Mathematics and Statistics for Financial Risk Management

Mathematics and Statistics for Financial Risk Management

by Michael B. Miller
Released March 2012
Publisher(s): Wiley
ISBN: 9781118170625

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Book description

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.

Table of contents

  1. Cover
  2. Series
  3. Title Page
  4. Copyright
  5. Preface
  6. Acknowledgments
  7. CHAPTER 1: Some Basic Math
    1. LOGARITHMS
    2. LOG RETURNS
    3. COMPOUNDING
    4. LIMITED LIABILITY
    5. GRAPHING LOG RETURNS
    6. CONTINUOUSLY COMPOUNDED RETURNS
    7. COMBINATORICS
    8. DISCOUNT FACTORS
    9. GEOMETRIC SERIES
    10. PROBLEMS
  8. CHAPTER 2: Probabilities
    1. DISCRETE RANDOM VARIABLES
    2. CONTINUOUS RANDOM VARIABLES
    3. MUTUALLY EXCLUSIVE EVENTS
    4. INDEPENDENT EVENTS
    5. PROBABILITY MATRICES
    6. CONDITIONAL PROBABILITY
    7. BAYES’ THEOREM
    8. PROBLEMS
  9. CHAPTER 3: Basic Statistics
    1. AVERAGES
    2. EXPECTATIONS
    3. VARIANCE AND STANDARD DEVIATION
    4. STANDARDIZED VARIABLES
    5. COVARIANCE
    6. CORRELATION
    7. APPLICATION: PORTFOLIO VARIANCE AND HEDGING
    8. MOMENTS
    9. SKEWNESS
    10. KURTOSIS
    11. COSKEWNESS AND COKURTOSIS
    12. BEST LINEAR UNBIASED ESTIMATOR (BLUE)
    13. PROBLEMS
  10. CHAPTER 4: Distributions
    1. PARAMETRIC DISTRIBUTIONS
    2. UNIFORM DISTRIBUTION
    3. BERNOULLI DISTRIBUTION
    4. BINOMIAL DISTRIBUTION
    5. POISSON DISTRIBUTION
    6. NORMAL DISTRIBUTION
    7. LOGNORMAL DISTRIBUTION
    8. CENTRAL LIMIT THEOREM
    9. APPLICATION: MONTE CARLO SIMULATIONS PART I: CREATING NORMAL RANDOM VARIABLES
    10. CHI-SQUARED DISTRIBUTION
    11. STUDENT'S T DISTRIBUTION
    12. F-DISTRIBUTION
    13. MIXTURE DISTRIBUTIONS
    14. PROBLEMS
  11. CHAPTER 5: Hypothesis Testing & Confidence Intervals
    1. THE SAMPLE MEAN REVISITED
    2. SAMPLE VARIANCE REVISITED
    3. CONFIDENCE INTERVALS
    4. HYPOTHESIS TESTING
    5. CHEBYSHEV'S INEQUALITY
    6. APPLICATION: VAR
    7. PROBLEMS
  12. CHAPTER 6: Matrix Algebra
    1. MATRIX NOTATION
    2. MATRIX OPERATIONS
    3. APPLICATION: TRANSITION MATRICES
    4. APPLICATION: MONTE CARLO SIMULATIONS PART II: CHOLESKY DECOMPOSITION
    5. PROBLEMS
  13. CHAPTER 7: Vector Spaces
    1. VECTORS REVISITED
    2. ORTHOGONALITY
    3. ROTATION
    4. PRINCIPAL COMPONENT ANALYSIS
    5. APPLICATION: THE DYNAMIC TERM STRUCTURE OF INTEREST RATES
    6. APPLICATION: THE STRUCTURE OF GLOBAL EQUITY MARKETS
    7. PROBLEMS
  14. CHAPTER 8: Linear Regression Analysis
    1. LINEAR REGRESSION (ONE REGRESSOR)
    2. LINEAR REGRESSION (MULTIVARIATE)
    3. APPLICATION: FACTOR ANALYSIS
    4. APPLICATION: STRESS TESTING
    5. PROBLEMS
  15. CHAPTER 9: Time Series Models
    1. RANDOM WALKS
    2. DRIFT-DIFFUSION
    3. AUTOREGRESSION
    4. VARIANCE AND AUTOCORRELATION
    5. STATIONARITY
    6. MOVING AVERAGE
    7. CONTINUOUS MODELS
    8. APPLICATION: GARCH
    9. APPLICATION: JUMP-DIFFUSION
    10. APPLICATION: INTEREST RATE MODELS
    11. PROBLEMS
  16. CHAPTER 10: Decay Factors
    1. MEAN
    2. VARIANCE
    3. WEIGHTED LEAST SQUARES
    4. OTHER POSSIBILITIES
    5. APPLICATION: HYBRID VAR
    6. PROBLEMS
  17. APPENDIX A: Binary Numbers
  18. APPENDIX B: Taylor Expansions
  19. APPENDIX C: Vector Spaces
  20. APPENDIX D: Greek Alphabet
  21. APPENDIX E: Common Abbreviations
  22. Answers
    1. CHAPTER 1
    2. CHAPTER 2
    3. CHAPTER 3
    4. CHAPTER 4
    5. CHAPTER 5
    6. CHAPTER 6
    7. CHAPTER 7
    8. CHAPTER 8
    9. CHAPTER 9
    10. CHAPTER 10
  23. References
  24. About the Author
  25. Index

Product information

  • Title: Mathematics and Statistics for Financial Risk Management
  • Author(s): Michael B. Miller
  • Release date: March 2012
  • Publisher(s): Wiley
  • ISBN: 9781118170625