Jumps and uncertainties in financial markets: applications of Lévy Processes and implied volatilities
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Hamburg
Verlag Dr. Kovač
2017
|
| Series: | Finanzmanagement
Band 122 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Buchcover |
| Physical Description: | XI, 146 Seiten Diagramme |
| ISBN: | 9783830094890 3830094892 |
Staff View
MARC
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| 245 | 1 | 0 | |a Jumps and uncertainties in financial markets |b applications of Lévy Processes and implied volatilities |c Johannes Stadler |
| 264 | 1 | |a Hamburg |b Verlag Dr. Kovač |c 2017 | |
| 300 | |a XI, 146 Seiten |b Diagramme | ||
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Record in the Search Index
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| adam_text | Contents
1 Introduction ........................................................................ 1
1.1 Related Research and Contribution to Literature on Lévy Processes............... 3
1.2 Related Research and Contribution to Literature on Asymmetric and Implied
Volatility ..................................................................... 6
2 Theoretical Background.............................................................. 11
2.1 Lévy Processes - An Introduction............................................... 12
2.1.1 The Generalized Hyperbolic Process....................................... 15
2.1.2 The Normal Inverse Gaussian Process...................................... 17
2.1.3 The Variance Gamma Process............................................... 18
2.1.4 From Univariate to Multivariate Lévy Processes .......................... 20
2.1.5 The apGH Model .......................................................... 21
2.1.6 The apNIG Model ......................................................... 22
2.1.7 The apVG Model........................................................... 23
2.1.8 Pseudo-Algorithm for ap Lévy Models.................................... 24
2.2 Simulation of Subordinators of Lévy Processes ............................... 25
2.2.1 Generalized Inverse Gaussian Random Variables............................ 25
2.2.2 inverse Gaussian Random Variables........................................ 28
2.2.3 Gamma Random Variables................................................... 29
3 Fitting of Lévy Processes .......................................................... 31
3.1 Simplified Method of Moments................................................... 32
3.1.1 SMoM for the GH Process.................................................. 32
3.1.2 SMoM for the NIG Process................................................. 34
3.1.3 SMoM for the VG Process.................................................. 34
3.2 Method of Moments ............................................................. 35
3.3 Maximum Likelihood Estimation.................................................. 35
3.4 Empirical Characteristic Function Method....................................... 36
3.5 Minimum %2 Method ............................................................. 36
3.6 Correlation Estimation ........................................................ 37
3.7 Risk-Neutral Fitting........................................................... 37
3.7.1 Risk-Neutral Valuation................................................... 38
IX
X Contents
3.7.2 Fast Fourier Transformation ............................................ 39
3.8 Fitting Evaluation Methods.................................................... 41
3.8.1 Kolmogorov-Smimov Test.................................................. 42
3.8.2 Anderson-Darling Test................................................... 43
3.8.3 Special Measures for Simulated Data..................................... 43
4 Brownian Motion, Lévy Processes, and Option Pricing................................ 45
4.1 European Option Pricing....................................................... 46
4.2 American Option Pricing ...................................................... 47
4.3 Implied Volatility Smile and Leverage Effect.................................. 49
5 Research Design and Data......................................................... 55
5.1 Simulation Study for the SMoM of the GH Process .............................. 56
5.2 Simulation Study for Multivariate Lévy Processes.............................. 56
5.3 Empirical Analysis for Implied Fitting of Lévy Processes ..................... 62
5.3.1 Research Approach..................................................... 62
5.3.2 Dividend Adjustments for DAX Futures ................................... 64
5.3.3 Interest Rates and Svensson Method...................................... 65
5.4 Event Study for Implied Volatility Smiles..................................... 66
5.4.1 Design of the Event Study............................................... 66
5.4.2 Classification of Ad-hoc News.......................................... 67
5.4.3 Estimation of Implied Volatility Smiles................................. 69
5.4.4 Description of Data Set .................................... 73 6 7 8 6 7 8
6 Results........................................................................... 77
6.1 Fitting of Lévy Processes..................................................... 78
6.1.1 Analysis of SMoM for the GH Process ................................... 78
6.1.2 Fitting of Multivariate Lévy Processes.................................. 81
6.1.3 Implied Fitting of Lévy Processes..................................... 90
6.2 Relation between Implied Volatility Smile and Leverage Effect................. 94
7 Discussion ...................................................................... 101
8 Conclusion....................................................................... 107
References........................................................................... Ill
Appendix............................................................................. 123
A Proofs of Sub-Classes of the GH Process...................................... 123
B Development of Central Moments of the VG Process............................. 125
C Proofs Convolution of Multivariate Lévy Processes ........................... 127
D Tschimhaus Method for SMoM of the GH Process ................................ 129
E Proofs Implied Volatility Smile and Leverage Effect.......................... 132
F Results Multivariate Lévy Processes............................................. 136
Contents
List of Abbreviations
List of Figures.....
List of Tables......
XI
141
143
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145
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| discipline | Wirtschaftswissenschaften |
| format | Thesis Book |
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| indexdate | 2024-07-10T07:48:42Z |
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| isbn | 9783830094890 3830094892 |
| language | English |
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| physical | XI, 146 Seiten Diagramme |
| publishDate | 2017 |
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| publisher | Verlag Dr. Kovač |
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| series | Finanzmanagement |
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| spelling | Stadler, Johannes 1986- Verfasser (DE-588)1072635127 aut Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities Johannes Stadler Hamburg Verlag Dr. Kovač 2017 XI, 146 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Finanzmanagement Band 122 Dissertation Universität Augsburg 2016 Unsicherheit (DE-588)4186957-6 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kreditmarkt (DE-588)4073788-3 s Volatilität (DE-588)4268390-7 s Unsicherheit (DE-588)4186957-6 s Lévy-Prozess (DE-588)4463623-4 s Optionspreistheorie (DE-588)4135346-8 s DE-604 Finanzmanagement Band 122 (DE-604)BV013087358 122 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029688775&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029688775&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Buchcover |
| spellingShingle | Stadler, Johannes 1986- Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities Finanzmanagement Unsicherheit (DE-588)4186957-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd Volatilität (DE-588)4268390-7 gnd Kreditmarkt (DE-588)4073788-3 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4186957-6 (DE-588)4463623-4 (DE-588)4268390-7 (DE-588)4073788-3 (DE-588)4135346-8 (DE-588)4113937-9 |
| title | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities |
| title_auth | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities |
| title_exact_search | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities |
| title_full | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities Johannes Stadler |
| title_fullStr | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities Johannes Stadler |
| title_full_unstemmed | Jumps and uncertainties in financial markets applications of Lévy Processes and implied volatilities Johannes Stadler |
| title_short | Jumps and uncertainties in financial markets |
| title_sort | jumps and uncertainties in financial markets applications of levy processes and implied volatilities |
| title_sub | applications of Lévy Processes and implied volatilities |
| topic | Unsicherheit (DE-588)4186957-6 gnd Lévy-Prozess (DE-588)4463623-4 gnd Volatilität (DE-588)4268390-7 gnd Kreditmarkt (DE-588)4073788-3 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Unsicherheit Lévy-Prozess Volatilität Kreditmarkt Optionspreistheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029688775&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029688775&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013087358 |
| work_keys_str_mv | AT stadlerjohannes jumpsanduncertaintiesinfinancialmarketsapplicationsoflevyprocessesandimpliedvolatilities |