Interest rate modeling: theory and practice
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2009
|
| Schriftenreihe: | Chapman & Hall/CRC financial mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIX, 333 S. graph. Darst. |
| ISBN: | 9781420090567 |
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| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
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| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Interest rates |x Mathematical models | |
| 650 | 4 | |a Interest rate futures |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804139922845597696 |
|---|---|
| adam_text | Contents
Preface
xiii
Acknowledgments
xvii
Author
xix
Chapter
1
The Basics of Stochastic Calculus
1
1.1
BROWNIAN MOTION
2
1.1.1
Simple Random Walks
2
1.1.2
Brownian Motion
4
1.1.3
Adaptive and Non-Adaptive Functions
6
1.2
STOCHASTIC INTEGRALS
8
1.2.1
Evaluation of Stochastic Integrals
11
1.3
STOCHASTIC DIFFERENTIALS AND ITO S LEMMA
13
1.4
MULTI-FACTOR EXTENSIONS
18
1.4.1
Multi-Factor Ito s Process
19
1.4.2
Ito s Lemma
20
vu
viii
■ Contents
1.4.3
Correlated Brownian Motions
20
1.4.4
The Multi-Factor
Lognormal
Model
21
1.5
MARTINGALES
22
Chapter
2
The Martingale Representation Theorem
27
2.1
CHANCING MEASURES WITH BINOMIAL MODELS
28
2.1.1
A Motivating Example
28
2.1.2
Binomial Trees and Path Probabilities
30
2.2
CHANGE OF MEASURES UNDER BROWNIAN
FILTRATION
34
2.2.1
The Radon-Nikodym Derivative of a Brownian Path
34
2.2.2
The CMG Theorem
37
2.3
THE MARTINGALE REPRESENTATION THEOREM
38
2.4
A COMPLETE MARKET WITH TWO SECURITIES
39
2.5
REPLICATING AND PRICING OF CONTINGENT
CLAIMS
40
2.6
MULTI-FACTOR EXTENSIONS
43
2.7
A COMPLETE MARKET WITH MULTIPLE SECURITIES
44
2.7.1
Existence of a Martingale Measure
44
2.7.2
Pricing Contingent Claims
47
2.8
THE BLACK-SCHOLES FORMULA
48
2.9
NOTES
51
Chapter
3
Interest Rates and Bonds
59
3.1
INTEREST RATES AND FIXED-INCOME INSTRUMENTS
60
3.1.1
Short Rate and Money Market Accounts
60
3.1.2
Term Rates and Certificates of Deposit
61
3.1.3
Bonds and Bond Markets
62
3.1.4
Quotation and Interest Accrual
64
3.2
YIELDS
66
3.2.1
Yield to Maturity
66
Contents ■ ix
3
.2.2
Par Bonds, Par Yields, and the Par Yield Curve
69
3.2.3
Yield Curves for U.S. Treasuries
69
3.3
ZERO-COUPON BONDS AND ZERO-COUPON
YIELDS
70
3.3.1
Zero-Coupon Bonds
70
3.3.2
Bootstrapping the Zero-Coupon Yields
72
3.3.2.1
Future Value and Present Value
73
3.4
FORWARD
RATESAND
FORWARD-RATE
AGREEMENTS
73
3.5
YIELD-BASED BOND RISK MANAGEMENT
75
3.5.1
Duration and Convexity
75
3.5.2
Portfolio Risk Management
78
Chapter
4
The Heath-Jarrow-Morton Model
81
4.1 LOGNORMAL
MODEL: THE STARTING POINT
83
4.2
THE HJM MODEL
86
4.3
SPECIAL CASES OF THE HJM MODEL
89
4.3.1
The
Но
-Lee
Model
90
4.3.2
The Hull-White (or Extended Vasicek) Model
91
4.4
ESTIMATING THE HJM MODEL FROM YIELD DATA
94
4.4.1
From a Yield Curve to a Forward-Rate Curve
94
4.4.2
Principal Component Analysis
99
4.5
A CASE
STU
DY
WITH A TWO-FACTOR MODEL
105
4.6
MONTE CARLO IMPLEMENTATIONS
107
4.7
FORWARD PRICES
110
4.8
FORWARD MEASURE
113
4.9
BLACK S FORMULA FOR CALL AND PUT OPTIONS
116
4.9.1
Equity Options under the Hull-White Model
118
4.9.2
Options on Coupon Bonds
122
4.10
NUMERAIRES AND CHANGES OF MEASURE
125
4.11
NOTES
127
χ
■ Contents
Chapter
5
Short-Rate Models and Lattice Implementation
133
5.1
FROM SHORT-RATE MODELS TO FORWARD-RATE
MODELS
134
5.2
GENERAL MARKOVIAN MODELS
137
5.2.1
One-Factor Models
144
5.2.2
Monte Carlo Simulations for Options Pricing
146
5.3
BINOMIAL TREES OF INTEREST RATES
147
5.3.1
A Binomial Tree for the
Но
-Lee
Model
148
5.3.2
Arrow-Debreu Prices
149
5.3.3
A Calibrated Tree for the
Но
-Lee
Model
152
5.4
A GENERAL TREE-BUILDING PROCEDURE
156
5.4.1
A Truncated Tree for the Hull-White Model
156
5.4.2
Trinomial Trees with Adaptive Time Steps
162
5.4.3
The Black-Karasinski Model
163
Chapter
6
The
LIBOR
Market Model
______________________167
6.1
LIBOR
MARKET INSTRUMENTS
167
6.1.1
LIBOR
Rates
168
6.1.2
Forward-Rate Agreements
169
6.1.3
Repurchasing Agreement
171
6.1.4
Eurodollar Futures
171
6.1.5
Floating-Rate Notes
172
6.1.6
Swaps
174
6.1.7
Caps
177
6.1.8
Swaptions
178
6.1.9
Bermudán
Swaptions
179
6.1.10
LIBOR
Exotics
179
6.2
THE
LIBOR
MARKET MODEL
182
6.3
PRICING OF CAPS AND FLOORS
187
6.4
PRICING OF SWAPTIONS
188
6.5
SPECIFICATIONS OF THE
LIBOR
MARKET MODEL
196
6.6
MONTE CARLO SIMULATION METHOD
200
6.6.1
The Log-Euler Scheme
200
Contents
■
XI
6.6.2
Calculation of the Greeks
201
6.6.3
Early Exercise
202
Chapter
7
Calibration of
LIBOR
Market
Model
211
7.1
IMPLIED CAP AND CAPLET VOLATILITIES
212
7.2
CALIBRATING THE
LIBOR
MARKET MODEL
TO CAPS
216
7.3
CALIBRATION TO CAPS, SWAPTIONS, AND INPUT
CORRELATIONS
218
7.4
CALIBRATION METHODOLOGIES
224
7.4.1
Rank-Reduction Algorithm
224
7.4.2
The Eigenvalue Problem for Calibrating
to Input Prices
237
7.5
SENSITIVITY WITH RESPECT TO THE INPUT PRICES
250
7.6
NOTES
253
Chapter
8
Volatility and Correlation Adjustments
255
8.1
ADJUSTMENT
DUETO
CORRELATIONS
256
8.1.1
Futures Price versus Forward Price
256
8.1.2
Convexity Adjustment for
LIBOR
Rates
261
8.1.3
Convexity Adjustment under the
Но
-Lee
Model
263
8.1.4
An Example of Arbitrage
264
8.2
ADJUSTMENT DUE TO CONVEXITY
266
8.2.1
Payment in Arrears versus Payment
in Advance
266
8.2.2
Geometric Explanation for Convexity Adjustment
268
8.2.3
General Theory of Convexity Adjustment
269
8.2.4
ConvexityAdjustmentforCMSand
CMT Swaps
273
8.3
TIMING ADJUSTMENT
276
8.4
QUANTO
DERIVATIVES
278
8.5
NOTES
284
xii ■ Contents
Chapter
9 Affine
Term Structure Models
__________________287
9.1
AN EXPOSITION WITH ONE-FACTOR MODELS
288
9.2
ANALYTICAL SOLUTION OF RICCARTI
EQUATIONS
297
9.3
PRICING OPTIONS ON COUPON BONDS
301
9.4
DISTRIBUTIONAL PROPERTIES OF SQUARE-ROOT
PROCESSES
302
9.5
MULTI-FACTOR MODELS
303
9.5.1
Admissible ATSMs
305
9.5.2
Three-Factor ATSMs
306
9.6
SWAPTION PRICING UNDER ATSMs
310
9.7
NOTES
315
References
____________________________________________319
Index
327
Interest
Rate Modeling
Theorv and Practice
Containing many results that are new or exist only in recent research articles,
Interest Rate Modeling: Theory and Practice portrays the theory of interest rate
modeling as a three-dimensional object of finance, mathematics, and computation.
It introduces all models with financial-economical justifications, develops options
along the martingale approach, and handles option evaluations with precise
numerical methods.
The text begins with the mathematical foundations, including Ito s calculus and
the martingale representation theorem. It then introduces bonds and bond yields,
followed by the Heath-Jarrow-Morton (HJM) model, which is the framework
for no-arbitrage pricing models. The next chapter focuses on when the HJM
model implies a Markovian short-rate model and discusses the construction and
calibration of short-rate lattice models. In the chapter on the
LIBOR
market model,
the author presents the simplest yet most robust formula for swaption pricing in
the literature. He goes on to address model calibration, an important aspect of
model applications in the markets; industrial issues; and the class of
affine
term
structure models for interest rates.
Features
•
Presents a complete cycle of model construction and applications, showing
readers how to build and use models
»
Incorporates high-power numerical methodologies
•
Provides a systematic treatment of intriguing industrial issues, such as
volatility and correlation adjustments
•
Contains exercise sets and a number of examples, with many based on real
market data
»
Includes comments on cutting-edge research, such as volatility-smile.
positive interest-rate models, and convexity adjustment
»
Offers code, tables, and figures on the author s Web site
Taking a top-down approach. Interest Rate Modeling provides readers with a
clear picture of this important subject by not overwhelming them with too many
specific models. The text captures the interdisciplinary nature of the field and
shows readers what it takes to be a competent quantitative analyst in today s
|
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| id | DE-604.BV035714741 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:51:47Z |
| institution | BVB |
| isbn | 9781420090567 |
| language | English |
| lccn | 2009009975 |
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| physical | XIX, 333 S. graph. Darst. |
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| spelling | Wu, Lixin 1961- Verfasser (DE-588)139302204 aut Interest rate modeling theory and practice Lixin Wu Boca Raton [u.a.] CRC Press 2009 XIX, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Includes bibliographical references and index Mathematisches Modell Interest rates Mathematical models Interest rate futures Mathematical models Zinsfuß (DE-588)4190927-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Zinsfuß (DE-588)4190927-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017991614&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017991614&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Wu, Lixin 1961- Interest rate modeling theory and practice Mathematisches Modell Interest rates Mathematical models Interest rate futures Mathematical models Zinsfuß (DE-588)4190927-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4190927-6 (DE-588)4114528-8 |
| title | Interest rate modeling theory and practice |
| title_auth | Interest rate modeling theory and practice |
| title_exact_search | Interest rate modeling theory and practice |
| title_full | Interest rate modeling theory and practice Lixin Wu |
| title_fullStr | Interest rate modeling theory and practice Lixin Wu |
| title_full_unstemmed | Interest rate modeling theory and practice Lixin Wu |
| title_short | Interest rate modeling |
| title_sort | interest rate modeling theory and practice |
| title_sub | theory and practice |
| topic | Mathematisches Modell Interest rates Mathematical models Interest rate futures Mathematical models Zinsfuß (DE-588)4190927-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematisches Modell Interest rates Mathematical models Interest rate futures Mathematical models Zinsfuß |
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