An elementary introduction to stochastic interest rate modeling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2012
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Advanced series on statistical science and applied probability
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIII, 228 S. graph. Darst. |
| ISBN: | 9814390852 9789814390859 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804149498672316416 |
|---|---|
| adam_text | Titel: An elementary introduction to stochastic interest rate modeling
Autor: Privault, Nicolas
Jahr: 2012
Contents
Preface vii
1. A Review of Stochastic Calculus 1
1.1 Brownian Motion....................... 1
1.2 Stochastic Integration.................... 2
1.3 Quadratic Variation..................... 8
1.4 Ito s Formula......................... 10
1.5 Exercises ........................... 12
2. A Review of Black-Scholes Pricing and Hedging 15
2.1 Call and Put Options .................... 15
2.2 Market Model and Portfolio................. 17
2.3 PDE Method......................... 18
2.4 The Girsanov Theorem ................... 20
2.5 Martingale Method...................... 23
2.6 Exercises ........................... 30
3. Short Term Interest Rate Models 33
3.1 Mean-Reverting Models................... 33
3.2 Constant Elasticity of Variance (CEV) Models...... 34
3.3 Time-Dependent Models................... 35
3.4 Exercises ........................... 35
4. Pricing of Zero-Coupon Bonds 3^
4.1 Definition and Basic Properties............... 39
4.2 Absence of Arbitrage and the Markov Property...... 40
4.3 Absence of Arbitrage and the Martingale Property .... 42
4.4 PDE Solution: Probabilistic Method............ 44
4.5 PDE Solution: Analytical Method............. 46
4.6 Numerical Simulations.................... 47
4.7 Exercises ........................... 50
5. Forward Rate Modeling 55
5.1 Forward Contracts...................... 55
5.2 Instantaneous Forward Rate................. 58
5.3 Short Rates.......................... 60
5.4 Parametrization of Forward Rates ............. 61
5.5 Curve Estimation....................... 62
5.6 Exercises ........................... 63
6. The Heath-Jarrow-Morton (HJM) Model 65
6.1 Restatement of Objectives.................. 65
6.2 Forward Vasicek Rates.................... 67
6.3 Spot Forward Rate Dynamics................ 72
6.4 The HJM Condition..................... 73
6.5 Markov Property of Short Rates .............. 76
6.6 The Hull-White Model.................... 78
6.7 Exercises ........................... 79
7. The Forward Measure and Derivative Pricing 81
7.1 Forward Measure....................... 81
7.2 Dynamics under the Forward Measure........... 85
7.3 Derivative Pricing ...................... 88
7.4 Inverse Change of Measure ................. 92
7.5 Exercises ........................... 93
8. Curve Fitting and a Two-Factor Model 97
8.1 Curve Fitting........-................. 97
8.2 Deterministic Shifts ..................... 100
8.3 The Correlation Problem .................. 101
8.4 Two-Factor Model...................... 104
8.5 Exercises ........................... HI
9. A Credit Default Model 115
9.1 Survival Probabilities .................... 115
9.2 Stochastic Default...................... 117
9.3 Defaultable Bonds...................... 119
9.4 Credit Default Swaps..................... 120
9.5 Exercises ........................... 122
10. Pricing of Caps and Swaptions on the LIBOR 125
10.1 Pricing of Caplets and Caps................. 125
10.2 Forward Rate Measure and Tenor Structure........ 127
10.3 Swaps and Swaptions .................... 131
10.4 The London InterBank Offered Rates (LIBOR) Model . . 133
10.5 Swap Rates on the LIBOR Market............. 134
10.6 Forward Swap Measures................... 137
10.7 Swaption Pricing on the LIBOR Market.......... 142
10.8 Exercises ........................... 143
11. The Brace-Gatarek-Musiela (BGM) Model 149
11.1 The BGM Model....................... 149
11.2 Cap Pricing.......................... 152
11.3 Swaption Pricing....................... 153
11.4 Calibration of the BGM Model............... 157
11.5 Exercises ........................... 160
12. Appendix A: Mathematical Tools 163
13. Appendix B: Some Recent Developments 171
14. Solutions to the Exercises 175
Bibliography 221
Index 225
Author Index 227
|
| any_adam_object | 1 |
| author | Privault, Nicolas |
| author_GND | (DE-588)1032387327 |
| author_facet | Privault, Nicolas |
| author_role | aut |
| author_sort | Privault, Nicolas |
| author_variant | n p np |
| building | Verbundindex |
| bvnumber | BV040442032 |
| classification_rvk | SK 820 SK 980 |
| ctrlnum | (OCoLC)802660271 (DE-599)BSZ364720131 |
| dewey-full | 332.63230151922 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.63230151922 |
| dewey-search | 332.63230151922 |
| dewey-sort | 3332.63230151922 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040442032 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:59Z |
| institution | BVB |
| isbn | 9814390852 9789814390859 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025289851 |
| oclc_num | 802660271 |
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| owner | DE-19 DE-BY-UBM DE-824 |
| owner_facet | DE-19 DE-BY-UBM DE-824 |
| physical | XIII, 228 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series on statistical science and applied probability |
| series2 | Advanced series on statistical science and applied probability |
| spelling | Privault, Nicolas Verfasser (DE-588)1032387327 aut An elementary introduction to stochastic interest rate modeling Nicolas Privault 2. ed. Singapore [u.a.] World Scientific 2012 XIII, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science and applied probability 16 Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Zinsfuß (DE-588)4190927-6 gnd rswk-swf Zins (DE-588)4067845-3 gnd rswk-swf Zinsfuß (DE-588)4190927-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Zins (DE-588)4067845-3 s 1\p DE-604 Advanced series on statistical science and applied probability 16 (DE-604)BV011932321 16 DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/715629328.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025289851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Privault, Nicolas An elementary introduction to stochastic interest rate modeling Advanced series on statistical science and applied probability Stochastisches Modell (DE-588)4057633-4 gnd Zinsfuß (DE-588)4190927-6 gnd Zins (DE-588)4067845-3 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4190927-6 (DE-588)4067845-3 |
| title | An elementary introduction to stochastic interest rate modeling |
| title_auth | An elementary introduction to stochastic interest rate modeling |
| title_exact_search | An elementary introduction to stochastic interest rate modeling |
| title_full | An elementary introduction to stochastic interest rate modeling Nicolas Privault |
| title_fullStr | An elementary introduction to stochastic interest rate modeling Nicolas Privault |
| title_full_unstemmed | An elementary introduction to stochastic interest rate modeling Nicolas Privault |
| title_short | An elementary introduction to stochastic interest rate modeling |
| title_sort | an elementary introduction to stochastic interest rate modeling |
| topic | Stochastisches Modell (DE-588)4057633-4 gnd Zinsfuß (DE-588)4190927-6 gnd Zins (DE-588)4067845-3 gnd |
| topic_facet | Stochastisches Modell Zinsfuß Zins |
| url | http://www.gbv.de/dms/tib-ub-hannover/715629328.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025289851&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
| work_keys_str_mv | AT privaultnicolas anelementaryintroductiontostochasticinterestratemodeling |
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