Computational Methods in Financial Engineering (eBook)

Preface 7
Contents 9
List of Contributors 11
Part I Portfolio Optimization and Option Pricing 16
Threshold Accepting Approach to Improve Bound- based Approximations for Portfolio Optimization 17
1 Introduction 17
2 Portfolio Problem 20
3 Time Discretization 22
4 Multistage Stochastic Programs 24
5 Space Discretization 26
6 Case Study 33
Acknowledgments 38
References 38
Risk Preferences and Loss Aversion in Portfolio Optimization 41
1 Assets and Asset Selection 41
2 Portfolio Optimization under Loss Aversion 44
3 Heuristic Methods for Portfolio Optimization 46
4 Empirical Study 50
5 Conclusion 57
Acknowledgements 58
References 58
Generalized Extreme Value Distribution and Extreme Economic Value at Risk ( EE- VaR) 61
1 Introduction 61
2 Model and Methodology 66
3 Data Description 69
4 Empirical Modelling and Results on Implied RNDs 70
5 Conclusions 82
Acknowledgements 83
References 83
Portfolio Optimization under VaR Constraints Based on Dynamic Estimates of the Variance- Covariance Matrix 87
1 Introduction 87
2 Model 90
3 Optimization Method 93
4 Empirical Analysis 96
5 Conclusion 105
Acknowledgements 106
References 106
Optimal Execution of Time-Constrained Portfolio Transactions 109
1 Introduction 109
2 Problem Definition 110
3 Price Dynamics 110
4 An Approximation Approach 111
5 Numerical Example 113
6 Monte Carlo Simulation 114
7 Concluding Remarks 114
Acknowledgements 116
References 116
Semidefinite Programming Approaches for Bounding Asian Option Prices 117
Preamble 117
1 Introduction 117
2 SDP Strategy for Bounding Option Prices 119
3 Conclusion 127
References 127
The Evaluation of Discrete Barrier Options in a Path Integral Framework 131
1 Introduction 131
2 The General Barrier Structure 133
3 The Barrier Option as a Functional Recurrence Relation Equation 135
4 The Fourier-Hermite Series Expansion 136
5 Results 142
6 Conclusion 145
Acknowledgements 146
References 146
Appendix 147
A The Coefficient 147
B The Coefficient 148
C The Coefficient 149
D The Coefficient 150
E The Coefficient 151
F The Coefficient 153
G The Coefficient 155
H Useful Notation 157
Part II Estimation and Classi.cation 159
Robust Prediction of Beta 161
Preamble 161
1 Introduction 161
2 Shrinkage Robust Estimators of Beta 163
3 Empirical Evidence 165
4 Monte Carlo Simulations 168
5 Conclusion 174
Acknowledgements 174
References 174
Neural Network Modelling with Applications to Euro Exchange Rates 177
1 Introduction 177
2 Feedforward Neural Network Models 180
3 Variable Selection in Neural Network Models 183
4 Numerical Examples and Monte Carlo Results 186
5 An Application to Euro Exchange Rates 190
6 Conclusions 193
Acknowledgements 194
References 194
Testing Uncovered Interest Rate Parity and Term Structure Using Multivariate Threshold Cointegration 205
Preamble 205
1 Introduction 206
2 The Economic Relations 208
3 The Econometric Framework 210
4 Empirical Analysis 216
5 Conclusion 220
Acknowledgements 220
References 220
Classification Using Optimization: Application to Credit Ratings of Bonds 225
1 Introduction 225
2 Description of Methodology 227
3 Constraints 232
4 Choosing Model Flexibility 237
5 Error Estimation 244
6 Bond Classi.cation Problem 245
7 Description of Data 246
8 Numerical Experiments 247
9 Concluding Remarks 250
References 251
Evolving Decision Rules to Discover Patterns in Financial Data Sets 253
1 Introduction 253
2 Previous Work 254
3 PerformanceMetrics 255
4 Evolving Comprehensible Rules 258
5 Results and Discussion 260
6 Conclusions 265
Acknowledgements 267
References 267
Part III Banking, Risk and Macroeconomic Modelling 271
A Banking Firm Model: The Role of Market, Liquidity and Credit Risks 273
1 Introduction 273
2 The Model 275
3 Conclusion 282
Acknowledgements 285
References 285
Identification of Critical Nodes and Links in Financial Networks with Intermediation and Electronic Transactions 287
1 Introduction 287
2 The Financial Network Model with Intermediation and Electronic Transactions 290
3 The Financial Network Performance Measure and the Importance of Financial Network Components 298
4 Numerical Examples 302
5 Summary and Conclusions 307
Acknowledgements 307
References 308
An Analysis of Settlement Risk Contagion in Alternative Securities Settlement Architectures 313
Preamble 313
1 Introduction 313
2 The Basic Framework 318
3 Numerical Analysis 320
4 Conclusions 327
Acknowledgements 328
References 328
Integrated Risk Management: Risk Aggregation and Allocation Using Intelligent Systems 331
1 Introduction 331
2 Current Silo-Based Approach to Risk Management 332
3 An Integrated Approach to Risk Management 334
4 Summary and Outlook 351
Acknowledgements 353
References 353
A Stochastic Monetary Policy Interest Rate Model 357
1 Introduction 357
2 Continuous-time Lattices 359
3 The Interest Rate Model 368
4 Conclusions 396
A Continuous-time Finite-state Markov Chains 397
B Markov Generator Discretization 400
C Option Pricing with Continuous-time Lattices 401
D Moments Method for Range Accruals 402
References 404
Duali: Software for Solving Stochastic Control Problems in Economics 407
Preamble 407
1 Introduction 408
2 The Beck and Wieland Model in Wieland’s Notation 409
3 The Beck and Wieland Model in Kendrick’s Notation 410
4 Open Loop 414
5 Optimal Feedback 415
6 Expected Optimal Feedback 417
7 OF versus EOF 422
8 Expected Optimal Feedback with Time-Varying Parameters (EOFwT) 423
9 OFwT versus EOFwT 424
10 Conclusion 425
References 425
A The Beck and Wieland Model in 427
Index 435