Mathematics and statistics for financial risk management /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, N.J. :
Wiley,
c2012.
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| Subjects: |
Table of Contents:
- ch. 1 Some Basic Math
- Logarithms
- Log Returns
- Compounding
- Limited Liability
- Graphing Log Returns
- Continuously Compounded Returns
- Combinatorics
- Discount Factors
- Geometric Series
- Problems
- ch. 2 Probabilities
- Discrete Random Variables
- Continuous Random Variables
- Mutually Exclusive Events
- Independent Events
- Probability Matrices
- Conditional Probability
- Bayes' Theorem
- Problems
- ch. 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
- ch. 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
- Mixture Distributions
- Problems
- ch. 5 Hypothesis Testing & Confidence Intervals
- The Sample Mean Revisited
- Sample Variance Revisited
- Confidence Intervals
- Hypothesis Testing
- Chebyshev's Inequality
- Application: VaR
- Problems
- ch. 6 Matrix Algebra
- Matrix Notation
- Matrix Operations
- Application: Transition Matrices
- Application: Monte Carlo Simulations Part II: Cholesky Decomposition
- Problems
- ch. 7 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
- ch. 8 Linear Regression Analysis
- Linear Regression (One Regressor)
- Linear Regression (Multivariate)
- Application: Factor Analysis
- Application: Stress Testing
- Problems
- ch. 9 Time Series Models
- Random Walks
- Drift-Diffusion
- Autoregression
- Variance and Autocorrelation
- Stationarity
- Moving Average
- Continuous Models
- Application: GARCH
- Application: Jump-Diffusion
- Application: Interest Rate Models
- Problems
- ch. 10 Decay Factors
- Mean
- Variance
- Weighted Least Squares
- Other Possibilities
- Application: Hybrid VaR
- Problems.