Financial modelling: theory, implementation and practice ; (with Matlab source)
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 719 S. Ill., graph. Darst. |
| ISBN: | 9780470744895 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV040505287 | ||
| 003 | DE-604 | ||
| 005 | 20170210 | ||
| 007 | t | ||
| 008 | 121025s2012 ad|| |||| 00||| eng d | ||
| 020 | |a 9780470744895 |c (cloth) |9 978-0-470-74489-5 | ||
| 035 | |a (OCoLC)820374804 | ||
| 035 | |a (DE-599)BVBBV040505287 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-11 |a DE-29T |a DE-20 |a DE-1049 |a DE-473 |a DE-19 |a DE-384 |a DE-83 |a DE-523 | ||
| 084 | |a QH 160 |0 (DE-625)141535: |2 rvk | ||
| 084 | |a QP 890 |0 (DE-625)141965: |2 rvk | ||
| 084 | |a SK 980 |0 (DE-625)143277: |2 rvk | ||
| 084 | |a 91Gxx |2 msc | ||
| 100 | 1 | |a Kienitz, Jörg |d 1970- |e Verfasser |0 (DE-588)1071747401 |4 aut | |
| 245 | 1 | 0 | |a Financial modelling |b theory, implementation and practice ; (with Matlab source) |c Jörg Kienitz ; Daniel Wetterau |
| 264 | 1 | |a Chichester |b Wiley |c 2012 | |
| 300 | |a XIII, 719 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Finanzplanungsmodell |0 (DE-588)4252015-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wirtschaftsmathematik |0 (DE-588)4066472-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a MATLAB |0 (DE-588)4329066-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kapitalmarktforschung |0 (DE-588)4390312-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wirtschaftsmathematik |0 (DE-588)4066472-7 |D s |
| 689 | 0 | 1 | |a Finanzplanungsmodell |0 (DE-588)4252015-0 |D s |
| 689 | 0 | 2 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | 3 | |a Kapitalmarktforschung |0 (DE-588)4390312-5 |D s |
| 689 | 0 | 4 | |a MATLAB |0 (DE-588)4329066-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Wetterau, Daniel |d 1982- |e Verfasser |0 (DE-588)1071747738 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-118-41329-6 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-118-41330-2 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-118-41331-9 |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025351934&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025351934 | ||
Datensatz im Suchindex
| _version_ | 1804149580321783808 |
|---|---|
| adam_text | Contents
Introduction
1
Introduction and Management Summary
2
Why We Have Written this Book
3
Why You Should Read this Book
4
The Audience
5
The Structure of this Book
6
What this Book Does Not Cover
7
Credits
8
Code
PART I FINANCIAL MARKETS AND POPULAR MODELS
1
Financial Markets
-
Data, Basics and Derivatives
9
1.1
Introduction and Objectives
9
1.2
Financial Time-Series, Statistical Properties of Market Data and Invariants
10
1.2.1
Real World Distribution
15
1.3
Implied Volatility Surfaces and Volatility Dynamics
17
1.3.1
Is There More than just a Volatility?
19
1.3.2
Implied Volatility
22
1.3.3
Time-Dependent Volatility
22
1.3.4
Stochastic Volatility
23
1.3.5
Volatility from Jumps
23
1.3.6
Traders Rule of Thumb
24
1.3.7
The Risk Neutral Density
24
1.4
Applications
26
1.4.1
Asset Allocation
26
1.4.2
Pricing, Hedging and Risk Management
27
1.5
General Remarks on Notation
30
1.6
Summary and Conclusions
31
1.7
Appendix
—
Quotes
32
Contents
2 Diffusion Models iS
2.1
Introduction
and
Objectives
35
2.2
Local Volatility
Models 35
2.2.1 The
Bachelier
and the Black-Scholes Model
37
2.2.2
The Hull-White Model
40
2.2.3
The Constant Elasticity of Variance Model
46
2.2.4
The Displaced Diffusion Model
50
2.2.5
CEV and DD Models
53
2.3
Stochastic Volatility Models
54
2.3.1
Pricing European Options
55
2.3.2
Risk Neutral Density
56
2.3.3
The Heston Model (and Extensions)
57
2.3.4
The SABR Model
67
2.3.5
SABR
-
Further Remarks
73
2.4
Stochastic Volatility and Stochastic Rates Models
81
2.4.1
The Hcston-Hull-White Model
81
2.5
Summary and Conclusions
90
3
Models with Jumps
93
3.
1 Introduction and Objectives
93
3.2
Poisson
Processes and Jump Diffusions
94
3.2.1
Poisson
Processes
94
3.2.2
The Merton Model
95
3.2.3
The Bates Model
99
3.2.4
The Bates-Hull-White Model
104
3.3
Exponential Levy Models
105
3.3.1
The Variance Gamma Model
107
3.3.2
The Normal Inverse Gaussian Model
112
3.4
Other Models
1
1
8
3.4.1
Exponential Levy Models with Stochastic Volatility
122
3.4.2
Stochastic Clocks
122
3.5
Martingale Correction
129
3.6
Summary and Conclusions
134
4
Multi-Dimensional Models
137
4.1
Introduction and Objectives
137
4.2
Multi-Dimensional Diffusions
137
4.2.1
GBM Baskets
137
4.2.2
Libor
Market Models
139
4.3
Multi-Dimensional Heston and SABR Models
141
4.3.1
Stochastic Volatility Models
141
4.4
Parameter Averaging
143
4.4.1
Applications to CMS Spread Options
144
4.5
Markovian Projection
159
4.5.1
Baskets with Local Volatility
162
4.5.2
Markovian Projection on Local Volatility and Heston Models
162
4.5.3
Markovian Projection onto DD SABR Models
164
Contents ix
4.6 Copulae 172
4.6.1
Measures of
Concordance
and Dependency
174
4.6.2
Examples
175
4.6.3
Elliptical Copulae
175
4.6.4
Archimedean Copulae
177
4.6.5
Building New Copulae from Given Copulae
179
4.6.6
Asymmetric Copulae
179
4.6.7
Applying Copulae to Option Pricing
180
4.6.8
Applying Copulae to Asset Allocation
180
4.7
Multi-Dimensional Variance Gamma Processes
187
4.8
Summary and Conclusions
193
PART II NUMERICAL METHODS AND RECIPES
5
Option Pricing by Transform Techniques and Direct Integration
197
5.1
Introduction and Objectives
197
5.2
Fourier Transform
197
5.2.1
Discrete Fourier Transform
199
5.2.2
Fast Fourier Transform
200
5.3
The Carr-Madan Method
202
5.3.1
The Optimal
α
207
5.4
The Lewis Method
210
5.4.1
Application to Other Payoffs
214
5.5
The Attari Method
215
5.6
The Convolution Method
216
5.7
The Cosine Method
220
5.8
Comparison, Stability and Performance
228
5.8.1
Other Issues
233
5.9
Extending the Methods to Forward Start Options
235
5.9.1
Forward Characteristic Function for Levy Processes and
CIR
Time Change
238
5.9.2
Forward Characteristic Function for Levy Processes and Gamma-OU
Time Change
239
5.9.3
Results
242
5.10
Density Recovery
245
5.11
Summary and Conclusions
250
6
Advanced Topics Using Transform Techniques
253
6.1
Introduction and Objectives
253
6.2
Pricing
Non-Standard
Vanilla Options
253
6.2.1
FFT with Lewis Method
254
6.3
Bermudán
and American Options
254
6.3.1
The Convolution Method
257
6.3.2
The Cosine Method
258
6.3.3
Numerical Results
266
6.3.4
The Fourier Space Time-Stepping
270
Contents
6.4
The Cosine Method and Barrier Options
277
6.5
Greeks 27S
6.6
Summary and Conclusions
287
Monte Carlo Simulation and Applications
289
7.1
Introduction and Objectives
28°
7.2
Sampling Diffusion Processes
289
7.2.1
The Exact Scheme
290
7.2.2
The
Euler
Scheme
290
7.2.3
The Predictor-Corrector Scheme
290
7.2.4
The Milstein Scheme
291
7.2.5
Implementation and Results
291
7.3
Special Purpose Schemes
292
7.3.
1 Schemes tor the Heston Model
294
7.3.2
Unbiased Scheme for the SABR Model
300
7.4
Adding Jumps
З І З
7.4.1
.lump Models
—
Poisson
Processes
3 13
7.4.2
Fixed Grid Sampling (FGS)
З І
5
7.4.3
Stochastic Grid Sampling (SGS)
З І
5
7.4.4
Simulation
-
Levy Models
322
7.4.5
Schemes for Levy Models with Stochastic Volatility
330
7.5
Bridge Sampling
339
7.6
Libor
Market Model
346
7.7
Multi-Dimensional Levy Models
351
7.8
Copulile
352
7.8.1
Distributional Sampling Approach (DSA)
353
7.8.2
Conditional Sampling Approach (CSA)
356
7.8.3
Simulation
from
Other Copulae
358
7.9
Summary and Conclusions
359
Monte Carlo Simulation
-
Advanced Issues
361
8.1
Introduction and Objectives
36
I
8.2
Monte Carlo and Early Exercise
361
8.2.1
Longstaff-Schwarz Regression
362
8.2.2
Policy Iteration Methods
369
8.2.3
Upper Bounds
374
8.2.4
Problems of the Method
376
8.2.5
Financial Examples and Numerical Results
378
8.3
Greeks with Monte Carlo
382
8.3.1
The Finite Difference Method
(FDM)
383
8.3.2
The Pathwise Method
385
8.3.3
The
Affine
Recursion Problem
(ARP)
389
8.3.4
Adjoint Method
39
j
8.3.5
Bermudán
ARPs
393
8.4
Euler
Schemes and General Greeks
396
8.4.1
SDE of Diffusions 396
8.4.2
Approximation by
Euler
Schemes
397
Contents
8.4.3
Approximating
General
Greeks Using
ARP
397
8.4.4
Greeks
404
8.5
Application to Trigger Swap
407
8.5.1
Mathematical Modelling
408
8.5.2
Numerical Results
410
8.5.3
The Likelihood Ratio Method (LRM)
413
8.5.4
Likelihood Ratio for Finite Differences
-
Proxy Simulation
416
8.5.5
Numerical Results
419
8.6
Summary and Conclusions
433
8.7
Appendix
-
Trees
434
9
Calibration and Optimization
435
9.1
Introduction and Objectives
435
9.2
The Nelder-Mead Method
437
9.2.1
Implementation
442
9.2.2
Calibration Examples
444
9.3
The Levenberg-Marquardt Method
449
9.3.1
Implementation
453
9.3.2
Calibration Examples
455
9.4
The L-BFGS Method
460
9.4.1
Implementation
463
9.4.2
Calibration Examples
464
9.5
The SQP Method
468
9.5.1
The Modified and Globally Convergent SQP Iteration
473
9.5.2
Implementation
475
9.5.3
Calibration Examples
477
9.6
Differential Evolution
482
9.6.1
Implementation
487
9.6.2
Calibration Examples
488
9.7
Simulated Annealing
493
9.7.1
Implementation
497
9.7.2
Calibration Examples
500
9.8
Summary and Conclusions
505
10
Model Risk
-
Calibration, Pricing and Hedging
507
10.1
Introduction and Objectives
507
10.2
Calibration
508
10.2.1
Similarities
-
Heston and Bates Models
508
10.2.2
Parameter Stability
511
10.3
Pricing Exotic Options
521
10.3.1
Exotic Options and Different Models
528
10.4
Hedging
528
10.4.1
Hedging
-
The Basics
531
10.4.2
Hedging in Incomplete Markets
533
10.4.3
Discrete Time Hedging
541
10.4.4
Numerical Examples
544
10.5
Summary and Conclusions
550
Contents
PART III IMPLEMENTATION, SOFTWARE DESIGN AND MATHEMATICS
11
Matlab
-
Basics
553
11.1
Introduction and Objectives
553
11.2
General Remarks
553
11.3
Matrices, Vectors and Cell Arrays
556
11.3.1
Matrices and Vectors
556
11.3.2
Cell Arrays
562
11.4
Functions and Function Handles
564
11.4.1
Functions
564
11.4.2
Function Handles
567
11.5
Toolboxes
570
11.5.1
Financial
570
11.5.2
Financial Derivatives
571
11.5.3
Fixed-Income
571
11.5.4
Optimization
573
11.5.5
Global Optimization
577
11.5.6
Statistics
578
11.5.7
Portfolio Optimization
581
11.6
Useful Functions and Methods
589
1
1.6.
1 FFT
589
1
1
.6.2
Solving Equations and ODE
589
11.6.3
Useful Functions
591
11.7
Plotting
593
11.7.1
Two-Dimensional Plots
593
W.I.
2
Three-Dimensional Plots
-
Surfaces
595
1
1
.8
Summary and Conclusions
597
12
Matlab
-
Object Oriented Development
599
12.1
Introduction and Objectives
599
12.2
The
Matlab OO
Model
599
12.2.1
Classes
599
12.2.2
Handling Classes in
Matlab
606
1
2.2.3
Inheritance, Base Classes and Superclasses
607
12.2.4
Handle and Value Classes
609
12.2.5
Overloading
610
12.3
A Model Class Hierarchy
611
12.4
A Pricer Class Hierarchy
613
12.5
An Optimizer Class Hierarchy
618
12.6
Design Patterns
620
12.6.1
The Builder Pattern
621
12.6.2
The Visitor Pattern
624
12.6.3
The Strategy Pattern
626
12.7
Example
-
Calibration Engine
629
12.7.1
Calibrating a Data Set or a History
631
Contents
12.8
Example
- The
Libor
Market Model and Greeks
634
12.8.1
An Abstract Class for LMM Derivatives
634
12.8.2
A Class for
Bermudán
Swaptions
637
12.8.3
A Class for Trigger Swaps
639
12.9
Summary and Conclusions
641
13
Math Fundamentals
643
13.1
Introduction and Objectives
643
13.2
Probability Theory and Stochastic Processes
643
13.2.1
Probability Spaces
644
13.2.2
Random Variables
644
13.2.3
Important Results
645
13.2.4
Distributions
649
13.2.5
Stochastic Processes
654
13.2.6
Levy Processes
655
13.2.7
Stochastic Differential Equations
660
13.3
Numerical Methods for Stochastic Processes
665
13.3.1
Random Number Generation
665
13.3.2
Methods for Computing
Variâtes
670
13.4
Basics on Complex Analysis
671
13.4.1
Complex Numbers
671
13.4.2
Complex Differentiation and Integration along Paths
672
13.4.3
The Complex Exponential and Logarithm
673
13.4.4
The Residual Theorem
674
13.5
The Characteristic Function and Fourier Transform
675
13.6
Summary and Conclusions
679
List of Figures
681
List of Tables
691
Bibliography
695
Index
705
|
| any_adam_object | 1 |
| author | Kienitz, Jörg 1970- Wetterau, Daniel 1982- |
| author_GND | (DE-588)1071747401 (DE-588)1071747738 |
| author_facet | Kienitz, Jörg 1970- Wetterau, Daniel 1982- |
| author_role | aut aut |
| author_sort | Kienitz, Jörg 1970- |
| author_variant | j k jk d w dw |
| building | Verbundindex |
| bvnumber | BV040505287 |
| classification_rvk | QH 160 QP 890 SK 980 |
| ctrlnum | (OCoLC)820374804 (DE-599)BVBBV040505287 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV040505287 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:25:17Z |
| institution | BVB |
| isbn | 9780470744895 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025351934 |
| oclc_num | 820374804 |
| open_access_boolean | |
| owner | DE-11 DE-29T DE-20 DE-1049 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-384 DE-83 DE-523 |
| owner_facet | DE-11 DE-29T DE-20 DE-1049 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-384 DE-83 DE-523 |
| physical | XIII, 719 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Wiley |
| record_format | marc |
| spelling | Kienitz, Jörg 1970- Verfasser (DE-588)1071747401 aut Financial modelling theory, implementation and practice ; (with Matlab source) Jörg Kienitz ; Daniel Wetterau Chichester Wiley 2012 XIII, 719 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finanzplanungsmodell (DE-588)4252015-0 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Kapitalmarktforschung (DE-588)4390312-5 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s Finanzplanungsmodell (DE-588)4252015-0 s Mathematisches Modell (DE-588)4114528-8 s Kapitalmarktforschung (DE-588)4390312-5 s MATLAB (DE-588)4329066-8 s DE-604 Wetterau, Daniel 1982- Verfasser (DE-588)1071747738 aut Erscheint auch als Online-Ausgabe 978-1-118-41329-6 Erscheint auch als Online-Ausgabe 978-1-118-41330-2 Erscheint auch als Online-Ausgabe 978-1-118-41331-9 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025351934&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kienitz, Jörg 1970- Wetterau, Daniel 1982- Financial modelling theory, implementation and practice ; (with Matlab source) Finanzplanungsmodell (DE-588)4252015-0 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd MATLAB (DE-588)4329066-8 gnd Kapitalmarktforschung (DE-588)4390312-5 gnd |
| subject_GND | (DE-588)4252015-0 (DE-588)4066472-7 (DE-588)4114528-8 (DE-588)4329066-8 (DE-588)4390312-5 |
| title | Financial modelling theory, implementation and practice ; (with Matlab source) |
| title_auth | Financial modelling theory, implementation and practice ; (with Matlab source) |
| title_exact_search | Financial modelling theory, implementation and practice ; (with Matlab source) |
| title_full | Financial modelling theory, implementation and practice ; (with Matlab source) Jörg Kienitz ; Daniel Wetterau |
| title_fullStr | Financial modelling theory, implementation and practice ; (with Matlab source) Jörg Kienitz ; Daniel Wetterau |
| title_full_unstemmed | Financial modelling theory, implementation and practice ; (with Matlab source) Jörg Kienitz ; Daniel Wetterau |
| title_short | Financial modelling |
| title_sort | financial modelling theory implementation and practice with matlab source |
| title_sub | theory, implementation and practice ; (with Matlab source) |
| topic | Finanzplanungsmodell (DE-588)4252015-0 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd MATLAB (DE-588)4329066-8 gnd Kapitalmarktforschung (DE-588)4390312-5 gnd |
| topic_facet | Finanzplanungsmodell Wirtschaftsmathematik Mathematisches Modell MATLAB Kapitalmarktforschung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025351934&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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