Selected infinitely divisible distributions as models for financial return data: unconditional fit and option pricing
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Pro Business
2002
|
| Edition: | 1. Aufl. |
| Series: | Quantitative Finanzwirtschaft
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001 |
| Physical Description: | XIV, 235 S. graph. Darst. 21 cm |
| ISBN: | 393452902X |
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MARC
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| 245 | 1 | 0 | |a Selected infinitely divisible distributions as models for financial return data |b unconditional fit and option pricing |c Matthias Fischer |
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Record in the Search Index
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| adam_text | Contents
List of Figures iii
List of Tables v
Frequently Used Notation vi
Introduction xi
1 Financial data and distributional stylized facts 1
1.1 Prices and returns of financial data 2
1.2 Graphical detection of non normality 6
1.3 Testing normality 11
1.4 Classification procedures for distributions 17
1.5 Testing infinite variances and higher moments 21
1.6 Empirical results and conclusions 24
References 40
2 Infinitely divisible distributions 45
2.1 Motivation 40
2.2 Distribution function and characteristic function 18
2.3 Infinitely divisible distributions and subclasses 52
2.4 Construction of infinitely divisible distributions 66
2.5 Tails of infinitely divisible distributions 79
2.6 Infinite divisibility and financial return data 81
References 83
3 Financial data and class C,. 93
3.1 Motivation 94
3.2 Selected ^ distributions 95
3.3 Selected ^ distributions 110
3.4 Selected ^ distributions 112
i
3.5 Comparison of fit: An empirical study 117
3.6 Logistic versus hyperbolic families 132
3.7 Conclusion 137
References 140
4 Option pricing 149
4.1 A review on Levy processes 151
4.2 A review on options 156
4.3 The option pricing model of Black and Scholes 159
4.4 Option pricing models: An overview 166
4.5 Generalizing Black and Scholes: Esscher pricing 173
References 210
A Mathematical functions 221
A.I Hyperbolic functions 221
A.2 Beta and Gamma functions 221
A.3 Bessel functions 222
A.4 Whittaker function 223
B Distributions and moments 225
B.I Gamma distribution and their transformations 225
C Data sets and computational aspects 229
C.I Data sets 229
C.2 Computational aspects 231
Summary and outlook 232
Index 235
ii
List of Figures
1.1 Levels and returns of DAX30 3
1.2 Returns of DAX30: Density estimation versus normal approximation .... 5
1.3 NQ plots for different samples 7
1.4 2Vplots for different samples 9
1.5 MDSDR plots for different samples 10
1.6 Graphical representation of the classification schemes 19
1.7 Converging variance test for different samples 22
1.8 Selected financial return data: NQ plot 27
1.9 Selected financial return data: 7Vpk)t 28
1.10 Selected financial return data: MDSDR plot 29
1.11 Selected financial return data: Moberg Ramberg Randles classification . . . 36
1.12 Selected financial return data: Hogg Yuh classification 37
1.13 Selected financial return data: Converging variance test with randomization 38
2.1 Density plots: Not infinitely divisible distributions 55
2.2 Density plots: Infinitely divisible distributions (I) 58
2.3 Density plots: Infinitely divisible distributions (II) 6(1
2.4 Density plots: Infinitely divisible distributions (III) 65
2.5 Density plots: Infinitely divisible distributions (IV) 67
2.6 Density plots: Infinitely divisible distributions (V) 77
2.7 Density plots: Infinitely divisible distributions (VI) 78
2.8 Selected tail functions 80
3.1 ^ function: EGB2 and Huber distribution 10(1
3.2 Density plots: CEGB2 distribution 101
3.3 Density plots: Generalized hyperbolic distribution 106
3.4 ^ function and log density: Generalized hyperbolic distribution 107
3.5 Density plots and tail function: SGT2 distribution 112
iii
3.6 Density plots: gh distribution 113
3.7 Density plots: Finite mixture models 116
3.8 Nikkei: Levels and returns 117
3.9 Nikkei: Normal approximation versus kernel density estimation 119
3.10 Nikkei: Fit of unconditional densities 120
3.11 Nikkei: Fit of unconditional densities: differences (I) 121
3.12 Nikkei: Fit of unconditional densities: differences (II) 122
3.13 Nikkei: Running AD plots (I) 125
3.14 Nikkei: Running _4P plots (II) 126
3.15 Nikkei: Empirical minus fitted quantils 129
3.16 GH, GL and normal densities with unit variance 136
4.1 Paths of simulated Levy processes 153
4.2 European call options: Pay off function, profit loss function and bounds . 159
4.3 Simulated sample path of a geometric Drownian motion 162
4.4 Cox Ross Rubinstein model: One period stock price movements 164
4.5 Cox Ross Rubinstein model: Multi period stock price movements 164
4.6 Esscher transformed densities 176
4.7 Impact of skewness and kurtosis on the martingale function 178
4.8 Esscher pricing in practice: A summary 194
4.9 Consors AG: Returns and goodness of fit 195
4.10 Consors AG: Different martingale functions 196
4.11 Consors AG: Statistical convolution densities 198
4.12 Consors AG: Risk neutral convolution densities 199
4.13 Consors AG: Option prices 200
4.14 Corrado Su model: Effects of skewness and kurtosis 206
4.15 Martingale and approximative martingale function 208
iv
List of Tables
1.1 Classification scheme of Shapiro, Wilk and Chen 17
1.2 Classification scheme of Hogg and Yuh 18
1.3 Classification scheme of Moberg, Rambcrg and Randies 20
1.4 Classification results for different samples 20
1.5 SGT2 test for different samples 23
1.6 Selected financial return data: Normality test (I) 30
1.7 Selected financial return data: Normality test (II) 31
1.8 Selected financial return data: Normality test (III) 32
1.9 Selected financial return data: Normality test (IV) 33
1.10 Selected financial return data: Empirical moments 34
1.11 Selected financial return data: Selector statistics 35
1.12 Selected financial return data: SGT2 test 39
2.1 Infinitely divisible distributions on R 81
2.2 Infinitely divisible distributions on R+ 82
3.1 Classification of probability distributions 95
3.2 Range of S(X): EGB2 distribution 99
3.3 Range of K(A ): EGB2 distribution 99
3.4 Range of S(A ) and K(A ): CEGB2 distribution 102
3.5 Nikkei: Goodness of fit (I) 123
3.6 Nikkei: Estimators of the parameter 121
3.7 Nikkei: Statistical properties 127
3.8 Nikkei: Hellinger matrix 127
3.9 Nikkei: Quantile fit 128
3.10 Nikkei: Goodness of fit (II) 130
3.11 Selected financial return data: Goodness of fit (I) 131
3.12 Selected financial return data: Goodness of fit (II) 132
v
3.13 Selected financial return data: Comparison of fit (EGB2 versus HYP) ... 133
3.14 Selected financial return data: Comparison of fit (EGB2 versus NIG) ... 134
3.15 Randoms samples: Parameters 136
3.16 Samples: Goodness of fit 138
3.17 Samples: Estimators of the parameters 139
3.18 Samples: Hellinger distance 140
4.1 Classification of plain vanilla options 157
4.2 Statistical properties of Esscher transformed distributions 176
4.3 Cdf approximation: Comparison of Bohman s methods 190
4.4 Cdf approximation: Impact of N and 6 191
4.5 Consors AG: Estimation results for the parameters 195
4.6 Consors AG: Roots of different martingale functions 196
4.7 Implied volatility for selected warrents (I) 202
4.8 Implied volatility for selected warrents (II) 202
C.I Assets from the DAX30 229
C.2 Assets from the MDAX 230
C.3 Assets from the NEUER MARKT 230
C.4 Selected stock indices 231
C.5 Selected exchange rates and precious metals 231
vi
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| spelling | Fischer, Matthias Verfasser aut Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing Matthias Fischer 1. Aufl. Berlin Pro Business 2002 XIV, 235 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Quantitative Finanzwirtschaft 2 Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001 Mathematisches Modell Distribution (Probability theory) Options (Finance) Prices Mathematical models Deutscher Aktienindex (DE-588)4266832-3 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Indexoption (DE-588)4309314-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Deutscher Aktienindex (DE-588)4266832-3 s Indexoption (DE-588)4309314-0 s Optionspreistheorie (DE-588)4135346-8 s Black-Scholes-Modell (DE-588)4206283-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Quantitative Finanzwirtschaft 2 (DE-604)BV014603618 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009906557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fischer, Matthias Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing Quantitative Finanzwirtschaft Mathematisches Modell Distribution (Probability theory) Options (Finance) Prices Mathematical models Deutscher Aktienindex (DE-588)4266832-3 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Indexoption (DE-588)4309314-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| subject_GND | (DE-588)4266832-3 (DE-588)4206283-4 (DE-588)4309314-0 (DE-588)4057630-9 (DE-588)4135346-8 (DE-588)4113937-9 |
| title | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing |
| title_auth | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing |
| title_exact_search | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing |
| title_full | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing Matthias Fischer |
| title_fullStr | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing Matthias Fischer |
| title_full_unstemmed | Selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing Matthias Fischer |
| title_short | Selected infinitely divisible distributions as models for financial return data |
| title_sort | selected infinitely divisible distributions as models for financial return data unconditional fit and option pricing |
| title_sub | unconditional fit and option pricing |
| topic | Mathematisches Modell Distribution (Probability theory) Options (Finance) Prices Mathematical models Deutscher Aktienindex (DE-588)4266832-3 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd Indexoption (DE-588)4309314-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Optionspreistheorie (DE-588)4135346-8 gnd |
| topic_facet | Mathematisches Modell Distribution (Probability theory) Options (Finance) Prices Mathematical models Deutscher Aktienindex Black-Scholes-Modell Indexoption Stochastischer Prozess Optionspreistheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009906557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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