cp\u003e4.5.1 The simple correlation model 88\u003c\/p\u003e \u003cp\u003e4.5.2 The restricted minimum-risk model 91\u003c\/p\u003e \u003cp\u003e4.5.3 The WMIS minimum-risk, max return model 94\u003c\/p\u003e \u003cp\u003e4.6 Discussion 95\u003c\/p\u003e \u003cp\u003e4.6.1 Hardware limitations 97\u003c\/p\u003e \u003cp\u003e4.6.2 Model limitations 97\u003c\/p\u003e \u003cp\u003e4.6.3 Implementation limitations 98\u003c\/p\u003e \u003cp\u003e4.6.4 Future research 98\u003c\/p\u003e \u003cp\u003e4.7 Conclusion 100\u003c\/p\u003e \u003cp\u003eAcknowledgments 100\u003c\/p\u003e \u003cp\u003eAppendix 4.A: WMIS Matlab Code 100\u003c\/p\u003e \u003cp\u003eReferences 103\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eIonut Florescu and Forrest Levin\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 107\u003c\/p\u003e \u003cp\u003e5.1.1 The original motivation 108\u003c\/p\u003e \u003cp\u003e5.1.2 The model and the problem 108\u003c\/p\u003e \u003cp\u003e5.1.3 A brief historical note 109\u003c\/p\u003e \u003cp\u003e5.2 The methodology 110\u003c\/p\u003e \u003cp\u003e5.2.1 Obtaining filtered empirical distributions at t1,…, tT 110\u003c\/p\u003e \u003cp\u003e5.2.2 Obtaining the parameters of the Markov chain 112\u003c\/p\u003e \u003cp\u003e5.3 Results obtained applying the model to real data 113\u003c\/p\u003e \u003cp\u003e5.3.1 Part i: financial applications 113\u003c\/p\u003e \u003cp\u003e5.3.2 Part ii: physical data application. temperature data 119\u003c\/p\u003e \u003cp\u003e5.3.3 Part iii: analysis of seismometer readings during an earthquake 121\u003c\/p\u003e \u003cp\u003e5.3.4 Analysis of the earthquake signal: beginning 123\u003c\/p\u003e \u003cp\u003e5.3.5 Analysis: during the earthquake 125\u003c\/p\u003e \u003cp\u003e5.3.6 Analysis: end of the earthquake signal, aftershocks 127\u003c\/p\u003e \u003cp\u003e5.4 Conclusion 127\u003c\/p\u003e \u003cp\u003e5.A Theoretical results and empirical testing 128\u003c\/p\u003e \u003cp\u003e5.A.1 How does the particle filter work? 128\u003c\/p\u003e \u003cp\u003e5.A.2 Theoretical results about convergence and parameter estimates 129\u003c\/p\u003e \u003cp\u003e5.A.3 Markov chain parameter estimates 131\u003c\/p\u003e \u003cp\u003e5.A.4 Empirical testing 132\u003c\/p\u003e \u003cp\u003e5.A.5 A list of supplementary documents 133\u003c\/p\u003e \u003cp\u003eReferences 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137\u003c\/b\u003e\u003cbr\u003e\u003ci\u003ePing-Chen Tsai and Mark B. Shackleton\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 137\u003c\/p\u003e \u003cp\u003e6.2 Review on the intraday jump tests 140\u003c\/p\u003e \u003cp\u003e6.2.1 Realized volatility measure and the BNS tests 140\u003c\/p\u003e \u003cp\u003e6.2.2 The ABD and LM tests 142\u003c\/p\u003e \u003cp\u003e6.3 A data-driven testing procedure 146\u003c\/p\u003e \u003cp\u003e6.3.1 Spy data and microstructure noise 146\u003c\/p\u003e \u003cp\u003e6.3.2 A generalized testing procedure 149\u003c\/p\u003e \u003cp\u003e6.4 Simulation study 153\u003c\/p\u003e \u003cp\u003e6.4.1 Model specification 153\u003c\/p\u003e \u003cp\u003e6.4.2 Simulation results 158\u003c\/p\u003e \u003cp\u003e6.5 Empirical results 161\u003c\/p\u003e \u003cp\u003e6.5.1 Results on the backward-looking test 162\u003c\/p\u003e \u003cp\u003e6.5.2 Results on the interpolated test 165\u003c\/p\u003e \u003cp\u003e6.6 Conclusion 165\u003c\/p\u003e \u003cp\u003eAcknowledgments 166\u003c\/p\u003e \u003cp\u003eAppendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167\u003c\/p\u003e \u003cp\u003eAppendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168\u003c\/p\u003e \u003cp\u003eAppendix 6.C: Minimized loss function loss(𝜌1, 𝜌2) for SV2FJ_2𝜌 model, SPY 169\u003c\/p\u003e \u003cp\u003eAppendix 6.D.1: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.08 170\u003c\/p\u003e \u003cp\u003eAppendix 6.D.2: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.40 171\u003c\/p\u003e \u003cp\u003eAppendix 6.D.3: Calibration of 𝜉 under SV2FJ_2𝜌 model at 5-min frequency, E[Nt] = 0.08 172\u003c\/p\u003e \u003cp\u003eAppendix 6.D.4: Calibration of 𝜉 under SV2FJ_2𝜌 Model at 5-min frequency, E[Nt] = 0.40 173\u003c\/p\u003e \u003cp\u003eAppendix 6.D.5: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.08 174\u003c\/p\u003e \u003cp\u003eAppendix 6.D.6: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.40 175\u003c\/p\u003e \u003cp\u003eReferences 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eBaron Law and Frederi G. Viens\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 183\u003c\/p\u003e \u003cp\u003e7.2 Point processes 184\u003c\/p\u003e \u003cp\u003e7.3 Hawkes processes 186\u003c\/p\u003e \u003cp\u003e7.3.1 Branching structure representation 188\u003c\/p\u003e \u003cp\u003e7.3.2 Stationarity 188\u003c\/p\u003e \u003cp\u003e7.3.3 Convergence 189\u003c\/p\u003e \u003cp\u003e7.4 Statistical inference of Hawkes processes 191\u003c\/p\u003e \u003cp\u003e7.4.1 Simulation 191\u003c\/p\u003e \u003cp\u003e7.4.2 Estimation 194\u003c\/p\u003e \u003cp\u003e7.4.3 Hypothesis testing 197\u003c\/p\u003e \u003cp\u003e7.5 Applications of Hawkes processes 198\u003c\/p\u003e \u003cp\u003e7.5.1 Modeling order arrivals 199\u003c\/p\u003e \u003cp\u003e7.5.2 Modeling price jumps 200\u003c\/p\u003e \u003cp\u003e7.5.3 Modeling jump-diffusion 205\u003c\/p\u003e \u003cp\u003e7.5.4 Measuring endogeneity (Reflexivity) 205\u003c\/p\u003e \u003cp\u003eAppendix 7.A: Point Processes 207\u003c\/p\u003e \u003cp\u003e7.A.1 Definition 207\u003c\/p\u003e \u003cp\u003e7.A.2 Moments 208\u003c\/p\u003e \u003cp\u003e7.A.3 Marked point processes 209\u003c\/p\u003e \u003cp\u003e7.A.4 Stochastic intensity 209\u003c\/p\u003e \u003cp\u003e7.A.5 Random time change 211\u003c\/p\u003e \u003cp\u003eAppendix 7.B: A Brief History of Hawkes processes 211\u003c\/p\u003e \u003cp\u003eReferences 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Multifractal Random Walk Driven by a Hermite Process 221\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eAlexis Fauth and Ciprian\u003c\/i\u003e A. Tudor\u003c\/p\u003e \u003cp\u003e8.1 Introduction 221\u003c\/p\u003e \u003cp\u003e8.2 Preliminaries 224\u003c\/p\u003e \u003cp\u003e8.2.1 Fractional brownian motion and hermite processes 224\u003c\/p\u003e \u003cp\u003e8.2.2 Wiener integrals with respect to the hermite process 226\u003c\/p\u003e \u003cp\u003e8.2.3 Infinitely divisible cascading noise 229\u003c\/p\u003e \u003cp\u003e8.3 Multifractal random walk driven by a Hermite process 231\u003c\/p\u003e \u003cp\u003e8.3.1 Definition and existence 231\u003c\/p\u003e \u003cp\u003e8.3.2 Properties of the hermite multifractal random walk 233\u003c\/p\u003e \u003cp\u003e8.4 Financial applications 234\u003c\/p\u003e \u003cp\u003e8.4.1 Simulation of the Hmrw 235\u003c\/p\u003e \u003cp\u003e8.4.2 Financial statistics 241\u003c\/p\u003e \u003cp\u003e8.5 Concluding remarks 243\u003c\/p\u003e \u003cp\u003eReferences 247\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eK. Basu and Maria C. Mariani\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 251\u003c\/p\u003e \u003cp\u003e9.2 Nonparametric regression models 253\u003c\/p\u003e \u003cp\u003e9.2.1 Local polynomial regression 255\u003c\/p\u003e \u003cp\u003e9.2.2 Lowess\/loess method 257\u003c\/p\u003e \u003cp\u003e9.2.3 Numerical applications 259\u003c\/p\u003e \u003cp\u003e9.3 Interpolation methods 271\u003c\/p\u003e \u003cp\u003e9.3.1 Nearest-neighbor interpolation 271\u003c\/p\u003e \u003cp\u003e9.3.2 Bilinear interpolation 272\u003c\/p\u003e \u003cp\u003e9.3.3 Bicubic interpolation 276\u003c\/p\u003e \u003cp\u003e9.3.4 Biharmonic interpolation 277\u003c\/p\u003e \u003cp\u003e9.3.5 Thin plate splines 282\u003c\/p\u003e \u003cp\u003e9.3.6 Numerical applications 285\u003c\/p\u003e \u003cp\u003e9.4 Conclusion 287\u003c\/p\u003e \u003cp\u003eAcknowledgments 292\u003c\/p\u003e \u003cp\u003eReferences 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eMaria C. Mariani, F. Biney, and I. SenGupta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 295\u003c\/p\u003e \u003cp\u003e10.2 Short memory models 297\u003c\/p\u003e \u003cp\u003e10.2.1 ARMA(p,q) model 297\u003c\/p\u003e \u003cp\u003e10.2.2 GARCH(p,q) model 297\u003c\/p\u003e \u003cp\u003e10.2.3 IGARCH(1,1) model 298\u003c\/p\u003e \u003cp\u003e10.3 Long memory models 298\u003c\/p\u003e \u003cp\u003e10.3.1 ARFIMA(p,d,q) model 299\u003c\/p\u003e \u003cp\u003e10.3.2 ARFIMA(p,d,q)-GARCH(r,s) 299\u003c\/p\u003e \u003cp\u003e10.3.3 Intermediate memory process 300\u003c\/p\u003e \u003cp\u003e10.3.4 Figarch model 300\u003c\/p\u003e \u003cp\u003e10.4 Detection and estimation of long memory 302\u003c\/p\u003e \u003cp\u003e10.4.1 Augmented dickey–fuller test(ADF test) 302\u003c\/p\u003e \u003cp\u003e10.4.2 KPSS test 303\u003c\/p\u003e \u003cp\u003e10.4.3 Whittle method 304\u003c\/p\u003e \u003cp\u003e10.5 Data collection, analysis, and result 306\u003c\/p\u003e \u003cp\u003e10.5.1 Analysis on dow Jones index (DJIA) returns 306\u003c\/p\u003e \u003cp\u003e10.5.2 Model selection and specification: conditional mean 306\u003c\/p\u003e \u003cp\u003e10.5.3 Conditional mean model (returns) 309\u003c\/p\u003e \u003cp\u003e10.5.4 Model diagnostics: ARMA(2, 2) 309\u003c\/p\u003e \u003cp\u003e10.5.5 Test for ARCH effect 311\u003c\/p\u003e \u003cp\u003e10.5.6 Model selection and specification: Conditional variance 313\u003c\/p\u003e \u003cp\u003e10.5.7 Standardized residuals test 314\u003c\/p\u003e \u003cp\u003e10.5.8 Model diagnostics 314\u003c\/p\u003e \u003cp\u003e10.5.9 Returns and variance equation 315\u003c\/p\u003e \u003cp\u003e10.5.10 standardized residuals test 317\u003c\/p\u003e \u003cp\u003e10.5.11 Model diagnostic of conditional returns with conditional variance 318\u003c\/p\u003e \u003cp\u003e10.5.12 One-step ahead prediction of last 10 observations 330\u003c\/p\u003e \u003cp\u003e10.5.13 Analysis on high-frequency, earthquake, and explosives series 330\u003c\/p\u003e \u003cp\u003e10.6 Discussion and conclusion 335\u003c\/p\u003e \u003cp\u003eReferences 337\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eM. P. Beccar-Varela, Ionut Florescu, and I. SenGupta\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 341\u003c\/p\u003e \u003cp\u003e11.2 Governing equations for the deterministic model 342\u003c\/p\u003e \u003cp\u003e11.2.1 Application to geophysical (earthquake data) 343\u003c\/p\u003e \u003cp\u003e11.2.2 Results 344\u003c\/p\u003e \u003cp\u003e11.3 L´evy flights and application to geophysics 345\u003c\/p\u003e \u003cp\u003e11.3.1 Truncated L´evy flight distribution 353\u003c\/p\u003e \u003cp\u003e11.3.2 Results 356\u003c\/p\u003e \u003cp\u003e11.4 Application to the high-frequency market data 360\u003c\/p\u003e \u003cp\u003e11.4.1 Methodology 360\u003c\/p\u003e \u003cp\u003e11.4.2 Results 361\u003c\/p\u003e \u003cp\u003e11.5 Brief program code description 362\u003c\/p\u003e \u003cp\u003e11.6 Conclusion 364\u003c\/p\u003e \u003cp\u003e11.A Appendix 366\u003c\/p\u003e \u003cp\u003e11.A.1 Stable distributions 366\u003c\/p\u003e \u003cp\u003e11.A.2 Characterization of stable distributions 367\u003c\/p\u003e \u003cp\u003eReferences 368\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eM. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 371\u003c\/p\u003e \u003cp\u003e12.2 Statistical preliminaries and results 373\u003c\/p\u003e \u003cp\u003e12.2.1 Sum of exponential random variables with different parameters 374\u003c\/p\u003e \u003cp\u003e12.3 Statistical and numerical analysis 377\u003c\/p\u003e \u003cp\u003e12.4 Analysis with Lévy distribution 380\u003c\/p\u003e \u003cp\u003e12.4.1 Characterization of Stable Distributions 383\u003c\/p\u003e \u003cp\u003e12.4.2 Truncated Lévy flight (TLF) distribution 384\u003c\/p\u003e \u003cp\u003e12.4.3 Data analysis with TLF distribution 389\u003c\/p\u003e \u003cp\u003e12.4.4 Sum of Lévy random variables with different parameters 390\u003c\/p\u003e \u003cp\u003e12.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 394\u003c\/p\u003e \u003cp\u003e12.6 Results and discussion 409\u003c\/p\u003e \u003cp\u003eAcknowledgments 421\u003c\/p\u003e \u003cp\u003e12.A Appendix A—Big ‘O’ notation 421\u003c\/p\u003e \u003cp\u003eReferences 422\u003c\/p\u003e \u003cp\u003eIndex 425\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406870716759,"sku":"9781118443989","price":117.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118443989.jpg?v=1730497397","url":"https:\/\/bookcurl.com\/products\/handbook-of-highfrequency-trading-and-modeling-in-finance-9781118443989","provider":"Book Curl","version":"1.0","type":"link"}