An elementary introduction to stochastic interest rate modeling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2008
|
| Schriftenreihe: | Advanced series on statistical science & applied probability
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 173 - 175 |
| Beschreibung: | XI, 178 S. graph. Darst. |
| ISBN: | 9812832734 9789812832733 |
Internformat
MARC
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| 100 | 1 | |a Privault, Nicolas |e Verfasser |0 (DE-588)1032387327 |4 aut | |
| 245 | 1 | 0 | |a An elementary introduction to stochastic interest rate modeling |c Nicolas Privault |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XI, 178 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Advanced series on statistical science & applied probability |v 12 | |
| 500 | |a Literaturverz. S. 173 - 175 | ||
| 650 | 4 | |a Interest rate futures / Mathematical models | |
| 650 | 4 | |a Stochastic models | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Interest rate futures |x Mathematical models | |
| 650 | 4 | |a Stochastic models | |
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| 650 | 0 | 7 | |a Zins |0 (DE-588)4067845-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804138609131913216 |
|---|---|
| adam_text | Contents
Preface
v
1.
A
Review
of Stochastic Calculus
1
1.1
Brownian Motion
....................... 1
1.2
Stochastic Integration
.................... 2
1.3
Quadratic Variation
..................... 8
1.4
Itô s
Formula
......................... 10
1.5
Exercises
........................... 12
2.
A Review of Black-Scholes Pricing
13
2.1
Call and Put Options
.................... 13
2.2
Market Model and Portfolio
................. 15
2.3
PDE Method
......................... 16
2.4
The Girsanov Theorem
................... 18
2.5
Martingale Method
...................... 20
2.6
Exercises
........................... 26
3.
Short Term Interest Rate Models
29
3.1
Mean-Reverting Models
................... 29
3.2
Constant Elasticity of Variance (CEV) Models
...... 30
3.3
Time-Dependent Models
................... 30
3.4
Exercises
........................... 31
4.
Pricing of Zero-Coupon Bonds
33
4.1
Definition and Basic Properties
............... 33
4.2
Absence of Arbitrage and the Markov Property
...... 34
4.3
Absence of Arbitrage and the Martingale Property
.... 36
χ
An Elementary Introduction to Stochastic Interest Rate Modeling
4.4
PDE Solution: Probabilistic Method
............ 37
4.5
PDE Solution: Analytical Method
............. 39
4.6
Numerical Simulations
.................... 40
4.7
Exercises
........................... 43
5.
Forward Rate Modeling
47
5.1
Forward Contracts
...................... 47
5.2
Instantaneous Forward Rate
................. 50
5.3
Short Rates
.......................... 52
5.4
Parametrization of Forward Rates
............. 53
5.5
Curve Estimation
....................... 54
5.6
Exercises
........................... 55
6.
The Heath-Jarrow-Morton (HJM) Model
57
6.1
Restatement of Objectives
.................. 57
6.2
Forward Vasicek Rates
.................... 59
6.3
Spot Forward Rate Dynamics
................ 64
6.4
The HJM Condition
..................... 65
6.5
Markov Property of Short Rates
.............. 68
6.6
The Hull-White Model
.................... 70
6.7
Exercises
........................... 71
7.
The Forward Measure and Derivative Pricing
73
7.1
Forward Measure
....................... 73
7.2
Dynamics under the Forward Measure
........... 76
7.3
Derivative Pricing
...................... 80
7.4
Inverse Change of Measure
................. 82
7.5
Exercises
........................... 83
8.
Curve Fitting and a Two Factor Model
85
8.1
Curve Fitting
......................... 85
8.2
Deterministic Shifts
..................... 88
8.3
The Correlation Problem
.................. 89
8.4
Two-Factor Model
...................... 91
8.5
Exercises
........................... 98
9.
Pricing of Caps and Swaptions on the
LIBOR
103
9.1
Pricing of Caplets and Caps
................. 103
9.2
Forward Rate Measure and Tenor Structure
........ 105
Contents xi
9.3
Swaps and Swaptions
.................... 107
9.4
The London Interbank Offered Rates
(LIBOR)
Model
. . 108
9.5
Swap Rates on the
LIBOR
Market
............. 110
9.6
Swaption Pricing on the
LIBOR
Market
.......... 112
9.7
Forward Swap Measures
................... 114
9.8
Exercises
........................... 118
10.
The
Brace-Gatarek-Musiela (BGM)
Model
121
10.1
The BGM Model
....................... 121
10.2
Cap Pricing
.......................... 124
10.3
Swaption Pricing
....................... 125
10.4
Calibration of the BGM Model
............... 129
10.5
Exercises
........................... 132
11.
Appendix A: Mathematical Tools
135
12.
Appendix B: Some Recent Developments
143
13.
Solutions to the Exercises
147
Bibliography
173
Index
177
|
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| callnumber-search | HG6024.5 |
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| callnumber-subject | HG - Finance |
| classification_rvk | QP 890 SK 820 |
| ctrlnum | (OCoLC)233142694 (DE-599)BVBBV035306566 |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.63230151922 |
| dewey-search | 332.63230151922 |
| dewey-sort | 3332.63230151922 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035306566 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:54Z |
| institution | BVB |
| isbn | 9812832734 9789812832733 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017111359 |
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| physical | XI, 178 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | World Scientific |
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| series | Advanced series on statistical science & applied probability |
| series2 | Advanced series on statistical science & applied probability |
| spelling | Privault, Nicolas Verfasser (DE-588)1032387327 aut An elementary introduction to stochastic interest rate modeling Nicolas Privault New Jersey [u.a.] World Scientific 2008 XI, 178 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced series on statistical science & applied probability 12 Literaturverz. S. 173 - 175 Interest rate futures / Mathematical models Stochastic models Mathematisches Modell Interest rate futures Mathematical models 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 Zins (DE-588)4067845-3 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Zinsfuß (DE-588)4190927-6 s 1\p DE-604 Advanced series on statistical science & applied probability 12 (DE-604)BV011932321 12 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111359&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 & applied probability Interest rate futures / Mathematical models Stochastic models Mathematisches Modell Interest rate futures Mathematical models 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 | Interest rate futures / Mathematical models Stochastic models Mathematisches Modell Interest rate futures Mathematical models Stochastisches Modell (DE-588)4057633-4 gnd Zinsfuß (DE-588)4190927-6 gnd Zins (DE-588)4067845-3 gnd |
| topic_facet | Interest rate futures / Mathematical models Stochastic models Mathematisches Modell Interest rate futures Mathematical models Stochastisches Modell Zinsfuß Zins |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017111359&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932321 |
| work_keys_str_mv | AT privaultnicolas anelementaryintroductiontostochasticinterestratemodeling |