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Practical financial optimization: decision making for financial engineers

Author: Zenios, Stavros A. Publisher: Blackwell, 2007.Language: EnglishDescription: 400 p. : Graphs/Ill. ; 25 cm.ISBN: 9781405132015Type of document: BookBibliography/Index: Includes bibliographical references and index
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Book Europe Campus
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Print HG106 .Z46 2007
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001272505
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Includes bibliographical references and index

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Practical Financial Optimization
Decision Making for Financial Engineers
Contents
Foreword, by Harry M. Markowitz xv......................................................................................................
Preface xvii...............................................................................................................................................
Acknowledgments xxi..............................................................................................................................
Text Credits xxiii......................................................................................................................................
Notation xxv.............................................................................................................................................
List of Models xxix....................................................................................................................................
I INTRODUCTION1
1 An Optimization View of Financial Engineering3
1.1 Preview 3............................................................................................................................................
1.2 Optimization in Financial Engineering 3.............................................................................................
1.3 Enterprise-Wide Risk Management 7..................................................................................................
1.3.1 What is enterprise-wide risk management? 7.......................................................................
1.3.2 Enterprise-wide risk management for a single business 10..................................................
1.3.3 Enterprise-wide risk management for a business portfolio 12..............................................
1.3.4 Integrating design, pricing, funding, and capitalization 12...................................................
1.3.5 Components of enterprise-wide risk management 13...........................................................
1.3.6 Why enterprise-wide risk management is important 17........................................................
1.3.7 Asset and liability management 18........................................................................................
1.4 The Scope for Optimization in Enterprise-Wide Risk Management 20..............................................
1.4.1 Caveat: What to optimize? 21
1.5 Overview of Financial Optimization Models 22.................................................................................
1.5.1 Basics of risk management 22...............................................................................................
1.5.2 Mean-variance portfolio optimization 22..............................................................................
1.5.3 Portfolio models for fixed income 23....................................................................................
1.5.4 Scenario optimization 24.......................................................................................................
1.5.5 Dynamic portfolio optimization 25.......................................................................................
1.5.6 Index funds 25.......................................................................................................................
1.5.7 Designing financial products 26...........................................................................................
1.5.8 Scenario generation 26..........................................................................................................
1.5.9 Applications 27......................................................................................................................
1.6 Postview 27.........................................................................................................................................
Notes and References 27...........................................................................................................................
2 Basics of Risk Management31
2.1 Preview 31..........................................................................................................................................
2.2 A Classification of Financial Risks 31................................................................................................
2.3 Risk Measurement for Equities 37......................................................................................................
2.4 Risk Measurement for Fixed-Income Securities ............................................................................ 44
2.4.1 Duration and convexity .................................................................................................... 46
2.4.2 Factor analysis of the term structure ................................................................................ 49
2.4.3 Option adjusted analysis ................................................................................................... 53
2.5 Scenario Analysis for Fixed-Income Securities ............................................................................. 56
2.6 Enterprise-Wide Risk Measurement ............................................................................................... 58
2.7 Coherent Risk Measurement .......................................................................................................... 61
2.8 Measurement of Reward and Performance Evaluation .................................................................. 63
2.8.1 Investor choice .................................................................................................................. 64
2.8.2 Performance evaluation .................................................................................................... 66
2.9 Classification of Risk Management Models ................................................................................... 66
2.10 Postview ....................................................................................................................................... 68
Notes and References ........................................................................................................................... 69
II PORTFOLIO OPTIMIZATION MODELS71
3 Mean-Variance Analysis73
3.1 Preview .......................................................................................................................................... 73
3.2 Mean-Variance Optimization ......................................................................................................... 73
3.2.1 Canonical formulation ...................................................................................................... 74
3.2.2 General formulations ........................................................................................................ 78
3.2.3 Trading sizes and transaction costs .................................................................................. 80
3.2.4 Portfolio revision .............................................................................................................. 82
3.3 Incorporating Liabilities ................................................................................................................. 84
3.4 Factor Models of Return ................................................................................................................. 85
3.4.1 Single-factor model........................................................................................................... 85
3.4.2 Multi-factor model ............................................................................................................ 88
3.5 Are Optimized Portfolios Optimal? ................................................................................................ 91
3.6 Postview ......................................................................................................................................... 92
Notes and References ........................................................................................................................... 93
4 Portfolio Models for Fixed Income95
4.1 Preview .......................................................................................................................................... 95
4.2 Portfolio Dedication....................................................................................................................... 95
4.2.1 Cashflow matching with perfect foresight ....................................................................... 96
4.2.2 Cashflow matching with borrowing and reinvestment .................................................... 98
4.2.3 Horizon returns ................................................................................................................. 99
4.2.4 Lot sizes, transaction costs, and portfolio revision .......................................................... 99
4.2.5 Diversification .................................................................................................................. 100
4.2.6 Bootstrapping the yield of dedicated portfolios ............................................................... 101
4.3 Portfolio Immunization ................................................................................................................... 101
4.4 Factor Immunization ....................................................................................................................... 104
4.5 Factor Immunization for Corporate Bonds ..................................................................................... 106
4.5.1 Factor analysis of corporate yields ................................................................................... 107
4.5.2 Factor immunization with uncorrelated credit ratings ..................................................... 109
4.5.3 Factor immunization with correlated credit ratings ......................................................... 112
4.6 Postview ......................................................................................................................................... 113
Notes and References ........................................................................................................................... 113
5 Scenario Optimization115
5.1 Preview ........................................................................................................................................ 115
5.2 Basics of Scenario Optimization .................................................................................................. 115
5.3 Mean Absolute Deviation Models ................................................................................................ 116
5.3.1 Semi-absolute deviation ................................................................................................. 119
5.3.2 Equivalence of absolute deviation measures .................................................................. 120
5.3.3 Tracking model ............................................................................................................... 121
5.4 Regret Models............................................................................................................................... 122
5.4.1 c-regret models ............................................................................................................... 123
5.5 Conditional Value-at-Risk Models ............................................................................................... 125
5.6 Expected Utility Maximization ..................................................................................................... 127
5.7 Put/Call Efficient Frontiers ........................................................................................................... 129
5.7.1 Put/call efficient frontiers without constraints ............................................................... 130
5.7.2 Put/call efficient frontiers with finite liquidity ............................................................... 133
5.8 Asset Valuation using Scenario Optimization .............................................................................. 136
5.8.1 Optimization models of arbitrage ................................................................................... 136
5.8.2 Valuation in complete markets ....................................................................................... 138
5.8.3 Valuation in dynamically complete markets .................................................................. 139
5.8.4 Valuation in incomplete markets .................................................................................... 140
5.8.5 Utility invariant pricing .................................................................................................. 142
5.9 Postview ....................................................................................................................................... 144
Notes and References ......................................................................................................................... 145
6 Dynamic Portfolio Optimization with Stochastic Programming147
6.1 Preview ....................................................................................................................................... 147
6.2 Setting the Stage for Dynamic Models ....................................................................................... 147
6.2.1 Notation for dynamic models.......................................................................................... 151
6.3 Decision Rules for Dynamic Portfolio Strategies ....................................................................... 152
6.3.1 Buy-and-hold strategy .................................................................................................... 152
6.3.2 Constant mix strategy ..................................................................................................... 152
6.3.3 Constant proportion strategy .......................................................................................... 154
6.3.4 Option-based portfolio insurance.................................................................................... 154
6.4 Stochastic Dedication .................................................................................................................. 155
6.5 Basic Concepts of Stochastic Programming ............................................................................... 157
6.5.1 The newsvendor problem ............................................................................................... 158
6.5.2 Canonical stochastic programming problems ................................................................ 159
6.5.3 Anticipative models ........................................................................................................ 160
6.5.4 Adaptive models ............................................................................................................. 160
6.5.5 Recourse models ............................................................................................................. 161
6.5.6 Deterministic equivalent formulation ............................................................................. 162
6.5.7 Split variable formulation ............................................................................................... 163
6.5.8 Multi-stage models ......................................................................................................... 164
6.6 Stochastic Programming for Dynamic Portfolio Strategies ........................................................ 165
6.6.1 Model formulation .......................................................................................................... 167
6.7 Comparison of Stochastic Programming with Other Methods ................................................... 172
6.7.1 Mean-variance models and downside risk ..................................................................... 172
6.7.2 Discrete-time, multi-period models ................................................................................ 172
6.7.3 Continuous-time models ................................................................................................. 173
6.7.4 Stochastic programming ................................................................................................. 174
6.8 Postview ..................................................................................................................................... 174
Notes and References ........................................................................................................................ 175
7 Index Funds177
7.1 Preview ......................................................................................................................................... 177
7.2 Basics of Market Indices ............................................................................................................... 177
7.3 Indexation Models ......................................................................................................................... 180
7.3.1 A structural model for index funds ................................................................................. 181
7.3.2 A model for index funds based on co-movements ......................................................... 181
7.4 Models for International Index Funds ........................................................................................... 183
7.4.1 Creating a global index ................................................................................................... 183
7.4.2 Integrated indexation models .......................................................................................... 184
7.4.3 Nonintegrated models ..................................................................................................... 185
7.4.4 Operational model ........................................................................................................... 186
7.5 Models for Corporate Bond Index Funds ..................................................................................... 188
7.6 Stochastic Programming for Index Funds ..................................................................................... 189
7.6.1 Notation ........................................................................................................................... 189
7.6.2 Model formulation .......................................................................................................... 191
7.7 Applications of Indexation Models ............................................................................................... 193
7.7.1 Tracking an international government bond index ......................................................... 194
7.7.2 Tracking a corporate bond index .................................................................................... 197
7.7.3 Enhanced index funds ..................................................................................................... 198
7.7.4 Stochastic programming models for index tracking ....................................................... 199
7.8 Postview ....................................................................................................................................... 202
Notes and References .......................................................................................................................... 204
8 Designing Financial Products205
8.1 Preview ......................................................................................................................................... 205
8.2 Financial Innovation ...................................................................................................................... 205
8.3 Financial Product Novelties .......................................................................................................... 206
8.3.1 Guaranteed investment contracts .................................................................................... 206
8.3.2 Callable bonds ................................................................................................................. 207
8.3.3 Single premium deferred annuities.................................................................................. 208
8.3.4 Asset-backed securities ................................................................................................... 210
8.3.5 Mortgage-backed and derivative securities .................................................................... 211
8.4 A Framework for Financial Product Design ................................................................................. 215
8.4.1 Risk aversion and certainty equivalent return ................................................................ 216
8.4.2 Model formulation .......................................................................................................... 217
8.5 Optimal Design of Callable Bonds ............................................................................................... 220
8.6 Postview ....................................................................................................................................... 222
Notes and References .......................................................................................................................... 222
9 Scenario Generation225
9.1 Preview ......................................................................................................................................... 225
9.2 Scenarios and their Properties ....................................................................................................... 225
9.2.1 Scenario definition .......................................................................................................... 226
9.2.2 Scenario properties ......................................................................................................... 227
9.3 A Framework for Scenario Generation ......................................................................................... 228
9.3.1 Scenarios for the liabilities ............................................................................................. 231
9.3.2 Scenarios of economic factors and asset returns ............................................................ 232
9.4 Scenario Generation Methodologies ............................................................................................. 233
9.4.1 Bootstrapping historical data .......................................................................................... 234
9.4.2 Statistical modeling: the Value-at-Risk approach .......................................................... 234
9.4.3 Statistical modeling: time series analysis ....................................................................... 236
9.4.4 Discrete lattice approximations of continuous models .................................................... 239
9.5 Constructing Event Trees ............................................................................................................. 242
9.5.1 Sampling and tree fitting ................................................................................................. 242
9.5.2 Arbitrage-free event trees ................................................................................................ 244
9.6 Postview ...................................................................................................................................... 247
Notes and References ....................................................................................................................... 247
III APPLICATIONS251
10 International Asset Allocation253
10.1 Preview .................................................................................................................................... 253
10.2 The Risks of International Asset Portfolios .............................................................................. 253
10.3 Hedging Strategies .................................................................................................................... 254
10.4 Statistical Characteristics of International Data ....................................................................... 255
10.5 Model for Selective Hedging .................................................................................................... 256
10.6 Asset Allocation ........................................................................................................................ 258
10.6.1 Asset allocation in treasuries ........................................................................................ 259
10.6.2 Asset allocation in equities ........................................................................................... 260
10.6.3 Asset allocation in treasuries and equities ................................................................... 260
10.7 Risk Measure for International Asset Allocation ..................................................................... 261
10.8 Postview ................................................................................................................................... 264
Notes and References ....................................................................................................................... 265
11 Corporate Bond Portfolios267
11.1 Preview .................................................................................................................................... 267
11.2 Credit Risk Securities ............................................................................................................... 267
11.3 Integrating Market and Credit Risk .......................................................................................... 268
11.3.1 Scenario generation for corporate bonds ..................................................................... 270
11.3.2 The simulation framework ........................................................................................... 270
11.4 Optimizing the Right Risk Metric ............................................................................................ 275
11.4.1 Tail effects on efficient frontiers .................................................................................. 275
11.4.2 Conditional Value-at-Risk efficient frontiers .............................................................. 277
11.5 Index Funds for Corporate Bond Portfolios ............................................................................. 282
11.5.1 Indexation by strategic asset allocation ....................................................................... 282
11.5.2 Tactical bond picking model ........................................................................................ 283
11.6 Tracking the Merrill Lynch Euro Dollar Corporate Bond Index ............................................. 284
11.6.1 Sensitivity to alternative risk factors ............................................................................ 285
11.6.2 Sensitivity to model choices ......................................................................................... 288
11.7 Funding Liabilities with Corporate Bonds ............................................................................... 291
11.8 Postview ................................................................................................................................... 292
Notes and References ....................................................................................................................... 294
12 Insurance Policies with Guarantees297
12.1 Preview .................................................................................................................................... 297
12.2 Participating Policies with Guarantees ..................................................................................... 297
12.3 The Italian Insurance Industry .................................................................................................. 299
12.3.1 Guaranteed products with bonus provisions ................................................................ 300
12.3.2 Current asset and liability management practices ........................................................ 301
12.4 The Scenario Optimization Model ............................................................................................ 302
12.4.1 Features of the model ................................................................................................... 302
12.4.2 Notation ......................................................................................................................... 302
12.4.3 Variable dynamics and constraints ............................................................................... 303
12.4.4 Linearly constrained optimization model ..................................................................... 305
12.4.5 Surrender option ............................................................................................................ 308
12.4.6 Model extensions .......................................................................................................... 309
12.4.7 Reversionary and terminal bonuses .............................................................................. 310
12.5 Model Testing and Validation ................................................................................................... 311
12.5.1 Integrative asset and liability management ................................................................... 312
12.5.2 Analysis of the trade-offs .............................................................................................. 314
12.5.3 Analysis of alternative debt structures .......................................................................... 316
12.5.4 The view from the regulator's desk................................................................................ 320
12.5.5 Additional model features ............................................................................................. 321
12.5.6 Benchmarks of Italian insurance policies ..................................................................... 324
12.5.7 Comparing Italian with UK policies ............................................................................. 326
12.6 Postview .................................................................................................................................... 329
Notes and References ........................................................................................................................ 330
13 Personal Financial Planning333
13.1 Preview ..................................................................................................................................... 333
13.2 The Demand for Personal Financial Planning ........................................................................... 333
13.3 The Provision of Financial Services .......................................................................................... 334
13.4 Web-Based Personal Financial Tools ........................................................................................ 337
13.4.1 Strategic decisions: the Personal Asset Allocation tool ............................................... 338
13.4.2 Tactical decisions: the Personal Rating tool ................................................................. 338
13.4.3 Control: the Personal Risk Analysis tool ...................................................................... 339
13.5 Model for Personal Financial Planning ..................................................................................... 339
13.5.1 Solving the linear dynamic equations ........................................................................... 341
13.5.2 Analysis of the model ................................................................................................... 342
13.6 Model Validation and Testing ................................................................................................... 343
13.6.1 Probability of success and how to improve it ............................................................... 347
13.6.2 An apparatus to explain the equity premium puzzle ..................................................... 348
13.7 The Integrated Decision Support System .................................................................................. 351
13.7.1 The case of the Rossi family ......................................................................................... 351
13.8 Postview .................................................................................................................................... 356
Notes and References .......................................................................................................................... 356
IV LIBRARY OF FINANCIAL OPTIMIZATION MODELS357
14 FINLIB: A Library of Financial Optimization Models359
14.1 Preview ..................................................................................................................................... 359
14.2 FINLIB: Financial Optimization Library .................................................................................. 359
14.3 Studio Designs: Project Suggestions ......................................................................................... 360
14.3.1 Basics of modeling ........................................................................................................ 361
14.3.2 Mean-variance analysis ................................................................................................. 361
14.3.3 Portfolio models for fixed income ................................................................................ 361
14.3.4 Scenario optimization ................................................................................................... 361
14.3.5 Dynamic portfolio optimization .................................................................................... 362
14.3.6 Index funds .................................................................................................................... 362
14.3.7 Designing financial products ........................................................................................ 362
14.3.8 Scenario generation ....................................................................................................... 363
14.3.9 Applications .................................................................................................................. 363
Notes and References ........................................................................................................................ 363
A Basics of Optimization365
A.I Duality ........................................................................................................................................ 365
A.2 Optimality Conditions ................................................................................................................ 366
A.3 Lagrange Multipliers .................................................................................................................. 367
B Basics of Probability Theory369
B.1 Probability Spaces ...................................................................................................................... 369
C Stochastic Processes371
C.1 The Poisson Process ................................................................................................................... 372
C.2 The Gaussian Process ................................................................................................................. 372
C.3 The Wiener Process .................................................................................................................... 373
C.4 Markov Chains ........................................................................................................................... 373
Bibliography375
Index393

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