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Essential mathematics for market risk management

Author: Simon Hubbert
Publisher: Hoboken, N.J. : Wiley, 2012.
Series: Wiley finance series.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Summary:
"Everything you need to know in order to manage risk effectively within your organizationYou cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive. This exciting branch of mathematics has very direct practical implications: when a new model is tested and implemented it can have an immediate impact on the financial environment. With risk management top of the agenda for  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Hubbert, Simon.
Essential mathematics for market risk management.
Hoboken, N.J. : Wiley, 2012
(DLC) 2011039267
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Simon Hubbert
ISBN: 9781118467213 1118467213 9781119953012 1119953014 9781119953029 1119953022
OCLC Number: 778431625
Description: 1 online resource (xiv, 335 pages) : illustrations.
Contents: Machine generated contents note: 1. Introduction --
1.1. Basic Challenges in Risk Management --
1.2. Value at Risk --
1.3. Further Challenges in Risk Management --
2. Applied Linear Algebra for Risk Managers --
2.1. Vectors and Matrices --
2.2. Matrix Algebra in Practice --
2.3. Eigenvectors and Eigenvalues --
2.4. Positive Definite Matrices --
3. Probability Theory for Risk Managers --
3.1. Univariate Theory --
3.1.1. Random variables --
3.1.2. Expectation --
3.1.3. Variance --
3.2. Multivariate Theory --
3.2.1. joint distribution function --
3.2.2. joint and marginal density functions --
3.2.3. notion of independence --
3.2.4. notion of conditional dependence --
3.2.5. Covariance and correlation --
3.2.6. mean vector and covariance matrix --
3.2.7. Linear combinations of random variables --
3.3. Normal Distribution --
4. Optimization Tools --
4.1. Background Calculus --
4.1.1. Single-variable functions --
4.1.2. Multivariable functions --
4.2. Optimizing Functions --
4.2.1. Unconstrained quadratic functions --
4.2.2. Constrained quadratic functions --
4.3. Over-determined Linear Systems --
4.4. Linear Regression --
5. Portfolio Theory I --
5.1. Measuring Returns --
5.1.1. comparison of the standard and log returns --
5.2. Setting Up the Optimal Portfolio Problem --
5.3. Solving the Optimal Portfolio Problem --
6. Portfolio Theory II --
6.1. Two-Fund Investment Service --
6.2. Mathematical Investigation of the Optimal Frontier --
6.2.1. minimum variance portfolio --
6.2.2. Covariance of frontier portfolios --
6.2.3. Correlation with the minimum variance portfolio --
6.2.4. zero-covariance portfolio --
6.3. Geometrical Investigation of the Optimal Frontier --
6.3.1. Equation of a tangent to an efficient portfolio --
6.3.2. Locating the zero-covariance portfolio --
6.4. Further Investigation of Covariance --
6.5. Optimal Portfolio Problem Revisited --
7. Capital Asset Pricing Model (CAPM) --
7.1. Connecting the Portfolio Frontiers --
7.2. Tangent Portfolio --
7.2.1. market's supply of risky assets --
7.3. CAPM --
7.4. Applications of CAPM --
7.4.1. Decomposing risk --
8. Risk Factor Modelling --
8.1. General Factor Modelling --
8.2. Theoretical Properties of the Factor Model --
8.3. Models Based on Principal Component Analysis (PCA) --
8.3.1. PCA in two dimensions --
8.3.2. PCA in higher dimensions --
9. Value at Risk Concept --
9.1. Framework for Value at Risk --
9.1.1. motivating example --
9.1.2. Defining value at risk --
9.2. Investigating Value at Risk --
9.2.1. suitability of value at risk to capital allocation --
9.3. Tail Value at Risk --
9.4. Spectral Risk Measures --
10. Value at Risk under a Normal Distribution --
10.1. Calculation of Value at Risk --
10.2. Calculation of Marginal Value at Risk --
10.3. Calculation of Tail Value at Risk --
10.4. Sub-additivity of Normal Value at Risk --
11. Advanced Probability Theory for Risk Managers --
11.1. Moments of a Random Variable --
11.2. Characteristic Function --
11.2.1. Dealing with the sum of several random variables --
11.2.2. Dealing with a scaling of a random variable --
11.2.3. Normally distributed random variables --
11.3. Central Limit Theorem --
11.4. Moment-Generating Function --
11.5. Log-normal Distribution --
12. Survey of Useful Distribution Functions --
12.1. Gamma Distribution --
12.2. Chi-Squared Distribution --
12.3. Non-central Chi-Squared Distribution --
12.4. F-Distribution --
12.5. t-Distribution --
13. Crash Course on Financial Derivatives --
13.1. Black-Scholes Pricing Formula --
13.1.1. model for asset returns --
13.1.2. second-order approximation --
13.1.3. Black-Scholes formula --
13.2. Risk-Neutral Pricing --
13.3. Sensitivity Analysis --
13.3.1. Asset price sensitivity: The delta and gamma measures --
13.3.2. Time decay sensitivity: The theta measure --
13.3.3. remaining sensitivity measures --
14. Non-linear Value at Risk --
14.1. Linear Value at Risk Revisited --
14.2. Approximations for Non-linear Portfolios --
14.2.1. Delta approximation for the portfolio --
14.2.2. Gamma approximation for the portfolio --
14.3. Value at Risk for Derivative Portfolios --
14.3.1. Multi-factor delta approximation --
14.3.2. Single-factor gamma approximation --
14.3.3. Multi-factor gamma approximation --
15. Time Series Analysis --
15.1. Stationary Processes --
15.1.1. Purely random processes --
15.1.2. White noise processes --
15.1.3. Random walk processes --
15.2. Moving Average Processes --
15.3. Auto-regressive Processes --
15.4. Auto-regressive Moving Average Processes --
16. Maximum Likelihood Estimation --
16.1. Sample Mean and Variance --
16.2. On the Accuracy of Statistical Estimators --
16.2.1. Sample mean example --
16.2.2. Sample variance example --
16.3. Appeal of the Maximum Likelihood Method --
17. Delta Method for Statistical Estimates --
17.1. Theoretical Framework --
17.2. Sample Variance --
17.3. Sample Skewness and Kurtosis --
17.3.1. Analysis of skewness --
17.3.2. Analysis of kurtosis --
18. Hypothesis Testing --
18.1. Testing Framework --
18.1.1. null and alternative hypotheses --
18.1.2. Hypotheses: simple vs compound --
18.1.3. acceptance and rejection regions --
18.1.4. Potential errors --
18.1.5. Controlling the testing errors/defining the acceptance region --
18.2. Testing Simple Hypotheses --
18.2.1. Testing the mean when the variance is known --
18.3. Test Statistic --
18.3.1. Example: Testing the mean when the variance is unknown --
18.3.2. p-value of a test statistic --
18.4. Testing Compound Hypotheses --
19. Statistical Properties of Financial Losses --
19.1. Analysis of Sample Statistics --
19.2. Empirical Density and Q-Q Plots --
19.3. Auto-correlation Function --
19.4. Volatility Plot --
19.5. Stylized Facts --
20. Modelling Volatility --
20.1. RiskMetrics Model --
20.2. ARCH Models --
20.2.1. ARCH(1) volatility model --
20.3. Garch Models --
20.3.1. GARCH(1, 1) volatility model --
20.3.2. RiskMetrics model revisited --
20.3.3. Summary --
20.4. Exponential GARCH --
21. Extreme Value Theory --
21.1. Mathematics of Extreme Events --
21.1.1. naive attempt --
21.1.2. Example 1: Exponentially distributed losses --
21.1.3. Example 2: Normally distributed losses --
21.1.4. Example 3: Pareto distributed losses --
21.1.5. Example 4: Uniformly distributed losses --
21.1.6. Example 5: Cauchy distributed losses --
21.1.7. extreme value theorem --
21.2. Domains of Attraction --
21.2.1. Frechet domain of attraction --
21.3. Extreme Value at Risk --
21.4. Practical Issues --
21.4.1. Parameter estimation --
21.4.2. choice of threshold --
22. Simulation Models --
22.1. Estimating the Quantile of a Distribution --
22.1.1. Asymptotic behaviour --
22.2. Historical Simulation --
22.3. Monte Carlo Simulation --
22.3.1. Choleski algorithm --
22.3.2. Generating random numbers --
23. Alternative Approaches to VaR --
23.1. t-Distributed Assumption --
23.2. Corrections to the Normal Assumption --
24. Backtesting --
24.1. Quantifying the Performance of VaR --
24.2. Testing the Proportion of VaR Exceptions --
24.3. Testing the Independence of VaR Exceptions.
Series Title: Wiley finance series.
Responsibility: Simon Hubbert.
More information:

Abstract:

Everything you need to know in order to manage risk effectively within your organization You cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive.  Read more...

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