Financial Data Analytics with Machine Learning, Optimization and Statistics

YONGZHAO CHEN (SAM) [BSC(ACTUARSC) & PHD (HKU)] is currently an Assistant Professor at the Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong. His research interests include actuarial science, especially credibility theory, and data analytics. KA CHUN CHEUNG [BSC(ACTUARSC) & PHD (HKU), ASA (SOA)] was the Director of the Actuarial Science Programme, and is currently Head and full Professor at the Department of Statistics and Actuarial Science in School of Computing and Data Science, The University of Hong Kong. His current research interests include various topics in actuarial science, including optimal reinsurance, stochastic orders, dependence structures, and extreme value theory. PHILLIP YAM [BSC(ACTUARSC) & MPHIL (HKU), MAST (CANTAB), DPHIL (OXON)] is currently Director of QFRM programme, and a full Professor at the Department of Statistics of The Chinese University of Hong Kong, also Assistant Dean (Education) of CUHK Faculty of Science, and a Visiting Professor in Columbia University and UTD Business School. He has more than 100 top journal articles in actuarial science, applied mathematics, data analytics, engineering, financial mathematics, operations management, and statistics. His research project CIBer won a Silver Medal in the 48th International Exhibition of Inventions Geneva in 2023.

• About the Authors xviiForeword xixPreface xxiAcknowledgements xxvIntroduction 1Development of Financial Data Analytics 1Organization of the Book 5References 7Part One Data Cleansing and Analytical ModelsChapter 1 Mathematical and Statistical Preliminaries 111.1 Random Vector 121.2 Matrix Theory 161.3 Vectors and Matrix Norms 231.4 Common Probability Distributions 241.5 Introductory Bayesian Statistics 30References 40Chapter 2 Introduction to Python and R 412.1 What is Python? 412.2 What is R? 422.3 Package Management in Python and R 422.4 Basic Operations in Python and R 442.5 One-Way ANOVA and Tukey’s HSD for Stock Market Indices 49References 64Chapter 3 Statistical Diagnostics of Financial Data 673.1 Normality Assumption for Relative Stock Price Changes 673.2 Student’s tν-distribution for Stock Price Changes 763.3 Testing for Multivariate Normality 813.4 Sample Correlation Matrix 843.5 Empirical Properties of Stock Prices 863.A Appendix 93References 97Chapter 4 Financial Forensics 994.1 Benford’s Law 994.2 Scaling Invariance and Benford’s Law 1014.3 Benford’s Law in Business Reports 1044.4 Benford’s Law in Growth Figures 1174.5 Zipf’s Law 1254.6 Zipf’s Law and COVID-19 Figures 1274.A Appendix 132References 136Chapter 5 Numerical Finance 1395.1 Fundamentals of Simulation 1395.2 Variance Reduction Technique 1465.3 A Review of Financial Calculus and Derivative Pricing 158*5.4 Greeks and their Approximations 179References 199Chapter 6 Approximation for Model Inference 2016.1 EM Algorithm 2016.2 mm Algorithm 216*6.3 A Short Course on the Theory of Markov Chains 222*6.4 Markov Chain Monte Carlo 236*6.A Appendix 261References 268Chapter 7 Time-Varying Volatility Matrix and Kelly Fraction 2717.1 Fluctuation of Volatilities 2717.2 Exponentially Weighted Moving Average 2757.3 ARIMA Time Series Model 2777.4 ARCH and GARCH Models 291*7.5 Kelly Fraction 3177.6 Calendar Effects 330*7.A Appendix 335References 343Chapter 8 Risk Measures, Extreme Values, and Copulae 3458.1 Value-at-Risk and Expected Shortfall 3458.2 Basel Accords and Risk Measures 3488.3 Historical Simulation (Bootstrapping) 3508.4 Statistical Model Building Approach 3548.5 Use of Extreme Value Theory 3568.6 Backtesting 3598.7 Estimates of Expected Shortfall 3648.8 Dependence Modelling via Copulae 369*8.A Appendix 402References 404Part Two Linear ModelsChapter 9 Principal Component Analysis and Recommender Systems 4099.1 US Zero-Coupon Rates 4099.2 PCA Algorithm 4119.3 Financial Interpretation of PCs for US Zero-Coupon Rates 4179.4 PCA as an Eigenvalue Problem 4219.5 Factor Models via PCA 4229.6 Value-at-Risk via PCA 4249.7 Portfolio Immunization 4279.8 Facial Recognition via PCA 4309.9 Non-Life Insurance via PCA 4399.10 Investment Strategies using PCA 442*9.11 Recommender System 447*9.A Appendix 456References 465Chapter 10 Regression Learning 46710.1 Simple and Multiple Linear Regression Models and Beyond 46710.2 Polynomial Regression 47310.3 Generalized Linear Models 47810.4 Logistic Regression 48410.5 Poisson Regression 49710.6 Model Evaluation and Considerations in Practice 501*10.7 Principal Component Regression 510*10.A Appendix 518References 522Chapter 11 Linear Classifiers 52511.1 Perceptron 52611.2 Support Vector Machine 533*11.A Appendix 545References 567Part Three Nonlinear ModelsChapter 12 Bayesian Learning 57112.1 Simple Credibility Theory 571*12.2 Bayesian Asymptotic Inference 57312.3 Revisiting Polynomial Regression 57512.4 Bayesian Classifiers 57812.5 Comonotone-Independence Bayes Classifier (CIBer) 58012.A Appendix 609References 612Chapter 13 Classification and Regression Trees, and Random Forests 61313.1 Classification (Decision) Trees 613*13.2 Concepts of Entropies 61513.3 Information Gain 62313.4 Other Impurity Measures for Information 62613.5 Splitting Against Continuous Attributes 62913.6 Overfitting in Classification Tree 63013.7 Classification Trees in Python and R 63313.8 Regression Trees 64113.9 Random Forest 64913.A Appendix 654References 659Chapter 14 Cluster Analysis 66114.1 K-Means Clustering 66114.2 K-Nearest Neighbour 694*14.3 Kernel Regression 703*14.A Appendix 714References 725Chapter 15 Applications of Deep Learning in Finance 72715.1 Human Brains and Artificial Neurons 72715.2 Feedforward Network 72915.3 ANN with Linear Outputs 73015.4 ANN with Logistic Outputs 73715.5 Adaptive Learning Rate 74015.6 Training Neural Networks via Backpropagation 74215.7 Multilayer Perceptron 74615.8 Universal Approximation Theorem 75215.9 Long Short-Term Memory (LSTM) 754References 764Postlude 767Index 769