Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120315-1092635-1-6 Inhaltsverzeichnis |
| Beschreibung: | 176 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling |c Holger Maria Fink |
| 264 | 1 | |c 2012 | |
| 300 | |a 176 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a München, Techn. Univ., Diss., 2012 | ||
| 650 | 0 | 7 | |a Brownsche Bewegung |0 (DE-588)4128328-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kreditrisiko |0 (DE-588)4114309-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lévy-Prozess |0 (DE-588)4463623-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Risikomanagement |0 (DE-588)4121590-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Kreditrisiko |0 (DE-588)4114309-7 |D s |
| 689 | 0 | 3 | |a Risikomanagement |0 (DE-588)4121590-4 |D s |
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Datensatz im Suchindex
| _version_ | 1804149192274214912 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
1 P R E L I M I N A R I E S - B A S I C S A N D F R A C T I O N A L P R
O C E S S E S 9
1.1 NOTATION 9
1.2 FRACTIONAL CALCULUS 10
1.2.1 ON COMPACTS 10
1.2.2 ON THE REAL LINE 11
1.3 RIEMANN-STIELTJES INTEGRATION AND P- VARIATION 12
1.4 LEVY PROCESSES 13
1.5 FRACTIONAL BROWNIAN MOTION 15
1.6 FRACTIONAL LEVY PROCESSES 20
1.6.1 DEFINITION BY MANDELBROT-VAN NESS KERNEL 20
1.6.2 DEFINITION BY MOLCHAN-GOLOSOV KERNEL 22
2 P R E L I M I N A R I E S - F R A C T I O N A L S T O C H A S T I C
DIFFERENTIAL E Q U A T I O N S 2 5
2.1 FRACTIONAL BROWNIAN STOCHASTIC DIFFERENTIAL EQUATIONS 25
2.2 FRACTIONAL LEVY STOCHASTIC DIFFERENTIAL EQUATIONS 28
2.2.1 FRACTIONAL LEVY ORNSTEIN-UHLENBECK PROCESSES 28
2.2.2 SOLUTIONS OF FRACTIONAL SDE S BY STATE SPACE TRANSFORMS AND PROPER
TRIPLES 29
2.2.3 EXAMPLES BY MEANS OF STRONGLY PROPER TRIPLES 31
2.2.4 FRACTIONAL COX-INGERSOLL-ROSS MODELS 34
I C O N D I T I O N A L D I S T R I B U T I O N S O F FRACTIONAL P R O C
E S S E S 3 9
3 F R A C T I O N A L B R O W N I A N M O T I O N A N D R E L A T E D P
R O C E S S E S 4 1
HTTP://D-NB.INFO/102571962X
IMAGE 2
3.1 ONE-DIMENSIONAL FRACTIONAL BROWNIAN MOTION 42
3.2 D-DIMENSIONAL FRACTIONAL BROWNIAN MOTION WITH INDEPENDENCE 52
3.3 APPLICATION: FRACTIONAL BOND MARKET 53
3.3.1 MOTIVATION 54
3.3.2 THE FRACTIONAL MARKET MODEL 55
3.3.3 MODELING UNDER Q 63
3.3.4 ZERO COUPON BONDS 63
3.4 TWO-DIMENSIONAL CASE WITH SAME DRIVING FACTOR 67
3.4.1 MOTIVATION 67
3.4.2 PREDICTION RESULTS 68
3.5 APPLICATION: DEFAULTABLE BONDS AND CREDIT DERIVATIVES 74
3.5.1 DEFAULTABLE CLAIMS 75
3.5.2 DEFAULTABLE ZERO COUPON BONDS 77
3.5.3 OPTION PRICING 80
4 M O L C H A N - G O L O S O V F R A C T I O N A L L E V Y P R O C E S
S E S 8 9
4.1 MULTIVARIATE MOLCHAN-GOLOSOV FRACTIONAL LEVY PROCESSES 90
4.1.1 DEFINITION 90
4.1.2 INTEGRATION 93
4.2 PREDICTION RESULTS 94
4.2.1 PREDICTION OF INTEGRALS 95
4.2.2 ORNSTEIN-UHLENBECK TYPE PROCESSES 98
4.3 APPLICATION: INTEREST RATES WITH CREDIT RISK 102
4.4 APPLICATION: FRACTIONAL VOLATILITY IN A BLACK SCHOLES MARKET I L L
4.4.1 THE MARKET MODEL I L L
4.4.2 ABSENCE OF ARBITRAGE AND OPTION PRICING 113
5 A P P L I C A T I O N : I N T E R E S T R A T E M O D E L S A N D P A
R A M E T E R S E N S I T I V I T Y 1 1 7
5.1 PARAMETER SENSITIVITY WITH RESPECT TO R(0) 121
5.2 PARAMETER SENSITIVITY WITH RESPECT TO A 122
5.3 PARAMETER SENSITIVITY WITH RESPECT TO A ; 126
5.4 PARAMETER SENSITIVITY WITH RESPECT TO A 127
5.5 PARAMETER SENSITIVITY WITH RESPECT TO 7 7 129
IMAGE 3
II H I G H T I C K D A T A M O D E L I N G B Y D I S C R E T E V A L U E
D P R O C E S S E S 1 3 1
6 D I S C R E T E - V A L U E D L E V Y M O D E L S 1 3 3
6.1 STOCHASTIC VOLATILITY 135
6.1.1 MODEL SPECIFICATION 136
6.1.2 LINEAR SUBORDINATOR 137
6.2 PROPERTIES OF THE MODEL 140
6.2.1 SECOND MOMENTS 140
6.2.2 STATISTICAL LEVERAGE 143
6.2.3 VOLATILITY CLUSTERING 147
6.2.4 CUMULANT FUNCTION 148
6.2.5 A SMALL TICK SIZE LIMIT 148
6.2.6 NO-ARBITRAGE AND INCOMPLETENESS 151
6.3 ECONOMETRIC INFERENCE 152
6.3.1 IDENTIFICATION 152
6.3.2 MOMENT BASED INFERENCE 153
6.3.3 INTENSITY FUNCTION INFERENCE 154
6.4 APPLICATION 156
6.4.1 DATASET 157
6.4.2 TRADES AND PRICES 158
6.4.3 SUMMARY STATISTICS 159
7 C O N C L U S I O N 1 6 3
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| spelling | Fink, Holger Verfasser aut Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling Holger Maria Fink 2012 176 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Lévy-Prozess (DE-588)4463623-4 s Brownsche Bewegung (DE-588)4128328-4 s Kreditrisiko (DE-588)4114309-7 s Risikomanagement (DE-588)4121590-4 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20120315-1092635-1-6 http://mediatum.ub.tum.de/node?id=1092635 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120315-1092635-1-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025050498&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fink, Holger Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling Brownsche Bewegung (DE-588)4128328-4 gnd Kreditrisiko (DE-588)4114309-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd Risikomanagement (DE-588)4121590-4 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4114309-7 (DE-588)4463623-4 (DE-588)4121590-4 (DE-588)4113937-9 |
| title | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling |
| title_auth | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling |
| title_exact_search | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling |
| title_full | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling Holger Maria Fink |
| title_fullStr | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling Holger Maria Fink |
| title_full_unstemmed | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling Holger Maria Fink |
| title_short | Stochastic processes beyond semimartingales with application to interest rates, credit risk and volatility modeling |
| title_sort | stochastic processes beyond semimartingales with application to interest rates credit risk and volatility modeling |
| topic | Brownsche Bewegung (DE-588)4128328-4 gnd Kreditrisiko (DE-588)4114309-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd Risikomanagement (DE-588)4121590-4 gnd |
| topic_facet | Brownsche Bewegung Kreditrisiko Lévy-Prozess Risikomanagement Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1092635 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120315-1092635-1-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025050498&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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