Practical Financial Optimization: A Library of GAMS Models

by Andrea Consiglio (Editor), Soren Nielsen (Editor), Stavros A. Zenios (Editor)

Overview

In Practical Financial Optimization: A Library of GAMS Models, the authors provide a diverse set of models for portfolio optimization, based on the General Algebraic Modelling System. 'GAMS' consists of a language which allows a high-level, algebraic representation of mathematical models and a set of solvers – numerical algorithms – to solve them. The system was developed in response to the need for powerful and flexible front-end tools to manage large, real-life models.

The work begins with an overview of the structure of the GAMS language, and discusses issues relating to the management of data in GAMS models. The authors provide models for mean-variance portfolio optimization which address the question of trading off the portfolio expected return against its risk. Fixed income portfolio optimization models perform standard calculations and allow the user to bootstrap a yield curve from bond prices. Dedication models allow for standard portfolio dedication with borrowing and re-investment decisions, and are extended to deal with maximisation of horizon return and to incorporate various practical considerations on the portfolio tradeability. Immunization models provide for the factor immunization of portfolios of treasury and corporate bonds.

The scenario-based portfolio optimization problem is addressed with mean absolute deviation models, tracking models, regret models, conditional VaR models, expected utility maximization models and put/call efficient frontier models. The authors employ stochastic programming for dynamic portfolio optimization, developing stochastic dedication models as stochastic extensions of the fixed income models discussed in chapter 4. Two-stage and multi-stage stochastic programs extend the scenario models analysed in Chapter 5 to allow dynamic rebalancing of portfolios as time evolves and new information becomes known. Models for structuring index funds and hedging interest rate risk on international portfolios are also provided.

The final chapter provides a set of 'case studies': models for large-scale applications of portfolio optimization, which can be used as the basis for the development of business support systems to suit any special requirements, including models for the management of participating insurance policies and personal asset allocation.

The title will be a valuable guide for quantitative developers and analysts, portfolio and asset managers, investment strategists and advanced students of finance.

Product Details

ISBN-13:	9781444317237
Publisher:	Wiley
Publication date:	02/05/2010
Series:	The Wiley Finance Series
Sold by:	JOHN WILEY & SONS
Format:	eBook
Pages:	200
File size:	4 MB

About the Author

ANDREA CONSIGLIO is professor of Mathematical Finance at the University of Palermo, Italy. He has held positions at the University of Calabria and at the University of Cyprus. He has participated in consultancy projects with the Banca della Svizzera Italiana, Switzerland and Prometeia, Italy. He has co-authored one book and numerous articles for various leading academic journals. In 2006 he was awarded the EURO Excellence in Practice Award, jointly with Stavros A. Zenios and Flavio Cocco. His research interests encompass many areas in the field of financial modeling and computational finance. He holds a PhD in applied mathematics to finance and economics.

SØREN NIELSEN (1959-2003) was an Associate Professor in the Department of Informatics and Mathematical Modeling at the Technical University of Denmark. He worked at the World Bank and the University of Texas at Austin. He held degrees in computer science and a PhD in decision sciences from the Wharton School of the University of Pennsylvania.

STAVROS A. ZENIOS is Professor of Finance and Management Science at the University of Cyprus, Director of the HERMES European Centre of Excellence on Computational Finance and Economics, and Senior Fellow at the Wharton Financial Institutions Centre of the University of Pennsylvania. He has co-authored more than 130 articles in some of the premier journals in the filed, serves on the editorial board of six journals, and received numerous awards for his research and publications. His previous books include Practical Financial Optimization: Decision Making for Financial Engineers (Blackwell Publishing, 2007); Performance of Financial Institutions: Efficiency, Innovation, Regulation (Cambridge University Press, 2000); Parallel Optimization: Theory, Algorithms, and Applications (Oxford University Press, 1997); and Financial Optimization (Cambridge University Press, 1996).

Table of Contents

Preface xi

Acknowledgments xiii

Notation xv

List of Models xix

1 An Introduction to the GAMS Modeling System 1

1.1 Preview 1

1.2 Basics of Modeling 1

1.3 The GAMS Language 2

1.3.1 Lexical conventions 3

1.3.2 Sets 4

1.3.3 Expressions, functions, and operators 6

1.3.4 Assignment statements 11

1.3.5 Variable declarations 12

1.3.6 Constraints: Equation declarations 13

1.3.7 Model declarations 14

1.3.8 The SOLVE statement and model types 15

1.3.9 Control structures 16

1.3.10 Conditional compilation 20

1.4 Getting Started 21

1.4.1 The Integrated Development Environment 21

1.4.2 Command line interaction 22

1.4.3 The model library 22

Notes and References 22

2 Data Management 25

2.1 Preview 25

2.2 Basics of Data Handling 25

2.2.1 Data entry: SCALARs, PARAMETERs, and TABLEs 26

2.2.2 External data files: INCLUDE 28

2.2.3 Output: DISPLAY and PUT 29

2.3 Data Generation 31

2.4 A Complete Example: Portfolio Dedication 31

2.4.1 The source file 32

2.4.2 The FINLIB files 39

3 Mean-Variance Portfolio Optimization 41

3.1 Preview 41

3.2 Basics of Mean-Variance Models 42

3.2.1 Data estimation for the mean-variance model 46

3.2.2 Allowing short sales 48

3.2.3 The FINLIB files 49

3.3 Sharpe Ratio Model 50

3.3.1 Risk-free borrowing 51

3.3.2 The FINLIB files 53

3.4 Diversification Limits and Transaction Costs 53

3.4.1 Transaction costs 54

3.4.2 Portfolio revision 56

3.4.3 The FINLIB files 57

3.5 International Portfolio Management 57

3.5.1 Implementation with dynamic sets 58

3.5.2 The FINLIB files 61

4 Portfolio Models for Fixed Income 63

4.1 Preview 63

4.2 Basics of Fixed-Income Modeling 64

4.2.1 Modeling time 64

4.2.2 GAMS as a financial calculator: continuous time 66

4.2.3 Bootstrapping the term structure of interest rates 68

4.2.4 Considerations for realistic modeling 73

4.2.5 The FINLIB files 74

4.3 Dedication Models 74

4.3.1 Horizon return model 78

4.3.2 Tradeability considerations 79

4.3.3 The FINLIB files 82

4.4 Immunization Models 83

4.4.1 The FINLIB files 85

4.5 Factor Immunization Model 85

4.5.1 Direct yield maximization 87

4.5.2 The FINLIB files 89

4.6 Factor Immunization for Corporate Bonds 89

4.6.1 The model data sets 89

4.6.2 The optimization models 90

4.6.3 The FINLIB files 94

5 Scenario Optimization 95

5.1 Preview 95

5.2 Data sets 96

5.2.1 The FINLIB files 97

5.3 Mean Absolute Deviation Models 97

5.3.1 Downside risk and tracking models 99

5.3.2 Comparing mean-variance and mean absolute deviation 101

5.3.3 The FINLIB files 103

5.4 Regret Models 104

5.4.1 The FINLIB files 106

5.5 Conditional Value-at-Risk Models 106

5.5.1 The FINLIB files 108

5.6 Utility Maximization Models 109

5.6.1 The FINLIB files 111

5.7 Put/Call Efficient Frontier Models 111

5.7.1 The FINLIB files 117

6 Dynamic Portfolio Optimization with Stochastic Programming 119

6.1 Preview 119

6.2 Dynamic Optimization for Fixed-Income Securities 119

6.2.1 Stochastic dedication 120

6.2.2 Stochastic dedication with borrowing and lending 122

6.2.3 The FINLIB files 124

6.3 Formulating Two-Stage Stochastic Programs 124

6.3.1 Deterministic and stochastic two-stage programs 125

6.3.2 The FINLIB files 128

6.4 Single Premium Deferred Annuities: A Multi-stage Stochastic Program 128

6.4.1 Background and data 128

6.4.2 The FINLIB files 133

7 Index Funds 137

7.1 Preview 137

7.2 Models for Index Funds 138

7.2.1 A structural model for index funds 138

7.2.2 A co-movement model for index funds 139

7.2.3 A selective hedging model for index funds 140

7.2.4 The FINLIB files 143

8 Case Studies in Financial Optimization 145

8.1 Preview 145

8.2 Application I: International Asset Allocation 146

8.2.1 Operational considerations 149

8.2.2 Results 151

8.2.3 The FINLIB files 156

8.3 Application II: Corporate Bond Portfolio Management 156

8.3.1 The FINLIB files 159

8.4 Application III: Insurance Policies with Guarantees 159

8.4.1 The FINLIB files 164

8.5 Application IV: Personal Financial Planning 164

8.5.1 The FINLIB files 168

Bibliography 169

Index 171