Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics.
The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics.
In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates.
This comprehensive resource covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing. Widely used risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing are also explored. A chapter on time series analysis introduces interest rate modeling, GARCH, and jump-diffusion models. Bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics are covered as well.
If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further.
Preface
Acknowledgments
Chapter 1: Some Basic Math
Logarithms
Log Returns
Compounding
Limited Liability
Graphing Log Returns
Continuously Compounded Returns
Combinatorics
Discount Factors
Geometric Series
Problems
Chapter 2: Probabilities
Discrete Random Variables
Mutually Exclusive Events
Independent Events
Probability Matrices
Conditional Probability
Bayes' Law
Problems
Chapter 3: Basic Statistics
Averages
Expectations
Variance and Standard Deviation
Standardized Variables
Covariance
Correlation
Moments
Skewness
Kurtosis
Coskewness and Cokurtosis
BLUE
Problems
Chapter 4: Distributions
Parametric Distributions
Uniform
Bernoulli
Binomial
Poisson Distribution
Normal
Lognormal
Central Limit Theorem
Chi-Squared Distribution
Student's t Distribution
F-Distribution
Mixture Distributions
Problems
Chapter 5: Hypothesis Testing
The Sample Mean Revisited
Sample Variance Revisited
Confidence Intervals
Hypothesis Testing
Chebyshev's Inequality
Application: VaR
Problems
Chapter 6: Matrix Algebra
Matrix Notation
Matrix Operations
Application: Transition Matrices
Application: Monte Carlool Simulations Part II: Cholesky Decomposition
Problems
Chapter 7: Vector Spaces
Vectors Revisited
Orthogonality
Rotation
Principal Component Analysis
Problems
Chapter 8: Linear Regression Analysis
Linear Regression (one regressor)
Optimal Hedging Revisited
Linear Regression (multivariate)
Application: Factor Analysis
Application: Stress Testing
Problems
Chapter 9: Time Series Models
Random Walks
Drift-Diffusion
Auto-regression
Variance and Autocorrelation
Stationarity
Moving Average
Continuous Models
Application: GARCH
Application: Jump-Diffusion
Application: Interest Rate Models
Problems
Chapter 10: Decay Factors
Mean
Variance
Weighted Least Squares
Other Possibilities
Application: Hybrid VaR
Problems
Appendix 1: Binary Numbers
Appendix 2: Taylor Expansions
Appendix 3: Vector Spaces
Appendix 4: Greek Alphabet
Appendix 5: Common Abbreviations
Answers
Bibliography
About the Author
Index
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