Numerical methods and optimization in finance:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Academic Press Elsevier
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 584 S. Ill., graph. Darst., Kt. |
| ISBN: | 9780123756626 |
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MARC
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| 100 | 1 | |a Gilli, Manfred |d 1942- |e Verfasser |0 (DE-588)170963047 |4 aut | |
| 245 | 1 | 0 | |a Numerical methods and optimization in finance |c Manfred Gilli ; Dietmar Maringer ; Enrico Schumann |
| 264 | 1 | |a Amsterdam [u.a.] |b Academic Press Elsevier |c 2011 | |
| 300 | |a XV, 584 S. |b Ill., graph. Darst., Kt. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Finanzplanungsmodell |0 (DE-588)4252015-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Finanzierung |0 (DE-588)4017182-6 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 3 | |a Finanzplanungsmodell |0 (DE-588)4252015-0 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Maringer, Dietmar G. |e Verfasser |0 (DE-588)171714393 |4 aut | |
| 700 | 1 | |a Schumann, Enrico |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-024402569 | ||
Record in the Search Index
| _version_ | 1804148370715967488 |
|---|---|
| adam_text | Contents
List of Algorithms
xiii
Acknowledgements
xv
1.
Introduction
1
1.1
About this book
1
1.2
Principles
3
1.3
On software
5
1.4
On approximations and accuracy
9
1.5
Summary: the theme of the book
14
Part One Fundamentals
15
2.
Numerical analysis in a nutshell
17
2.1
Computer arithmetic
17
Representation of real numbers
17
Machine precision
20
Example of limitations of floating point arithmetic
20
2.2
Measuring errors
21
2.3
Approximating derivatives with finite differences
22
Approximating first-order derivatives
22
Approximating second-order derivatives
23
Partial derivatives
23
How to choose
h
24
Truncation error for forward difference
24
2.4
NmnericfilmstabMtvandiU-conditionmg
26
Example of a numerically unstable algorithm
26
Example of an ill-conditioned problem
27
2.5
Condition number of a matrix
28
Comments and examples
29
2.6
A primer on algorithmic and computational complexity
31
2.6.1
Criteria for comparison
■ 31
Order of complexity and classification
32
2
A Operation count for basic linear algebra operations
33
3.
linear equations and Least Squares problems
35
Choice of method
36
3.1
Direct methods
36
3.1.1
Triangular systems
36
3.1.2
LU
factorization
37
vi
Contents
3.1.3
Cholesky
factorization
40
3.1.4
QR
decomposition
43
3.1.5
Singular value decomposition
44
3.2
Iterative methods
44
3.2.1
Jacobi, Gauss-Seidel, and
SOR
45
Successive overrelaxation
46
3.2.2
Convergence of iterative methods
48
3.2.3
General structure of algorithms for iterative methods
49
3.2.4
Block iterative methods
52
3.3
Sparse linear systems
53
3.3.1
Tridiagonal systems
53
3.3.2
Irregular sparse matrices
55
3.3.3
Structural properties of sparse matrices
57
3.4
The Least Squares problem
60
3.4.1
Method of normal equations
61
3.4.2
Least Squares via QR factorization
64
3.4.3
Least Squares via
SVD
decomposition
65
3.4.4
Final remarks
67
The backslash operator in
Matlab
67
4.
Finite difference methods
69
4.1
An example of a numerical solution
69
A first numerical approximation
70
A second numerical approximation
71
4.2
Classification of differential equations
73
4.3
The Bkck-Scholes equation
74
4.3.1
Explicit, implicit, and 6-methods
76
4.3.2
Initial and boundary conditions and definition of the grid
76
4.3.3
Implementation of the 0-method with
Matlab
82
4.3.4
Stability
85
4.3.5
Coordinate transformation of space variables
88
4.4
American options
90
4.A A note on Matiab s function spdiags
101
5.
Binomial trees
103
5.1
Motivation
103
Matching moments
104
5.2
Growing the tree
105
5.2.1
Implementing a tree
106
5.2.2
Vectorization
107
5.2.3
Binomial expansion
108
5.3
Early
enerase
ПО
5.4
Dividends
ці
53
The Greeks
цз
Greeks from the tree
цз
Contents
vii
Part Two Simulation
117
6.
Generating random numbers
119
6.1
Monte Carlo methods and sampling
119
6.1.1
How it all began
119
6.1.2
Financial applications
120
6.2
Uniform random number generators
121
6.2.1
Congruential generators
121
6.2.2
Mersenne Twister
124
6.3
Nonuniform
distributions
125
6.3.1
The inversion method
125
6.3.2
Acceptance-rejection method
127
6.4
Specialized methods for selected distributions
129
6.4.1
Normal distribution
129
6.4.2
Higher order moments and the Cornish-Fisher expansion
132
6.4.3
Further distributions
134
6.5
Sampling from a discrete set
136
6.5.1
Discrete uniform selection
136
6.5.2
Roulette wheel selection
137
6.5.3
Random permutations and shuffling
138
6.6
Sampling errors
—
and how to reduce them
139
6.6.1
The basic problem
139
6.6.2
Quasi-Monte
Carlo
140
6.6.3
Stratified sampling
142
6.6.4
Variance reduction
143
6.7
Drawing from empirical distributions
145
6.7.1
Data randomization
145
6.7.2
Bootstrap
146
6.8
Controlled experiments and experimental
design
152
6.8.1
Replicability and ceteris
paribus
analysis
152
6.8.2
Available random number generators in
Matlab
153
6.8.3
Uniform random numbers from Matlab s rand function
154
6.8.4
Gaussian random numbers from Matlab s randn function
155
6.8.5
Remedies
156
7.
Modeling dependencies
159
7.1
Transformation methods
159
7.1.1 Linearcorrelation 159
7.1.2
Rank correlation
165
7.2
Markov chains
173
7.2.1
Concepts
173
7.2.2
The Metropolis algorithm
175
7.3
Copula models
178
7.3.1
Concepts
178
7.3.2
Simulation using copulas
181
Contents
8.
A gentle introduction to financial simulation
185
8.1
Setting the stage
185
8.2
Single-period simulations
186
8.2.1
Terminal asset prices
186
8.2.2
l-over-N portfolios
188
8.2.3
European options
190
8.2.4
VaR of a covered put portfolio
193
8.3
Simple price processes
196
8.4
Processes with memory in the levels of returns
198
8.4.1
Efficient versus adaptive markets
198
8.4.2
Moving averages
199
8.4.3
Autoregressive
models
200
8.4.4
Autoregressive
moving average
(ARMA)
models
202
8.4.5
Simulating
ARMA
models
203
8.4.6
Models with long-term memory
205
8.5
Time-varying volatility
206
8.5.1
The concepts
206
8.5.2
Autocorrelated time-varying volatility
208
8.5.3
Simulating GARCH processes
211
8.5.4
Selected further
autoregressive
volatility models
214
8.6
Adaptive expectations and patterns in price processes
218
8.6.1
Price-earnings models
218
8.6.2
Models with learning
220
8.7
Historical simulation
222
8.7.1
Backtesting
222
8.7.2
Bootstrap
223
8.8
Agent-based
mođels
and complexity
228
9.
Financial
Simulation
at work: some case studies
233
9.1
Constant proportion portfolio insurance (CPPI)
233
9.1.1
Basic concepts
233
9.1.2
Bootstrap
235
9Л
VaR estimation with Extreme Value Theory
237
9.2.1
Basic concepts
237
9.2.2
Scaling the data
238
9.2.3
Using Extreme Value Theory
238
9.3
Option pricing
242
9.3.1
Modeling prices
243
9.3.2
Pricing models
246
9.3.3
Greeks
258
9.3.4
Quasi-Monte
Carlo
261
Part Three Optimization
269
10.
Optimization problems in finance
271
10.1
What to optimize;
271
Contents ix
10.2
Solving the model
273
10.2.1
Problems
273
10.2.2
Classical methods and heuristics
275
10.3
Evaluating solutions
276
10.4
Examples
278
Portfolio optimization with alternative risk measures
278
Model selection
280
Robust/resistant regression
280
Agent-based models
281
Calibration of option-pricing models
282
Calibration of yield structure models
283
10.5
Summary
284
11.
Basic methods
287
11.1
Finding the roots of
ƒ
(x)=0
287
11.1.1
A naïve
approach
287
Graphical solution
288
Random search
289
11.1.2
Bracketing
289
11.1.3
Bisection
290
11.1.4
Fixed point method
292
Convergence
294
11.1.5
Newton s method
298
Comments
300
11.2
Classical unconstrained optimization
301
Convergence
302
11.3
Unconstrained optimization in one dimension
303
11.3.1
Newton s method
303
11.3.2
Golden section search
305
11.4
Unconstrained optimization in multiple dimensions
306
11.4.1
Steepest descent method
306
11.4.2
Newton s method
308
11.4.3
Quasi-Newton
method
310
11.4.4
Direct search methods
311
11.4.5
Practical issues with
Matlab
317
11.5
Nonlinear Least Squares
318
11.5.1
Problem statement and notation
318
11.5.2
Gauss-Newton method
320
11.5.3
Levenberg-Marquardt method
320
11.6
SoMng systems of nonlinear equations F(x} = 0
323
11.6.1
General considerations
323
11.6.2
Fixed point methods
325
11.6.3
Newton s method
328
11.6.4
Quasi-Newton
methods
332
11.6.5
Further approaches
334
11.7
Synoptic view of
solution
methods
336
Contents
12.
Heuristic methods in a nutshell
337
12.1
Heuristics
337
12.2
Trajectory methods
341
12.2.1
Stochastic local search
341
12.2.2
Simulated Annealing
342
12.2.3
Threshold Accepting
344
12.2.4
Tabu Search
344
123
Population-based methods
345
12.3.1
Genetic Algorithms
345
12.3.2
Differential Evolution
346
12.3.3
Particle Swarm Optimization
347
12.3.4
Ant Colony Optimization
348
12.4
Hybrids
349
123
Constraints
352
12.6
The stochastics of heuristic search
354
12.6.1
Stochastic solutions and computational resources
354
12.6.2
An illustrative experiment
356
12.7
General considerations
359
12.7.
1 What technique to choose?
359
12.7.2
Efficient implementations
359
12.7.3
Parameter settings
362
12.8
Summary
363
12
Λ
Implementing heuristic methods with
Matlab
364
12Λ.1
Threshold Accepting
367
12.A.2 Genetic Algorithm
371
12.A.3 Differential Evolution
375
12Λ.4
Partide Swarm Optimization
377
13.
Portfolio optimization
381
13.1
The investment problem
381
13.2
The
сЬцяігя!
case: mean—variance optimization
383
13.2.1
The model
383
13.2.2
Solving the model
385
13.2.3
Mean-variance models
386
13.2.4
True, estimated, and realized frontiers
393
13.2.5
Repairing matrices
396
133
Heuristic optimization of one-period models
403
13.3.1
Asset selection with local search
403
13.3.2
Scenario optimization with Threshold Accepting
409
13.3.3
Examples
421
13.3.4
Diagnostics
437
13.A More implementation issues in
R
440
13.A.1 Scoping rules in
R
and objective functions
440
13.A.2 Vectorized objective functions
441
Contents xi
14.
Econometrie
models
445
14.1
Term structure models
445
14.1.1
Yield curves
445
14.1.2
The
Nelson-Siegel
model
451
14.1.3
Calibration strategies
456
14.1.4
Experiments
474
14.2
Robust and resistant regression
480
14.2.1
The regression model
484
14.2.2
Estimation
486
14.2.3
An example
491
14.2.4
Numerical experiments
494
14.2.5
Final remarks
500
14.A Maximizing the
Sharpe
ratio
502
15.
Calibrating option pricing models
505
15.1
Implied volatility with Black-Scholes
506
The smile
509
15.2
Pricing with the characteristic function
510
15.2.1
A pricing equation
510
15.2.2
Numerical integration
516
15.3
Calibration
541
15.3.1
Techniques
541
15.3.2
Organizing the problem and implementation
544
15.3.3
Two experiments
552
15.4
Final remarks
557
15.A Quadrature rules for infinity
558
Bibliography
563
Index
577
|
| any_adam_object | 1 |
| author | Gilli, Manfred 1942- Maringer, Dietmar G. Schumann, Enrico |
| author_GND | (DE-588)170963047 (DE-588)171714393 |
| author_facet | Gilli, Manfred 1942- Maringer, Dietmar G. Schumann, Enrico |
| author_role | aut aut aut |
| author_sort | Gilli, Manfred 1942- |
| author_variant | m g mg d g m dg dgm e s es |
| building | Verbundindex |
| bvnumber | BV039550685 |
| classification_rvk | QP 700 QP 890 SK 980 |
| ctrlnum | (OCoLC)852525703 (DE-599)GBV657518808 |
| dewey-full | 332.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.015195 |
| dewey-search | 332.015195 |
| dewey-sort | 3332.015195 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV039550685 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:06:04Z |
| institution | BVB |
| isbn | 9780123756626 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024402569 |
| oclc_num | 852525703 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-824 DE-19 DE-BY-UBM DE-20 DE-945 DE-1102 DE-858 DE-521 DE-523 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-824 DE-19 DE-BY-UBM DE-20 DE-945 DE-1102 DE-858 DE-521 DE-523 |
| physical | XV, 584 S. Ill., graph. Darst., Kt. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Academic Press Elsevier |
| record_format | marc |
| spelling | Gilli, Manfred 1942- Verfasser (DE-588)170963047 aut Numerical methods and optimization in finance Manfred Gilli ; Dietmar Maringer ; Enrico Schumann Amsterdam [u.a.] Academic Press Elsevier 2011 XV, 584 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Finanzplanungsmodell (DE-588)4252015-0 gnd rswk-swf Finanzierung (DE-588)4017182-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Optimierung (DE-588)4043664-0 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024402569&sequence=000002&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 Finanzplanungsmodell (DE-588)4252015-0 gnd Finanzierung (DE-588)4017182-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4252015-0 (DE-588)4017182-6 (DE-588)4017195-4 (DE-588)4043664-0 |
| 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 ; Dietmar Maringer ; Enrico Schumann |
| title_fullStr | Numerical methods and optimization in finance Manfred Gilli ; Dietmar Maringer ; Enrico Schumann |
| title_full_unstemmed | Numerical methods and optimization in finance Manfred Gilli ; Dietmar Maringer ; Enrico Schumann |
| title_short | Numerical methods and optimization in finance |
| title_sort | numerical methods and optimization in finance |
| topic | Finanzplanungsmodell (DE-588)4252015-0 gnd Finanzierung (DE-588)4017182-6 gnd Finanzmathematik (DE-588)4017195-4 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Finanzplanungsmodell Finanzierung Finanzmathematik Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024402569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gillimanfred numericalmethodsandoptimizationinfinance AT maringerdietmarg numericalmethodsandoptimizationinfinance AT schumannenrico numericalmethodsandoptimizationinfinance |