Financial Data Analytics with Machine Learning, Optimization and Statistics

Sam Chen , Ka Chun Cheung , Phillip Yam 지음

Wiley 2024년 10월 18일 출간

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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. The book begins with a brief introduction to basic sampling theory and the fundamentals of simulation techniques, followed by a comparison between R and Python. It then discusses statistical diagnosis for financial security data and introduces some common tools in financial forensics such as Benford's Law, Zipf's Law, and anomaly detection. The statistical estimation and Expectation-Maximization (EM) & Majorization-Minimization (MM) algorithms are also covered. The book next focuses on univariate and multivariate dynamic volatility and correlation forecasting, and emphasis is placed on the celebrated Kelly's formula, followed by a brief introduction to quantitative risk management and dependence modelling for extremal events. A practical topic on numerical finance for traditional option pricing and Greek computations immediately follows as w

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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

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저자(글) Sam Chen

저자(글) Ka Chun Cheung

저자(글) Phillip Yam