Financial Data Analytics with Machine Learning, Optimization and Statistics

An essential introduction to data analytics and Machine Learning techniques in the business sector In Financial Data Analytics with Machine Learning, Optimization and Statistics, a team consisting of a distinguished applied mathematician and statistician, experienced actuarial professionals and working data analysts delivers an expertly balanced combination of traditional financial statistics, effective machine learning tools, and mathematics. The book focuses on contemporary techniques used for data analytics in the financial sector and the insurance industry with an emphasis on mathematical understanding and statistical principles and connects them with common and practical financial problems. Each chapter is equipped with derivations and proofs—especially of key results—and includes several realistic examples which stem from common financial contexts. The computer algorithms in the book are implemented using Python and R, two of the most widely used programming languages for applied science and in academia and industry, so that readers can implement the relevant models and use the programs themselves. This book can help readers become well-equipped with the following skills: To evaluate financial and insurance data quality, and use the distilled knowledge obtained from the data after applying data analytic tools to make timely financial decisions To apply effective data dimension reduction tools to enhance supervised learning To describe and select suitable data analytic tools as introduced above for a given dataset depending upon classification or regression prediction purpose The book covers the competencies tested by several professional examinations, such as the Predictive Analytics Exam offered by the Society of Actuaries, and the Institute and Faculty of Actuaries' Actuarial Statistics Exam. Besides being an indispensable resource for senior undergraduate and graduate students taking courses in financial engineering, statistics, quantitative finance, risk management, actuarial science, data science, and mathematics for AI, Financial Data Analytics with Machine Learning, Optimization and Statistics also belongs in the libraries of aspiring and practicing quantitative analysts working in commercial and investment banking.

Table of Contents:
About the Authors xvii Foreword xix Preface xxi Acknowledgements xxv Introduction 1 Development of Financial Data Analytics 1 Organization of the Book 5 References 7 Part One Data Cleansing and Analytical Models Chapter 1 Mathematical and Statistical Preliminaries 11 1.1 Random Vector 12 1.2 Matrix Theory 16 1.3 Vectors and Matrix Norms 23 1.4 Common Probability Distributions 24 1.5 Introductory Bayesian Statistics 30 References 40 Chapter 2 Introduction to Python and R 41 2.1 What is Python? 41 2.2 What is R? 42 2.3 Package Management in Python and R 42 2.4 Basic Operations in Python and R 44 2.5 One-Way ANOVA and Tukey’s HSD for Stock Market Indices 49 References 64 Chapter 3 Statistical Diagnostics of Financial Data 67 3.1 Normality Assumption for Relative Stock Price Changes 67 3.2 Student’s tν-distribution for Stock Price Changes 76 3.3 Testing for Multivariate Normality 81 3.4 Sample Correlation Matrix 84 3.5 Empirical Properties of Stock Prices 86 3.A Appendix 93 References 97 Chapter 4 Financial Forensics 99 4.1 Benford’s Law 99 4.2 Scaling Invariance and Benford’s Law 101 4.3 Benford’s Law in Business Reports 104 4.4 Benford’s Law in Growth Figures 117 4.5 Zipf’s Law 125 4.6 Zipf’s Law and COVID-19 Figures 127 4.A Appendix 132 References 136 Chapter 5 Numerical Finance 139 5.1 Fundamentals of Simulation 139 5.2 Variance Reduction Technique 146 5.3 A Review of Financial Calculus and Derivative Pricing 158 *5.4 Greeks and their Approximations 179 References 199 Chapter 6 Approximation for Model Inference 201 6.1 EM Algorithm 201 6.2 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 261 References 268 Chapter 7 Time-Varying Volatility Matrix and Kelly Fraction 271 7.1 Fluctuation of Volatilities 271 7.2 Exponentially Weighted Moving Average 275 7.3 ARIMA Time Series Model 277 7.4 ARCH and GARCH Models 291 *7.5 Kelly Fraction 317 7.6 Calendar Effects 330 *7.A Appendix 335 References 343 Chapter 8 Risk Measures, Extreme Values, and Copulae 345 8.1 Value-at-Risk and Expected Shortfall 345 8.2 Basel Accords and Risk Measures 348 8.3 Historical Simulation (Bootstrapping) 350 8.4 Statistical Model Building Approach 354 8.5 Use of Extreme Value Theory 356 8.6 Backtesting 359 8.7 Estimates of Expected Shortfall 364 8.8 Dependence Modelling via Copulae 369 *8.A Appendix 402 References 404 Part Two Linear Models Chapter 9 Principal Component Analysis and Recommender Systems 409 9.1 US Zero-Coupon Rates 409 9.2 PCA Algorithm 411 9.3 Financial Interpretation of PCs for US Zero-Coupon Rates 417 9.4 PCA as an Eigenvalue Problem 421 9.5 Factor Models via PCA 422 9.6 Value-at-Risk via PCA 424 9.7 Portfolio Immunization 427 9.8 Facial Recognition via PCA 430 9.9 Non-Life Insurance via PCA 439 9.10 Investment Strategies using PCA 442 *9.11 Recommender System 447 *9.A Appendix 456 References 465 Chapter 10 Regression Learning 467 10.1 Simple and Multiple Linear Regression Models and Beyond 467 10.2 Polynomial Regression 473 10.3 Generalized Linear Models 478 10.4 Logistic Regression 484 10.5 Poisson Regression 497 10.6 Model Evaluation and Considerations in Practice 501 *10.7 Principal Component Regression 510 *10.A Appendix 518 References 522 Chapter 11 Linear Classifiers 525 11.1 Perceptron 526 11.2 Support Vector Machine 533 *11.A Appendix 545 References 567 Part Three Nonlinear Models Chapter 12 Bayesian Learning 571 12.1 Simple Credibility Theory 571 *12.2 Bayesian Asymptotic Inference 573 12.3 Revisiting Polynomial Regression 575 12.4 Bayesian Classifiers 578 12.5 Comonotone-Independence Bayes Classifier (CIBer) 580 12.A Appendix 609 References 612 Chapter 13 Classification and Regression Trees, and Random Forests 613 13.1 Classification (Decision) Trees 613 *13.2 Concepts of Entropies 615 13.3 Information Gain 623 13.4 Other Impurity Measures for Information 626 13.5 Splitting Against Continuous Attributes 629 13.6 Overfitting in Classification Tree 630 13.7 Classification Trees in Python and R 633 13.8 Regression Trees 641 13.9 Random Forest 649 13.A Appendix 654 References 659 Chapter 14 Cluster Analysis 661 14.1 K-Means Clustering 661 14.2 K-Nearest Neighbour 694 *14.3 Kernel Regression 703 *14.A Appendix 714 References 725 Chapter 15 Applications of Deep Learning in Finance 727 15.1 Human Brains and Artificial Neurons 727 15.2 Feedforward Network 729 15.3 ANN with Linear Outputs 730 15.4 ANN with Logistic Outputs 737 15.5 Adaptive Learning Rate 740 15.6 Training Neural Networks via Backpropagation 742 15.7 Multilayer Perceptron 746 15.8 Universal Approximation Theorem 752 15.9 Long Short-Term Memory (LSTM) 754 References 764 Postlude 767 Index 769