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Mathematics and Statistics for Financial Risk Management 2nd Edition by Michael Miller ISBN 1118757645 9781118757642

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ISBN 10: 1118757645
ISBN 13: 978-1118757642
Author: Michael B. Miller
Mathematics and Statistics for Financial Risk Management 2nd Edition:  Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics.

Now in its second edition with more topics, more sample problems and more real world examples, this popular guide to financial risk management introduces readers to practical quantitative techniques for analyzing and managing financial risk.

In a concise and easy-to-read style, each chapter 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 Web site includes interactive Excel spreadsheet examples and templates.

Mathematics and Statistics for Financial Risk Management is an indispensable reference for today’s financial risk professional.

 

Mathematics and Statistics for Financial Risk Management 2nd Edition Table of contents:

  • 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
    • Continuous Random Variables
    • Mutually Exclusive Events
    • Independent Events
    • Probability Matrices
    • Conditional Probability
    • Problems

  • Chapter 3: Basic Statistics

    • Averages
    • Expectations
    • Variance and Standard Deviation
    • Standardized Variables
    • Covariance
    • Correlation
    • Application: Portfolio Variance and Hedging
    • Moments
    • Skewness
    • Kurtosis
    • Coskewness and Cokurtosis
    • Best Linear Unbiased Estimator (BLUE)
    • Problems

  • Chapter 4: Distributions

    • Parametric Distributions
    • Uniform Distribution
    • Bernoulli Distribution
    • Binomial Distribution
    • Poisson Distribution
    • Normal Distribution
    • Lognormal Distribution
    • Central Limit Theorem
    • Application: Monte Carlo Simulations Part I: Creating Normal Random Variables
    • Chi-Squared Distribution
    • Student’s t Distribution
    • F-Distribution
    • Triangular Distribution
    • Beta Distribution
    • Mixture Distributions
    • Problems

  • Chapter 5: Multivariate Distributions and Copulas

    • Multivariate Distributions
    • Copulas
    • Problems

  • Chapter 6: Bayesian Analysis

    • Overview
    • Bayes’ Theorem
    • Bayes Versus Frequentists
    • Many-State Problems
    • Continuous Distributions
    • Bayesian Networks
    • Bayesian Networks Versus Correlation Matrices
    • Problems

  • Chapter 7: Hypothesis Testing and Confidence Intervals

    • Sample Mean Revisited
    • Sample Variance Revisited
    • Confidence Intervals
    • Hypothesis Testing
    • Chebyshev’s Inequality
    • Application: VaR
    • Problems

  • Chapter 8: Matrix Algebra

    • Matrix Notation
    • Matrix Operations
    • Application: Transition Matrices
    • Application: Monte Carlo Simulations Part II: Cholesky Decomposition
    • Problems

  • Chapter 9: Vector Spaces

    • Vectors Revisited
    • Orthogonality
    • Rotation
    • Principal Component Analysis
    • Application: The Dynamic Term Structure of Interest Rates
    • Application: The Structure of Global Equity Markets
    • Problems

  • Chapter 10: Linear Regression Analysis

    • Linear Regression (One Regressor)
    • Linear Regression (Multivariate)
    • Application: Factor Analysis
    • Application: Stress Testing
    • Problems

  • Chapter 11: Time Series Models

    • Random Walks
    • Drift-Diffusion Model
    • Autoregression
    • Variance and Autocorrelation
    • Stationarity
    • Moving Average
    • Continuous Models
    • Application: GARCH
    • Application: Jump-Diffusion Model
    • Application: Interest Rate Models
    • Problems

  • Chapter 12: Decay Factors

    • Mean
    • Variance
    • Weighted Least Squares
    • Other Possibilities
    • Application: Hybrid VaR
    • Problems

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