Term-structure models: a graduate course
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2009
|
| Series: | Springer finance
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| Subjects: | |
| Online Access: | Cover Inhaltstext Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 256 Seiten Illustrationen |
| ISBN: | 9783540097266 |
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MARC
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| 100 | 1 | |a Filipović, Damir |d 1970- |0 (DE-588)139025278 |4 aut | |
| 245 | 1 | 0 | |a Term-structure models |b a graduate course |c Damir Filipović |
| 264 | 1 | |a Berlin |b Springer |c 2009 | |
| 300 | |a XII, 256 Seiten |b Illustrationen | ||
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Record in the Search Index
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Contents
1
Introduction
. 1
2
Interest Rates and Related Contracts
. 5
2.1
Zero-Coupon Bonds
. 5
2.2
Interest Rates
. 6
2.2.1
Market Example:
LIBOR
. 7
2.2.2
Simple vs. Continuous Compounding
. 8
2.2.3
Forward vs. Future Rates
. 9
2.3
Money-Market Account and Short Rates
. 9
2.3.1
Proxies for the Short Rate
. 10
2.4
Coupon Bonds, Swaps and Yields
. 11
2.4.1
Fixed Coupon Bonds
. 11
2.4.2
Floating Rate Notes
. 12
2.4.3
Interest Rate Swaps
. 12
2.4.4
Yield and Duration
. 15
2.5
Market Conventions
. 17
2.5.1
Day-Count Conventions
. 17
2.5.2
Coupon Bonds
. 18
2.5.3
Accrued Interest, Clean Price and Dirty Price
. 18
2.5.4
Yield-to-Maturity
. 19
2.6
Caps and Floors
. 19
2.6.1
Caps
. 20
2.6.2
Floors
. 20
2.6.3
Caps, Floors and Swaps
. 21
2.6.4
Black's Formula
. 21
2.7
Swaptions
. 22
2.7.1
Black's Formula
. 24
2.8
Exercises
. 24
2.9
Notes
. 27
3
Estimating the Term-Structure
. 29
3.1
A Bootstrapping Example
. 29
3.2
Non-parametric Estimation Methods
. 34
3.2.1
BondMarkets
. 35
3.2.2
Money Markets
. 36
3.2.3
Problems
. 38
3.3
Parametric Estimation Methods
. 38
3.3.1
Estimating the Discount Function with Cubic B-splines
. . 38
Contents
3.3.2
Smoothing Splines
. 43
3.3.3
Exponential-Polynomial Families
. 49
3.4
Principal Component Analysis
. 51
3.4.1
Principal Components of a Random Vector
. 51
3.4.2
Sample Principle Components
. 52
3.4.3
PCA of the Forward Curve
. 53
3.4.4
Correlation
. 55
3.5
Exercises
. 56
3.6
Notes
. 57
Arbitrage Theory
. 59
4.1
Stochastic Calculus
. 59
4.1.1
Stochastic Integration
. 60
4.1.2
Quadratic Variation and Covariation
. 61
4.1.3
Itô's
Formula
. 62
4.1.4
Stochastic Differential Equations
. 63
4.1.5
Stochastic Exponential
. 64
4.2
Financial Market
. 65
4.2.1
Self-Financing Portfolios
. 65
4.2.2
Numeraires
. 66
4.3
Arbitrage and Martingale Measures
. 67
4.3.1
Martingale Measures
. 68
4.3.2
Market Price of Risk
. 69
4.3.3
Admissible Strategies
. 70
4.3.4
The First Fundamental Theorem of Asset Pricing
. 70
4.4
Hedging and Pricing
. 71
4.4.1
Complete Markets
. 71
4.4.2
Arbitrage Pricing
. 74
4.5
Exercises
. 75
4.6
Notes
. 77
Short-Rate Models
. 79
5.1
Generalities
. 79
5.2
Diffusion Short-Rate Models
. 80
5.2.1
Examples
. 82
5.2.2
Inverting the Forward Curve
. 83
5.3
Affine
Term-Structures
. 84
5.4
Some Standard Models
. 85
5.4.1
Vasiček
Model
. 85
5.4.2
CIR
Model
. 87
5.4.3
Dothan Model
. 88
5.4.4
Но
-Lee
Model
. 89
5.4.5
Hull-White Model
. 90
5.5
Exercises
. 91
5.6
Notes
. 92
Contents xi
6
Heath-
Jarrow-Morton (HJM)
Methodology.
93
6.1
Forward Curve Movements
. 93
6.2
Absence of Arbitrage
. 95
6.3
Short-Rate Dynamics
. 96
6.4
HJM Models
. 97
6.4.1
Proportional Volatility
. 98
6.5
Fubini's Theorem
. 99
6.6
Exercises
. 102
6.7
Notes
. 103
7
Forward Measures
.105
7.1
Γ
-Bond as Numeraire
. 105
7.2
Bond Option Pricing
. 109
7.2.1
Example:
Vasiček
Short-Rate Model
. 110
7.3
Black-Scholes Model with Gaussian Interest Rates
. 110
7.3.1
Example:
Black-Scholes-Vasiček
Model
. 113
7.4
Exercises
. 114
7.5
Notes
. 116
8
Forwards and Futures
.117
8.1
Forward Contracts
. 117
8.2
Futures Contracts
. 118
8.2.1
Interest Rate Futures
. 119
8.3
Forward vs. Futures in a Gaussian Setup
. 120
8.4
Exercises
. 121
8.5
Notes
. 122
9
Consistent Term-Structure
Parametriza
tions
.123
9.1
Multi-factor Models
. 123
9.2
Consistency Condition
. 125
9.3 Affine
Term-Structures
. 127
9.4
Polynomial Term-Structures
. 128
9.4.1
Special Case:
m
= 1.129
9.4.2
General Case:
m
> 1.131
9.5
Exponential-Polynomial Families
.134
9.5.1 Nelson-Siegel
Family
. 134
9.5.2
Svensson
Family
. 135
9.6
Exercises
. 138
9.7
Notes
. 140
10
Affine
Processes
.143
10.1
Definition and Characterization of
Affine
Processes
.143
10.2
Canonical State Space
.146
10.3
Discounting and Pricing in
Affine
Models
.151
10.3.1
Examples of Fourier Decompositions
.157
10.3.2
Bond Option Pricing in
Affine
Models
.161
xii
Contents
10.3.3
Heston
Stochastic Volatility Model
. 166
10.4
Affine
Transformations and Canonical Representation
. 168
10.5
Existence and Uniqueness of
Affine
Processes
. 171
10.6
On the Regularity of Characteristic Functions
. 173
10.7
Auxiliary Results for Differential Equations
. 177
10.7.1
Some
Invariance
Results
. 177
10.7.2
Some Results on Riccati Equations
. 180
10.7.3
Proof of Theorem
10.3. 185
10.8
Exercises
. 186
10.9
Notes
. 194
11
Market Models
.197
11.1
Heuristic Derivation
. 197
11.2
LIBOR
Market Model
. 199
11.2.1
LIBOR
Dynamics Under Different Measures
. 201
11.3
Implied Bond Market
. 201
11.4
Implied Money-Market Account
. 204
11.5
Swaption Pricing
. 206
11.5.1
Forward Swap Measure
. 207
11.5.2
Analytic Approximations
. 209
11.6
Monte Carlo Simulation of the
LIBOR
Market Model
. 210
11.7
Volatility Structure and Calibration
. 212
11.7.1
Principal Component Analysis
. 212
11.7.2
Calibration to Market Quotes
. 213
11.8
Continuous-Tenor Case
. 219
11.9
Exercises
. 221
11.10
Notes
. 223
12
Default Risk
.225
12.1
Default and Transition Probabilities
.225
12.2
Structural Approach
.227
12.3
Intensity-Based Approach
.229
1
2.3.1
Construction of Doubly Stochastic Intensity-Based Models
235
12.3.2
Computation of Default Probabilities
.236
12.3.3
Pricing Default Risk
.236
12.3.4
Measure Change
.240
12.4
Exercises
.242
12.5
Notes
.243
References
.245
Index
.253
Damir Filipović
Changing interest rates constitute one of the major risk sources for banks, in¬
surance companies, and other financial institutions. Modeling the term-structure
movements of interest rates is a challenging task. This volume gives an introduc¬
tion to the mathematics of term-structure models in continuous time. It includes
practical aspects for fixed-income markets such as day-count conventions, dura¬
tion of coupon-paying bonds and yield curve construction; arbitrage theory;
short-rate models; the Heath-Jarrow-Morton methodology; consistent term-struc¬
ture parametrizations;
affine
diffusion
processes and option pricing with Fourier
transform;
LIBOR
market models; and credit risk.
theory. Students, researches
Each chapter endswith a setof exercises, that
pravi^-sourceforhöfflewoíkarif
exain questions. Readers are
èxpectèdîo
te f^mitìsafwjth
elementary
Ito
calcuíuSr
basic probability theory, and; leal arid compiexanalysis;
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| any_adam_object | 1 |
| author | Filipović, Damir 1970- |
| author_GND | (DE-588)139025278 |
| author_facet | Filipović, Damir 1970- |
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| dewey-full | 332.8 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.8 |
| dewey-search | 332.8 |
| dewey-sort | 3332.8 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035683307 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:17:01Z |
| institution | BVB |
| isbn | 9783540097266 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017737533 |
| oclc_num | 633317087 |
| open_access_boolean | |
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| physical | XII, 256 Seiten Illustrationen |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance |
| spelling | Filipović, Damir 1970- (DE-588)139025278 aut Term-structure models a graduate course Damir Filipović Berlin Springer 2009 XII, 256 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer finance Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Zinsstrukturtheorie (DE-588)4117720-4 gnd rswk-swf Zinsstrukturtheorie (DE-588)4117720-4 s Finanzmathematik (DE-588)4017195-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-68015-4 DE-576;springer image/jpeg http://swbplus.bsz-bw.de/bsz285145320cov.htm 20090113135254 Cover X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3938046&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737533&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Filipović, Damir 1970- Term-structure models a graduate course Finanzmathematik (DE-588)4017195-4 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4117720-4 |
| title | Term-structure models a graduate course |
| title_auth | Term-structure models a graduate course |
| title_exact_search | Term-structure models a graduate course |
| title_full | Term-structure models a graduate course Damir Filipović |
| title_fullStr | Term-structure models a graduate course Damir Filipović |
| title_full_unstemmed | Term-structure models a graduate course Damir Filipović |
| title_short | Term-structure models |
| title_sort | term structure models a graduate course |
| title_sub | a graduate course |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Zinsstrukturtheorie (DE-588)4117720-4 gnd |
| topic_facet | Finanzmathematik Zinsstrukturtheorie |
| url | http://swbplus.bsz-bw.de/bsz285145320cov.htm http://deposit.dnb.de/cgi-bin/dokserv?id=3938046&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017737533&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=017737533&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT filipovicdamir termstructuremodelsagraduatecourse |