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Mathematics and Statistics for Financial Risk Management

Autor(es): Michael B. Miller
Editor: Wiley
Edição: 1
Ano de publicação: 2012
Idioma: eng
ISBN: 9781118227770
Numero de páginas: 336
Disponibilidade e condições:
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REQUISITAR

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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