Numerical methods and optimization in finance:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
London ; San Diego ; Cambridge ; Oxford
Academic Press, an imprint of Elsevier
[2019]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält Literaturverzeichnis (Seite 599-608) und Index |
| Physical Description: | xxiv, 614 Seiten Diagramme |
| ISBN: | 9780128150658 0128150653 |
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| 245 | 1 | 0 | |a Numerical methods and optimization in finance |c Manfred Gilli (Geneva School of Economics and Management, University of Geneva), Dietmar Maringer (Faculty of Business and Economics, University of Basel), Enrico Schumann (Faculty of Business and Economics, University of Basel) |
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| adam_text | Contents List of figures List of tables List of algorithms Acknowledgments Foreword to the second edition xi xvii xix xxi xxiii Part ! Fundamentals 1. Introduction 1.1 About this book The growth of computing power Computational finance 1.2 Principles 1.3 On software 1.4 On approximations and accuracy 1.5 Summary: the theme of the book 3 3 4 6 7 10 15 2. Numerical analysis in a nutshell 2.1 Computer arithmetic Representation of real numbers Machine precision Example of limitations of floating point arithmetic 2.2 Measuring errors 2.3 Approximating derivatives with finite differences Approximating first-order derivatives Approximating second-order derivatives Partial derivatives How to choose h Truncation error for forward difference 2.4 Numerical instability and ill-conditioning Example of a numerically unstable algorithm 17 17 19 19 20 21 21 22 22 22 23 24 24 Example of an ill-conditioned problem 2.5 Condition number of a matrix Comments and examples 2.6 A primer on algorithmic and computational complexity Criteria for comparison Order of complexity and classification Appendix 2.A Operation count for basic linear algebra operations 25 26 27 28 28 29 30 3. Linear equations and Least Squares problems 3.1 Direct methods 3.1.1 Triangular systems 3.1.2 LU factorization 3.1.3 Cholesky factorization 3.1.4 QR decomposition 3.1.5 Singular value decomposition 3.2 Iterative methods 3.2.1 Jacobi, Gauss-Seidel, and SOR Successive overrelaxation 3.2.2 Convergence of iterative methods 3.2.3 General structure of algorithms for iterative methods 3.2.4 Block iterative methods 3.3 Sparse
linear systems 3.3.1 Tridiagonal systems 3.3.2 Irregular sparse matrices 3.3.3 Structural properties of sparse matrices 3.4 The Least Squares problem 3.4.1 Method of normal equations 3.4.2 Least Squares via QR factorization 3.4.3 Least Squares via SVD decomposition 3.4.4 Final remarks 32 32 33 35 37 37 38 39 40 41 42 44 45 45 47 48 50 51 54 55 56 v
vi Contents The backslash operator in MATLAB Appendix 3.A Solving linear systems in R solve Least Squares 4. 56 56 57 58 Finite difference methods 4.1 An example of a numerical solution A first numerical approximation A second numerical approximation 4.2 Classification of differential equations 4.3 The Black-Scholes equation 4.3.1 Explicit, implicit, and 0-methods 4.3.2 Initial and boundary conditions and definition of the grid 4.3.3 Implementation of the 0-method with MATLAB 4.3.4 Stability 4.3.5 Coordinate transformation of space variables 4.4 American options Appendix 4.A A note on MATLAB s function spdiags 61 62 63 64 65 67 67 71 73 76 79 86 5. Binomial trees 5.1 Motivation Matching moments 5.2 Crowing the tree 5.2.1 Implementing a tree 5.2.2 Vectorization 5.2.3 Binomial expansion 5.3 Early exercise 5.4 Dividends 5.5 The Greeks Greeks from the tree 89 89 90 91 92 93 95 95 97 97 Part 11 Simulation 6. Generating random numbers 6.1 Monte Carlo methods and sampling 6.1.1 How it all began 6.1.2 Financial applications 6.2 Uniform random number generators 6.2.1 Congruential generators 103 103 104 104 104 6.2.2 Mersenne Twister 6.3 Nonuniform distributions 6.3.1 The inversion method 6.3.2 Acceptance-rejection method 6.4 Specialized methods for selected distributions 6.4.1 Normal distribution 6.4.2 Higher order moments and the Cornish-Fisher expansion 6.4.3 Further distributions 6.5 Sampling from a discrete set 6.5.1 Discrete uniform selection 6.5.2 Roulette wheel selection 6.5.3 Random permutations and shuffling 6.6 Sampling errors—and how to reduce them 6.6.1 The basic problem
6.6.2 Quasi-Monte Carlo 6.6.3 Stratified sampling 6.6.4 Variance reduction 6.7 Drawing from empirical distributions 6.7.1 Data randomization 6.7.2 Bootstrap 6.8 Controlled experiments and experimental design 6.8.1 Replicability and ceteris paribus analysis 6.8.2 Available random number generators in MATLAB 6.8.3 Uniform random numbers from MATLAB s rand function 6.8.4 Gaussian random numbers from MATLAB s randn function 6.8.5 Remedies 107 107 107 109 111 111 113 114 116 116 117 118 118 118 119 120 121 122 122 122 127 127 128 128 129 131 7. Modeling dependencies 7.1 Transformation methods 7.1.1 Linear correlation 7.1.2 Rank correlation 7.2 Markov chains 7.2.1 Concepts 7.2.2 The Metropolis algorithm 7.3 Copula models 7.3.1 Concepts 7.3.2 Simulation using copulas 133 133 138 144 144 146 148 148 150 8. A gentle introduction to financial simulation 8.1 Setting the stage 8.2 Single-period simulations 153 154
Contents 8.2.1 8.2.2 8.2.3 8.2.4 8.3 8.4 8.5 8.6 8.7 8.8 Terminal asset prices 1-over-iV portfolios European options VaR of a covered put portfolio Simple price processes Processes with memory in the levels of returns 8.4.1 Efficient versus adaptive markets 8.4.2 Moving averages 8.4.3 Autoregressive models 8.4.4 Autoregressive moving average (ARMA) models 8.4.5 Simulating ARMA models 8.4.6 Models with long-term memory Time-varying volatility 8.5.1 The concepts 8.5.2 Autocorreiated time-varying volatility 8.5.3 Simulating GARCH processes 8.5.4 Selected further autoregressive volatility models Adaptive expectations and patterns in price processes 8.6.1 Price-earnings models 8.6.2 Models with learning Historical simulation 8.7.1 Backtesting 8.7.2 Bootstrap Agent-based models and complexity 154 155 157 159 161 163 163 163 164 165 166 167 169 169 170 173 Part III Optimization 10. Optimization problems in finance 10.1 What to optimize? 10.2 Solving the model 10.2.1 Problems 10.2.2 Classical methods and heuristics 10.3 Evaluating solutions 10.4 Examples Portfolio optimization with alternative risk measures Model selection Robust/resistant regression Agent-based models Calibration of option-pricing models Calibration of yield structure models 10.5 Summary 219 220 220 222 222 224 224 225 225 226 226 227 228 11. Basic methods 175 178 178 179 180 180 181 185 9. Financial simulation at work: some case studies 9.1 Constant proportion portfolio insurance (CPPI) 9.1.1 Basic concepts 9.1.2 Bootstrap 9.2 VaR estimation with Extreme Value Theory 9.2.1 Basic concepts 9.2.2 Scaling the data
9.2.3 Using Extreme Value Theory 9.3 Option pricing 9.3.1 Modeling prices 9.3.2 Pricing models 9.3.3 Greeks 9.3.4 Quasi-Monte Carlo vii 189 189 191 192 192 193 193 195 196 199 208 210 11.1 Finding the roots of ƒ (x) = 0 11.1.1 A naïve approach Graphical solution Random search 11.1.2 Bracketing 11.1.3 Bisection 11.1.4 Fixed point method Convergence 11.1.5 Newton s method Comments 11.2 Classical unconstrained optimization Convergence 11.3 Unconstrained optimization in one dimension 11.3.1 Newton s method 11.3.2 Golden section search 11.4 Unconstrained optimization in multiple dimensions 11.4.1 Steepest descent method 11.4.2 Newton s method 11.4.3 Quasi-Newton method 11.4.4 Direct search methods 11.4.5 Practical issues with MATLAB 11.5 Nonlinear Least Squares 11.5.1 Problem statement and notation 11.5.2 Gauss-Newton method 229 229 230 231 231 232 233 235 238 240 241 242 243 243 244 245 245 247 248 250 254 256 256 257
viii Contents 11.5.3 Levenberg-Marquardt method 11.6 Solving systems of nonlinear equations F(x) = 0 11.6.1 General considerations 11.6.2 Fixed point methods 11.6.3 Newton s method 11.6.4 Quasi-Newton methods 11.6.5 Further approaches 11.7 Synoptic view of solution methods 258 260 260 262 263 268 269 270 Heuristic methods in a nutshell 12.1 Heuristics What is a heuristic? Iterative search 12.2 Single-solution methods 12.2.1 Stochastic Local Search 12.2.2 Simulated Annealing 12.2.3 Threshold Accepting 12.2.4 Tabu Search 12.3 Population-based methods 12.3.1 Genetic Algorithms 12.3.2 Differential Evolution 12.3.3 Particle Swarm Optimization 12.3.4 Ant Colony Optimization 12.4 Hybrids 12.5 Constraints 12.6 The stochastics of heuristic search 12.6.1 Stochastic solutions and computational resources 12.6.2 An illustrative experiment 12.7 General considerations 12.7.1 What technique to choose? 12.7.2 Efficient implementations 12.7.3 Parametersettings 12.8 Outlook Appendix 12.A Implementing heuristic methods with MATLAB 12.A.1 The problems 12.A.2 Threshold Accepting 12.A.3 Genetic Algorithm 12.A.4 Differential Evolution 12.A.5 Particle Swarm Optimization Appendix 12.B Parallel computations in MATLAB 12.B.1 Parallel execution of restart loops Appendix 12.C Heuristic methods in the NMOF package 12.C.1 Local Search 12.C.2 Simulated Annealing 12.C.3 Threshold Accepting 12.C.4 Genetic Algorithm 12.C.5 Differential Evolution 12.C.6 Particle Swarm Optimization 12.C.7 Restarts 309 311 314 314 315 315 315 316 316 317 13. Heuristics: a tutorial 273 274 275 276 276 277 278 279 279 279 280 281
282 282 284 285 285 287 289 289 289 293 294 294 296 298 303 306 308 13.1 On Optimization 319 13.1.1 Models 319 13.1.2 Methods 320 13.2 The problem: choosing few from many 320 13.2.1 The subset-sum problem 320 13.2.2 Representing a solution 321 13.2.3 Evaluating a solution 321 13.2.4 Knowing the solution 322 13.3 Solution strategies 323 13.3.1 Being thorough 323 13.3.2 Being constructive 324 13.3.3 Being random 325 13.3.4 Getting better 327 13.4 Heuristics 330 13.4.1 On heuristics 330 13.4.2 Local Search 331 13.4.3 Threshold Accepting 336 13.4.4 Settings, or: how (long) to run an algorithm 340 13.4.5 Stochastics of LS and TA 340 13.5 Application: selecting variables in a regression 342 13.5.1 Linear models 342 13.5.2 Fast least squares 343 13.5.3 Selection criterion 344 13.5.4 Putting it all together 345 13.6 Application: portfolio selection 347 13.6.1 Models 347 13.6.2 Local-Search algorithms 348 14. Portfolio optimization 14.1 The investment problem 14.2 Mean-variance optimization 14.2.1 The model 355 357 357
Contents 14.2.2 Solving the model 14.2.3 Examples of mean-variance models 14.2.4 True, estimated, and realized frontiers 14.2.5 Repairing matrices 14.3 Optimization with heuristics 14.3.1 Asset selection with Local Search 14.3.2 Scenario Optimization with Threshold Accepting 14.3.3 Portfolio optimization with TA: examples 14.3.4 Diagnostics for techniques based on Local Search 14.4 Portfolios under Value-at-Risk 14.4.1 Why Value-at-Risk matters 14.4.2 Setting up experiments 14.4.3 Numerical results Appendix 14.A Computing returns Appendix 14.B More implementation issues in R 14.B.1 Scoping rules in R and objective functions 14.B.2 Vectorized objective functions Appendix 14.C A neighborhood for switching elements 358 358 366 368 377 377 383 392 411 413 413 414 415 419 420 420 422 424 15. Backtesting 15.1 What is (the problem with) backtesting? 15.1.1 The ugly: intentional overfitting 15.1.2 The bad: unintentional overfitting and other difficulties 15.1.3 The good: getting insights (and confidence) in strategies 15.2 Data and software 15.2.1 What data to use? 15.2.2 Designing backtesting software 15.2.3 The btestfunction 15.3 Simple backtests 15.3.1 btest: a tutorial 15.3.2 Robert Shi tier s Irrational-Exuberance data 427 428 434 436 437 437 439 439 440 440 450 15.4 Backtesting portfolio strategies 15.4.1 Kenneth French s data library 15.4.2 Momentum 15.4.3 Portfolio optimization Appendix 15.A Prices in btest Appendix 15.В Notes on zoo Appendix 15.C Parallel computations in R 15.C.1 Distributed computing 15.C.2 Loops and apply functions 15.C.3 Distributing data 15.C.4
Distributing data, continued 15.C.5 Other functions in the parallel package 15.C.6 Parallel computations in the NMOF package ix 459 459 464 470 479 479 480 480 481 482 484 486 486 16. Econometric models 16.1 Term structure models 16.1.1 Yield curves 16.1.2 The Nelson-Siege! model 16.1.3 Calibration strategies 16.1.4 Experiments 16.2 Robust and resistant regression 16.2.1 The regression model 16.2.2 Estimation 16.2.3 An example 16.2.4 Numerical experiments 16.2.5 Final remarks 16.3 Estimating Time Series Models 16.3.1 Adventures with time series estimation 16.3.2 The case of GARCH models 16.3.3 Numerical experiments with Differential Evolution Appendix 16.A Maximizing the Sharpe ratio 487 487 492 496 518 522 525 527 532 535 540 542 542 543 545 549 17. Calibrating option pricing models 17.1 Implied volatility with Black-Scholes The smile 17.2 Pricing with the characteristic function 17.2.1 A pricing equation 552 554 555 555
x Contents 17.2.2 Numerical integration 17.3 Calibration 17.3.1 Techniques 17.3.2 Organizing the problem and implementation 17.3.3 Two experiments 17.4 Final remarks Appendix 17.A Quadrature rules for infinity 560 580 580 582 589 593 594 A. The NMOF package A.1 Installing the package A.2 News, feedback and discussion A.3 Using the package Bibliography Index 597 597 597 599 609
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| id | DE-604.BV046041436 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:33:34Z |
| institution | BVB |
| isbn | 9780128150658 0128150653 |
| language | English |
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| spelling | Gilli, Manfred 1942- Verfasser (DE-588)170963047 aut Numerical methods and optimization in finance Manfred Gilli (Geneva School of Economics and Management, University of Geneva), Dietmar Maringer (Faculty of Business and Economics, University of Basel), Enrico Schumann (Faculty of Business and Economics, University of Basel) Second edition London ; San Diego ; Cambridge ; Oxford Academic Press, an imprint of Elsevier [2019] © 2019 xxiv, 614 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Enthält Literaturverzeichnis (Seite 599-608) und Index Optimierung (DE-588)4043664-0 gnd rswk-swf Finanzierung (DE-588)4017182-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzplanungsmodell (DE-588)4252015-0 gnd rswk-swf Finanzierung (DE-588)4017182-6 s Finanzmathematik (DE-588)4017195-4 s Optimierung (DE-588)4043664-0 s Finanzplanungsmodell (DE-588)4252015-0 s b DE-604 Maringer, Dietmar G. Verfasser (DE-588)171714393 aut Schumann, Enrico Verfasser aut Erscheint auch als Online-Ausgabe 978-0-12-815065-8 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031423124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gilli, Manfred 1942- Maringer, Dietmar G. Schumann, Enrico Numerical methods and optimization in finance Optimierung (DE-588)4043664-0 gnd Finanzierung (DE-588)4017182-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Finanzplanungsmodell (DE-588)4252015-0 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4017182-6 (DE-588)4017195-4 (DE-588)4252015-0 |
| title | Numerical methods and optimization in finance |
| title_auth | Numerical methods and optimization in finance |
| title_exact_search | Numerical methods and optimization in finance |
| title_full | Numerical methods and optimization in finance Manfred Gilli (Geneva School of Economics and Management, University of Geneva), Dietmar Maringer (Faculty of Business and Economics, University of Basel), Enrico Schumann (Faculty of Business and Economics, University of Basel) |
| title_fullStr | Numerical methods and optimization in finance Manfred Gilli (Geneva School of Economics and Management, University of Geneva), Dietmar Maringer (Faculty of Business and Economics, University of Basel), Enrico Schumann (Faculty of Business and Economics, University of Basel) |
| title_full_unstemmed | Numerical methods and optimization in finance Manfred Gilli (Geneva School of Economics and Management, University of Geneva), Dietmar Maringer (Faculty of Business and Economics, University of Basel), Enrico Schumann (Faculty of Business and Economics, University of Basel) |
| title_short | Numerical methods and optimization in finance |
| title_sort | numerical methods and optimization in finance |
| topic | Optimierung (DE-588)4043664-0 gnd Finanzierung (DE-588)4017182-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Finanzplanungsmodell (DE-588)4252015-0 gnd |
| topic_facet | Optimierung Finanzierung Finanzmathematik Finanzplanungsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031423124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gillimanfred numericalmethodsandoptimizationinfinance AT maringerdietmarg numericalmethodsandoptimizationinfinance AT schumannenrico numericalmethodsandoptimizationinfinance |