Uncertain volatility models: theory and application
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Springer finance : Lecture notes
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Systemvoraussetzung für CD-ROM: Windows 98 or higher, 128 MB RAM minimum, Java |
| Physical Description: | XI, 243 S. graph. Darst. CD-ROM (12 cm) |
| ISBN: | 3540426574 |
Staff View
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Prices |x Mathematical models | |
| 650 | 4 | |a Exotic options (Finance) | |
| 650 | 4 | |a Finance |x Mathematical models | |
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Record in the Search Index
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| adam_text | Table of Contents
1 Introduction 1
1.1 Uncertain Volatility Scenarios and Exotic Options 2
1.2 Volatility Shock Scenarios 3
1.3 Object Oriented Implementation 4
1.4 User Interfaces: Scripting and Mathematica 5
1.5 How to Best Read This Book 6
Part I Computational Finance: Theory
2 Notation and Basic Definitions 11
2.1 Linear Algebra 11
2.2 Probability and Stochastic Processes 11
2.3 Partial Portfolios and Positions 12
2.4 Accents, Superscript, Subscript 13
3 Continuous Time Finance 15
3.1 Deterministic Volatility 15
3.1.1 One Factor Black Scholes Analysis 15
3.1.2 Hedging with Black Scholes 17
3.1.3 Interest Rate Models 19
3.2 Stochastic Volatility 24
3.2.1 Tradable and Nontradable Factors 24
3.2.2 Some Concrete One Dimensional Models 25
3.3 Model Calibration 30
3.3.1 Parametric Methods 30
3.3.2 Non Parametric Methods 31
4 Scenario Based Evaluation and Uncertainty 33
4.1 Preliminaries 33
4.2 The Worst Case Volatility Scenario 35
4.2.1 Worst Case Pricing 36
4.2.2 The Optimal Hedge Portfolio 38
4.2.3 Calibration to the Worst Case 39
4.3 Minimum Entropy Calibration 41
4.4 Scenarios and Nonlinearity 43
Part II Algorithms for Uncertain Volatility Models
5 A Lattice Framework 47
5.1 Multi Lattice Dynamic Programming 48
5.1.1 Data Structures 49
5.1.2 Dataflow for Explicit Methods 50
5.1.3 Dataflow for Mixed Explicit/Implicit Methods 51
5.2 Numerical Issues 51
6 Algorithms for Vanilla Options 57
7 Algorithms for Barrier Options 61
7.1 The Hierarchy of PDE s 63
7.1.1 Construction 63
7.1.2 Complexity 66
7.2 Empirical Results 71
7.2.1 Numerical Convergence 71
7.2.2 Introducing Uncertainty 73
8 Algorithms for American Options 77
8.1 Early Exercise Combinations 78
8.1.1 Long and Short Positions 78
8.1.2 Best Worst Case Evaluation Formalized 81
8.2 Speedup Techniques 90
8.2.1 Maintaining the Corridor of Uncertainty 93
8.2.2 Collapsing the Corridor of Uncertainty 98
8.2.3 Miscellaneous Issues 105
8.3 Empirical Results 110
8.3.1 Computational Complexity 110
8.3.2 Stress Tests 115
8.4 American Options and Calibration 122
9 Exotic Volatility Scenarios 123
9.1 Volatility Shocks for Portfolios of Vanilla Options 123
9.1.1 Worst Case Volatility Shocks 125
9.1.2 Empirical Results 133
9.2 Volatility Shocks and Exotic Options 138
Part III Object Oriented Implementation
10 The Architecture of Mtg 143
11 The Class Hierarchy of MtgLib—External 145
11.1 Instruments 146
11.2 Portfolios 151
11.3 Models 152
11.4 Model Coefficients 158
11.4.1 The Base Class tTermStruct 159
11.4.2 Classes Derived from tTermStruct 162
11.4.3 Classes with tTermStruct Components 162
11.5 Scenarios 166
11.5.1 The Base Class tScenario 167
11.5.2 Classes Derived from tScenario 170
11.6 Numerical Methods 171
11.6.1 Lattice Templates and Instances 172
11.6.2 Finite Difference Solvers 179
11.7 Evaluators 182
12 The Class Hierarchy of MtgLib—Internal 185
12.1 Compute Engines 185
12.1.1 The Abstract Class tEngine 186
12.1.2 The Abstract Class tFDEngine 188
12.1.3 The Abstract Class tOFEngine 190
12.1.4 The Concrete Class tGeoEngine 193
12.1.5 The Concrete Class tShockEngine 193
12.2 Other Groups of Classes 194
13 Extensions for Monte Carlo Pricing and Calibration 195
A The Network Application MtgClt/MtgSvr 197
B The Scripting Language MtgScript 203
B.I Factor Objects 204
B.2 Claim and Portfolio Objects 205
B.3 Model, Drift and Volatility Objects 208
B.4 Lattice and Path Space Objects 212
B.5 Bootstrapping, Curve and Image Objects 213
B.6 Scenario and Optimizer Objects 216
B.7 Evaluation Objects and Examples 217
C Mathematica Extensions 227
C.I The Syntax of Object Expressions 227
C.2 Turning Scripts into Functions 230
C.3 Profiling and Diagrams 231
References 233
Index 237
|
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| dewey-ones | 332 - Financial economics |
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| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Thesis Book |
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| id | DE-604.BV014187831 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:59:14Z |
| institution | BVB |
| isbn | 3540426574 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009725252 |
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| series2 | Springer finance : Lecture notes |
| spelling | Buff, Robert 1969- Verfasser (DE-588)123438470 aut Uncertain volatility models theory and application Robert Buff Berlin [u.a.] Springer 2002 XI, 243 S. graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Springer finance : Lecture notes Systemvoraussetzung für CD-ROM: Windows 98 or higher, 128 MB RAM minimum, Java Teilw. zugl.: New York, Univ., Diss., 1999 u.d.T.: Buff, Robert: Algorithms for nonlinear models in computational finance and their object oriented implementation Derivat <Wertpapier> - Optionspreis - Volatilität - Black-Scholes-Modell - C++ Optionspreistheorie / Black-Scholes-Modell / Volatilität / Stochastischer Prozess / PC-Software / Theorie Mathematisches Modell Derivative securities Prices Mathematical models Exotic options (Finance) Finance Mathematical models Risk assessment Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf C++ (DE-588)4193909-8 gnd rswk-swf Risikoanalyse (DE-588)4137042-9 gnd rswk-swf Optionspreis (DE-588)4115453-8 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kreditmarkt (DE-588)4073788-3 s Volatilität (DE-588)4268390-7 s Risikoanalyse (DE-588)4137042-9 s Mathematisches Modell (DE-588)4114528-8 s DE-188 Derivat Wertpapier (DE-588)4381572-8 s Optionspreis (DE-588)4115453-8 s Black-Scholes-Modell (DE-588)4206283-4 s C++ (DE-588)4193909-8 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buff, Robert 1969- Uncertain volatility models theory and application Derivat <Wertpapier> - Optionspreis - Volatilität - Black-Scholes-Modell - C++ Optionspreistheorie / Black-Scholes-Modell / Volatilität / Stochastischer Prozess / PC-Software / Theorie Mathematisches Modell Derivative securities Prices Mathematical models Exotic options (Finance) Finance Mathematical models Risk assessment Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd C++ (DE-588)4193909-8 gnd Risikoanalyse (DE-588)4137042-9 gnd Optionspreis (DE-588)4115453-8 gnd Volatilität (DE-588)4268390-7 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4206283-4 (DE-588)4193909-8 (DE-588)4137042-9 (DE-588)4115453-8 (DE-588)4268390-7 (DE-588)4381572-8 (DE-588)4073788-3 (DE-588)4113937-9 |
| title | Uncertain volatility models theory and application |
| title_auth | Uncertain volatility models theory and application |
| title_exact_search | Uncertain volatility models theory and application |
| title_full | Uncertain volatility models theory and application Robert Buff |
| title_fullStr | Uncertain volatility models theory and application Robert Buff |
| title_full_unstemmed | Uncertain volatility models theory and application Robert Buff |
| title_short | Uncertain volatility models |
| title_sort | uncertain volatility models theory and application |
| title_sub | theory and application |
| topic | Derivat <Wertpapier> - Optionspreis - Volatilität - Black-Scholes-Modell - C++ Optionspreistheorie / Black-Scholes-Modell / Volatilität / Stochastischer Prozess / PC-Software / Theorie Mathematisches Modell Derivative securities Prices Mathematical models Exotic options (Finance) Finance Mathematical models Risk assessment Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd C++ (DE-588)4193909-8 gnd Risikoanalyse (DE-588)4137042-9 gnd Optionspreis (DE-588)4115453-8 gnd Volatilität (DE-588)4268390-7 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| topic_facet | Derivat <Wertpapier> - Optionspreis - Volatilität - Black-Scholes-Modell - C++ Optionspreistheorie / Black-Scholes-Modell / Volatilität / Stochastischer Prozess / PC-Software / Theorie Mathematisches Modell Derivative securities Prices Mathematical models Exotic options (Finance) Finance Mathematical models Risk assessment Mathematical models Black-Scholes-Modell C++ Risikoanalyse Optionspreis Volatilität Derivat Wertpapier Kreditmarkt Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT buffrobert uncertainvolatilitymodelstheoryandapplication |