Essential Mathematics for Market Risk Management
(Sprache: Englisch)
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.
You cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive.
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Produktinformationen zu „Essential Mathematics for Market Risk Management “
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.
You cannot afford to ignore the explosion in mathematical finance in your quest to remain competitive.
Klappentext zu „Essential Mathematics for Market Risk Management “
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 many organizations, this book is essential reading for getting to grips with the mathematical story behind the subject of financial risk management. It will take you on a journey--from the early ideas of risk quantification up to today's sophisticated models and approaches to business risk management.
To help you investigate the most up-to-date, pioneering developments in modern risk management, the book presents statistical theories and shows you how to put statistical tools into action to investigate areas such as the design of mathematical models for financial volatility or calculating the value at risk for an investment portfolio.
* Respected academic author Simon Hubbert is the youngest director of a financial engineering program in the U.K. He brings his industry experience to his practical approach to risk analysis
* Captures the essential mathematical tools needed to explore many common risk management problems
* Website with model simulations and source code enables you to put models of risk management into practice
* Plunges into the world of high-risk finance and examines the crucial relationship between the risk and the potential reward of holding a portfolio of risky financial assets
This book is your one-stop-shop for effective risk management.
In finance the universally held view is that the more risk we take the more reward we stand to gain but, just as importantly, the greater the chance of loss. The role of the financial risk manager is to be aware of the presence of risk, to understand how it can damage a potential investment and, most of all, be able to reduce the exposure to it in order to avert a potential disaster.
Essential Mathematics for Market Risk Management provides readers with the mathematical tools for managing and controlling the major sources of risk in the financial markets. Unlike most books on investment risk management which tend to be either panoptic in their coverage or narrowly focused on advanced mathematical procedures, this book offers a thorough understanding of the basic mathematical concepts and procedures required to satisfy the two key criteria of financial risk management: to ensure a healthy return on investment for a tolerable amount of risk, and to insulate a portfolio against catastrophic market events.
To this end, Dr Simon Hubbert, has drawn from his previous industrial experience to develop a format which clearly and methodically
- Traces the evolution of quantitative risk management - from Markowitz's landmark solution to the portfolio problem in the 1950s, to the emergence of Value at Risk (VaR) in the mid 1990s and its subsequent impact.
- Provides the basic mathematical tools needed to understand and solve common risk management problems, including applied linear algebra, probability theory and mathematical optimization.
- Introduces and explains the statistical theory, tools and techniques behind cutting-edge research into financial risk management taking place in professional and academic institutions globally.
- Explores a range of advanced topics in quantitative risk management, including derivative pricing, non-linear Value at Risk, volatility modelling and extreme value theory.
By focusing on the key issues a typical financial risk manager faces on both a daily and long-term basis - from monitoring portfolio performance to modelling the volatility of specific assets - this book is essential reading for finance professionals and students who recognize the need to be conversant in modern quantitative methods for financial risk management.1990s and its subsequent impact.
- Provides the basic mathematical tools needed to understand and solve common risk management problems, including applied linear algebra, probability theory and mathematical optimization.
- Introduces and explains the statistical theory, tools and techniques behind cutting-edge research into financial risk management taking place in professional and academic institutions globally.
- Explores a range of advanced topics in quantitative risk management, including derivative pricing, non-linear Value at Risk, volatility modelling and extreme value theory.
By fo
Essential Mathematics for Market Risk Management provides readers with the mathematical tools for managing and controlling the major sources of risk in the financial markets. Unlike most books on investment risk management which tend to be either panoptic in their coverage or narrowly focused on advanced mathematical procedures, this book offers a thorough understanding of the basic mathematical concepts and procedures required to satisfy the two key criteria of financial risk management: to ensure a healthy return on investment for a tolerable amount of risk, and to insulate a portfolio against catastrophic market events.
To this end, Dr Simon Hubbert, has drawn from his previous industrial experience to develop a format which clearly and methodically
- Traces the evolution of quantitative risk management - from Markowitz's landmark solution to the portfolio problem in the 1950s, to the emergence of Value at Risk (VaR) in the mid 1990s and its subsequent impact.
- Provides the basic mathematical tools needed to understand and solve common risk management problems, including applied linear algebra, probability theory and mathematical optimization.
- Introduces and explains the statistical theory, tools and techniques behind cutting-edge research into financial risk management taking place in professional and academic institutions globally.
- Explores a range of advanced topics in quantitative risk management, including derivative pricing, non-linear Value at Risk, volatility modelling and extreme value theory.
By focusing on the key issues a typical financial risk manager faces on both a daily and long-term basis - from monitoring portfolio performance to modelling the volatility of specific assets - this book is essential reading for finance professionals and students who recognize the need to be conversant in modern quantitative methods for financial risk management.1990s and its subsequent impact.
- Provides the basic mathematical tools needed to understand and solve common risk management problems, including applied linear algebra, probability theory and mathematical optimization.
- Introduces and explains the statistical theory, tools and techniques behind cutting-edge research into financial risk management taking place in professional and academic institutions globally.
- Explores a range of advanced topics in quantitative risk management, including derivative pricing, non-linear Value at Risk, volatility modelling and extreme value theory.
By fo
Inhaltsverzeichnis zu „Essential Mathematics for Market Risk Management “
Preface xiii1 Introduction 1
1.1 Basic Challenges in Risk Management 1
1.2 Value at Risk 3
1.3 Further Challenges in Risk Management 6
2 Applied Linear Algebra for Risk Managers 11
2.1 Vectors and Matrices 11
2.2 Matrix Algebra in Practice 17
2.3 Eigenvectors and Eigenvalues 21
2.4 Positive Definite Matrices 24
3 Probability Theory for Risk Managers 27
3.1 Univariate Theory 27
3.1.1 Random variables 27
3.1.2 Expectation 31
3.1.3 Variance 32
3.2 Multivariate Theory 33
3.2.1 The joint distribution function 33
3.2.2 The joint and marginal density functions 34
3.2.3 The notion of independence 34
3.2.4 The notion of conditional dependence 35
3.2.5 Covariance and correlation 35
3.2.6 The mean vector and covariance matrix 37
3.2.7 Linear combinations of random variables 38
3.3 The Normal Distribution 39
4 Optimization Tools 43
4.1 Background Calculus 43
4.1.1 Single-variable functions 43
4.1.2 Multivariable functions 44
4.2 Optimizing Functions 47
4.2.1 Unconstrained quadratic functions 48
4.2.2 Constrained quadratic functions 50
4.3 Over-determined Linear Systems 52
4.4 Linear Regression 54
5 Portfolio Theory I 63
5.1 Measuring Returns 63
5.1.1 A comparison of the standard and log returns 64
5.2 Setting Up the Optimal Portfolio Problem 67
5.3 Solving the Optimal Portfolio Problem 70
6 Portfolio Theory II 77
6.1 The Two-Fund Investment Service 77
6.2 A Mathematical Investigation of the Optimal Frontier 78
6.2.1 The minimum variance portfolio 78
6.2.2 Covariance of frontier portfolios 78
6.2.3 Correlation with the minimum variance portfolio 79
6.2.4 The zero-covariance portfolio
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79
6.3 A Geometrical Investigation of the Optimal Frontier 80
6.3.1 Equation of a tangent to an efficient portfolio 80
6.3.2 Locating the zero-covariance portfolio 82
6.4 A Further Investigation of Covariance 83
6.5 The Optimal Portfolio Problem Revisited 86
7 The Capital Asset Pricing Model (CAPM) 91
7.1 Connecting the Portfolio Frontiers 91
7.2 The Tangent Portfolio 94
7.2.1 The market's supply of risky assets 94
7.3 The CAPM 95
7.4 Applications of CAPM 96
7.4.1 Decomposing risk 97
8 Risk Factor Modelling 101
8.1 General Factor Modelling 101
8.2 Theoretical Properties of the Factor Model 102
8.3 Models Based on Principal Component Analysis (PCA) 105
8.3.1 PCA in two dimensions 106
8.3.2 PCA in higher dimensions 112
9 The Value at Risk Concept 117
9.1 A Framework for Value at Risk 117
9.1.1 A motivating example 120
9.1.2 Defining value at risk 121
9.2 Investigating Value at Risk 122
9.2.1 The suitability of value at risk to capital allocation 124
9.3 Tail Value at Risk 126
9.4 Spectral Risk Measures 127
10 Value at Risk under a Normal Distribution 131
10.1 Calculation of Value at Risk 131
10.2 Calculation of Marginal Value at Risk 132
10.3 Calculation of Tail Value at Risk 134
10.4 Sub-additivity of Normal Value at Risk 135
11 Advanced Probability Theory for Risk Managers 137
11.1 Moments of a Random Variable 137
11.2 The Characteristic Function 140
1
6.3 A Geometrical Investigation of the Optimal Frontier 80
6.3.1 Equation of a tangent to an efficient portfolio 80
6.3.2 Locating the zero-covariance portfolio 82
6.4 A Further Investigation of Covariance 83
6.5 The Optimal Portfolio Problem Revisited 86
7 The Capital Asset Pricing Model (CAPM) 91
7.1 Connecting the Portfolio Frontiers 91
7.2 The Tangent Portfolio 94
7.2.1 The market's supply of risky assets 94
7.3 The CAPM 95
7.4 Applications of CAPM 96
7.4.1 Decomposing risk 97
8 Risk Factor Modelling 101
8.1 General Factor Modelling 101
8.2 Theoretical Properties of the Factor Model 102
8.3 Models Based on Principal Component Analysis (PCA) 105
8.3.1 PCA in two dimensions 106
8.3.2 PCA in higher dimensions 112
9 The Value at Risk Concept 117
9.1 A Framework for Value at Risk 117
9.1.1 A motivating example 120
9.1.2 Defining value at risk 121
9.2 Investigating Value at Risk 122
9.2.1 The suitability of value at risk to capital allocation 124
9.3 Tail Value at Risk 126
9.4 Spectral Risk Measures 127
10 Value at Risk under a Normal Distribution 131
10.1 Calculation of Value at Risk 131
10.2 Calculation of Marginal Value at Risk 132
10.3 Calculation of Tail Value at Risk 134
10.4 Sub-additivity of Normal Value at Risk 135
11 Advanced Probability Theory for Risk Managers 137
11.1 Moments of a Random Variable 137
11.2 The Characteristic Function 140
1
... weniger
Autoren-Porträt von Simon Hubbert
Dr SIMON HUBBERT is a lecturer in Mathematics and Mathematical Finance at Birkbeck College, University of London, where he is currently the programme director for the graduate diploma in Financial Engineering. He has taught masters level courses on Risk Management and Financial Mathematics for many years and also has valuable industrial experience having engaged in consultation work with IBM global business services and as a risk analyst for the debt management office, a branch of HM-Treasury.
Bibliographische Angaben
- Autor: Simon Hubbert
- 2011, 1. Auflage, 350 Seiten, mit Abbildungen, Maße: 17,7 x 24,7 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 1119979528
- ISBN-13: 9781119979524
- Erscheinungsdatum: 28.02.2012
Sprache:
Englisch
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