Arbitrage theory in continuous time:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2004
|
| Ausgabe: | 2. ed., 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVIII, 466 S. |
| ISBN: | 0199271267 9780199271269 |
Internformat
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| 100 | 1 | |a Björk, Tomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Arbitrage theory in continuous time |c Tomas Bjørk |
| 250 | |a 2. ed., 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2004 | |
| 300 | |a XVIII, 466 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Arbitrage pricing theory |2 shbe | |
| 650 | 7 | |a Arbitrage |2 shbe | |
| 650 | 7 | |a Arbitrageverksamhet - matematiska modeller |2 sao | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Arbitrage | |
| 650 | 4 | |a Arbitrage |v Problems, exercises, etc | |
| 650 | 4 | |a Arbitrage |x Mathematical models | |
| 650 | 4 | |a Arbitrage |x Mathematical models |v Problems, exercises, etc | |
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Datensatz im Suchindex
| _version_ | 1804131867908112384 |
|---|---|
| adam_text | CONTENTS
Introduction
1
1.1 Problem
Formulation
1
The Binomial Model
5
2.1
The One Period Model
5
2.1.1
Model Description
5
2.1.2
Portfolios and Arbitrage
6
2.1.3
Contingent Claims
9
2.1.4
Risk Neutral Valuation
11
2.2
The Multiperiod Model
15
2.2.1
Portfolios and Arbitrage
15
2.2.2
Contingent Claims
17
2.3
Exercises
25
2.4
Notes
25
A More General One Period Model
26
3.1
The Model
26
3.2
Absence of Arbitrage
27
3.3
Martingale Pricing
30
3.4
Completeness
31
3.5
Stochastic Discount Factors
34
3.6
Exercises
35
Stochastic Integrals
36
4.1
Introduction
36
4.2
Information
38
4.3
Stochastic Integrals
40
4.4
Martingales
42
4.5
Stochastic Calculus and the
Ito
Formula
45
4.6
Examples
50
4.7
The Multidimensional
Ito
Formula
53
4.8
Correlated Wiener Processes
55
4.9
Exercises
5Í)
4.10
Notes
61
Differential Equations
62
5.1
Stochastic Differential Equations
62
5.2
Geometric Brownian Motion
63
5.3
The Linear SDE
66
5.4
The Infinitesimal Operator
67
CONTENTS xiii
5.5
Partial
Differential
Equations
68
5.6
The Kolmogorov Equations
72
5.7
Exercises
75
5.8
Notes
79
6
Portfolio Dynamics
80
6.1
Introduction
80
6.2
Self-financing Portfolios
83
6.3
Dividends
85
6.4
Exercise
87
7
Arbitrage Pricing
88
7.1
Introduction
88
7.2
Contingent Claims and Arbitrage
89
7.3
The Black-Scholes Equation
94
7.4
Risk Neutral Valuation
98
7.5
The Black-Scholes Formula
100
7.6
Options on Futures
102
7.6.1
Forward Contracts
102
7.6.2
Futures Contracts and the Black Formula
103
7.7
Volatility
104
7.7.1
Historic Volatility
105
7.7.2
Implied Volatility
106
7.8
American options
106
7.9
Exercises
108
7.10
Notes
П0
8
Completeness and Hedging HI
8.1
Introduction HI
8.2
Completeness in the Black-Scholes Model
112
8.3
Completeness
—
Absence of Arbitrage
117
8.4
Exercises
Π
8
8.5
Notes 12°
9
Parity Relations and Delta Hedging
121
9.1
Parity Relations 121
9.2
The Greeks 123
9.3
Delta and Gamma Hedging 126
9.4
Exercises 130
10
The Martingale Approach to Arbitrage Theory*
133
10.1
The Case with Zero Interest Rate
133
10.2
Absence of Arbitrage
136
10.2.1
A Rough Sketch of the Proof
137
10.2.2
Precise Results 14°
CONTENTS
10.3 The General
Case
142
10.4
Completeness
145
10.5
Martingale Pricing
147
10.6
Stochastic Discount Factors
149
10.7
Summary for the Working Economist
150
10.8
Notes
153
11
The Mathematics of the Martingale Approach*
154
11.1
Stochastic Integral Representations
154
11.2
The Girsanov Theorem: Heuristics
158
11.3
The Girsanov Theorem
160
11.4
The Converse of the Girsanov Theorem
164
11.5
Girsanov Transformations and Stochastic Differentials
164
11.6
Maximum Likelihood Estimation
165
11.7
Exercises
167
11.8
Notes
168
12
Black-Scholes from a Martingale Point of View*
169
12.1
Absence of Arbitrage
169
12.2
Pricing
171
12.3
Completeness
172
13
Multidimensional Models: Classical Approach
175
13.1
Introduction
175
13.2
Pricing
177
13.3
Risk Neutral Valuation
183
13.4
Reducing the State Space
184
13.5
Hedging
188
13.6
Exercises
191
14
Multidimensional Models: Martingale Approach*
192
14.1
Absence of Arbitrage
193
14.2
Completeness
195
14.3
Hedging
196
14.4
Pricing
198
14.5
Markovian Models and PDEs
199
14.6
Market Prices of Risk
200
14.7
Stochastic Discount Factors
201
14.8 Tbc Hansen-
-Jagarmatnan Bounds
201
14.9
Exercises
204
14.10
Notes
204
15
Incomplete Markets
205
15.1
Introduction
205
15.2
A Scalar Nonpriccd Underlying Asset
205
15.3
The Multidimensional Case
214
CONTENTS
15.4
A Stochastic Short Rate
15.5
The Martingale
Approach*
15.6
Summing Up
15.7
Exercises
15.8
Notes
218
219
220
223
224
16
Dividends
22Г)
16.1
Discrete Dividends
225
16.1.1
Price Dynamics and Dividend Structure
225
16.1.2
Pricing Contingent Claims
226
16.2
Continuous Dividends
231
16.2.1
Continuous Dividend Yield
232
16.2.2
The General Case
235
16.3
Exercises
237
17
Currency Derivatives
239
17.1
Pure Currency Contracts
239
17.2
Domestic and Foreign Equity Markets
242
17.3
Domestic and Foreign Market Prices of Risk
248
17.4
Exercises
252
17.5
Notes
253
18
Barrier Options
254
18.1
Mathematical Background
254
18.2
Out Contracts
256
18.2.1
Down-and-Out Contracts
256
18.2.2
Up-and-Out Contracts
260
18.2.3
Examples
261
18.3
In Contracts
265
18.4
Ladders
267
18.5
Lookbacks 268
18.6
Exercises 270
18.7
Notes 2 °
19
Stochastic Optimal Control
271
19.1
An Example 271
19.2
The Formal Problem 272
19.3
The Hamilton-Jacobi-Bellman Equation
275
19.4
Handling the HJB Equation 2*3
19.5
The Linear Regulator
^4
19.6
Optimal Consumption and Investment
2x6
19.6.1
A Generalization 2*6
19.6.2
Optimal Consumption 2^
19.7
The Mutual Fund Theorems 2·^
19.7.1
The Case with No Risk Free Asset
291
19.7.2
The Case with a Risk Free Asset
295
CONTENTS
19.8
Exercises
297
19.9 Notes 301
20 Bonds and
Interest
Rates 302
20.1
Zero
Coupon Bonds 302
20.2
Interest
Rates 303
20.2.1
Definitions
303
20.2.2
Relations between
åf (t, T), dp(t, T), and dr {t)
305
20.2.3
An Alternative View of the Money Account
308
20.3
Coupon Bonds, Swaps, and Yields
309
20.3.1
Fixed Coupon Bonds
310
20.3.2
Floating Rate Bonds
310
20.3.3
Interest Rate Swaps
312
20.3.4
Yield and Duration
313
20.4
Exercises
314
20.5
Notes
315
21
Short Rate Models
316
21.1
Generalities
316
21.2
The Term Structure Equation
319
21.3
Exercises
324
21.4
Notes
325
22
Martingale Models for the Short Rate
326
22.1
Ç-dynamics
326
22.2
Inversion of the Yield Curve
327
22.3
Affine
Term Structures
329
22.3.1
Definition and Existence
329
22.3.2
A Probabilistic Discussion
331
22.4
Some Standard Models
333
22.4.1
The
Vasiček
Model
333
22.4.2
The
Но
-Lee
Model
334
22.4.3
The
CIR
Model
335
22.4.4
The Hull-White Model
335
22.5
Exercises
338
22.6
Notes
339
23
Forward Rate Models
340
23.1
The Heath-Jarrow--Morton Framework
340
23.2
Martingale Modeling
342
23.3
The
Musióla
Parameterization
344
23.4
Exercises
345
23.5
Notes
347
24
Change of Numeraire*
348
24.1
Introduction
348
CONTENTS
24.2
Generalities
349
24.3
Changing the Numeraire
353
24.4
Forward Measures
355
24.4.1
Using the
Т
-bond
as Numeraire
355
24.4.2
An Expectation Hypothesis
357
24.5
A General Option Pricing Formula
358
24.6
The Hull-White Model
361
24.7
The General Gaussian Model
363
24.8
Caps and Floors
365
24.9
Exercises
366
24.10
Notes
366
25
LIBOR
and Swap Market Models
368
25.1
Caps: Definition and Market Practice
369
25.2
The
LIBOR
Market Model
371
25.3
Pricing Caps in the
LIBOR
Model
372
25.4
Terminal Measure Dynamics and Existence
373
25.5
Calibration and Simulation
376
25.6
The Discrete Savings Account
378
25.7
Swaps
379
25.8
Swaptions: Definition and Market Practice
381
25.9
The Swap Market Models
382
25.10
Pricing Swaptions in the Swap Market Model
383
25.11
Drift Conditions for the Regular Swap Market Model
384
25.12
Concluding Comment
387
25.13
Exercises
388
25.14
Notes
388
26
Forwards and Futures
389
26.1
Forward Contracts
389
26.2
Futures Contracts
391
26.3
Exercises
394
26.4
Notes
394
A Measure and Integration*
395
A.I Sets and Mappings
395
A.2 Measures and Sigma Algebras
397
A.3 Integration
399
A.4 Sigma-Algebras and Partitions
404
A.5 Sets of Measure Zero
405
A.6 The Lp Spaces
406
A.7 Hubert Spaces
407
A.8 Sigma-Algebras and Generators
410
A.9 Product measures
414
A.10 The Lebesgue Integral
415
xviii CONTENTS
Α.
11
The Radon-Nikodym Theorem
416
A.12 Exercises
419
A.13 Notes
421
В
Probability Theory*
422
B.I Random Variables and Processes
422
B.2 Partitions and Information
425
B.3 Sigma-algebras and Information
427
B.4 Independence
430
B.5 Conditional Expectations
432
B.6 Equivalent Probability Measures
438
B.7 Exercises
441
B.8 Notes
442
С
Martingales and Stopping Times*
443
C.I Martingales
443
C.2 Discrete Stochastic Integrals
446
C.3 Likelihood Processes
447
C.4 Stopping Times
448
C.5 Exercises
451
References
453
Index
461
Tomas
Björk
is Professor of Mathematical
Finance at the Stockholm School of
Economics. He is co-editor
oí
Mathematical
Finance and is on the editorial board of
Finance and Stochastics
.
He has published
numerous journal articles on probability
theory, mathematical finance in general,
and in particular on interest rate theory.
The second edition of this popular introduction to the classical underpinnings
of the mathematics behind finance continues to combine sound mathematical
principles with economic applications.
Concentrating on the probabilistic theory of continuous arbitrage pricing of
financial derivatives, including stochastic optimal control theory and Merlon s
fund separation theory, the book is designed for graduate students and combines
necessary mathematical background with a solid economic focus. It includes a
solved example for every new technique presented, contains numerous exercises,
and suggests farther reading in each chapter.
In this substantially extended new edition
Tomas Björk
has added completely new
chapters on measure theory and probability theory, including the Radon-Nikodym
Theorem, Girsanov transformations, and stochastic integral martingale representa¬
tions. There is also an extensive new chapter on the abstract martingale approach
to arbitrage theory, including a guided tour through the Delbaen-Schachermayer
proof of the
irsi
fundamental
theorem, as well as a new chapter on the
LIBOR
aad swap market models. Providing two full treatments of arbitrage theory
—
the
classical delta hedging approach and the modern martingale approach
—
the book
is written in such a way that these approaches can be studied independently of
each other, thus providing the less mathematically oriented reader with a self
contained introduction to arbitrage theory, while at the same time allowing
the more advanced student
to
see the full theory in action.
This is the textbook of choice for graduate students and advanced undergraduates
studying finance and an invaluable introduction to mathematical finance for
mathematicians and professionals in financial markets.
|
| any_adam_object | 1 |
| author | Björk, Tomas |
| author_facet | Björk, Tomas |
| author_role | aut |
| author_sort | Björk, Tomas |
| author_variant | t b tb |
| building | Verbundindex |
| bvnumber | BV019294261 |
| classification_rvk | QK 620 QK 622 QK 660 SK 980 |
| classification_tum | MAT 624f WIR 170f |
| ctrlnum | (OCoLC)186164822 (DE-599)BVBBV019294261 |
| dewey-full | 332.645 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.645 |
| dewey-search | 332.645 |
| dewey-sort | 3332.645 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., 1. publ. |
| format | Book |
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| id | DE-604.BV019294261 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:43:45Z |
| institution | BVB |
| isbn | 0199271267 9780199271269 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012045701 |
| oclc_num | 186164822 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-20 DE-739 DE-M49 DE-BY-TUM DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-20 DE-739 DE-M49 DE-BY-TUM DE-11 DE-188 |
| physical | XVIII, 466 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Björk, Tomas Verfasser aut Arbitrage theory in continuous time Tomas Bjørk 2. ed., 1. publ. Oxford [u.a.] Oxford Univ. Press 2004 XVIII, 466 S. txt rdacontent n rdamedia nc rdacarrier Arbitrage pricing theory shbe Arbitrage shbe Arbitrageverksamhet - matematiska modeller sao Mathematisches Modell Arbitrage Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Arbitrage (DE-588)4002820-3 gnd rswk-swf Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd rswk-swf Arbitrage-Pricing-Theorie (DE-588)4112584-8 s Derivat Wertpapier (DE-588)4381572-8 s DE-604 Arbitrage (DE-588)4002820-3 s Ökonometrie (DE-588)4132280-0 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Björk, Tomas Arbitrage theory in continuous time Arbitrage pricing theory shbe Arbitrage shbe Arbitrageverksamhet - matematiska modeller sao Mathematisches Modell Arbitrage Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4132280-0 (DE-588)4002820-3 (DE-588)4112584-8 |
| title | Arbitrage theory in continuous time |
| title_auth | Arbitrage theory in continuous time |
| title_exact_search | Arbitrage theory in continuous time |
| title_full | Arbitrage theory in continuous time Tomas Bjørk |
| title_fullStr | Arbitrage theory in continuous time Tomas Bjørk |
| title_full_unstemmed | Arbitrage theory in continuous time Tomas Bjørk |
| title_short | Arbitrage theory in continuous time |
| title_sort | arbitrage theory in continuous time |
| topic | Arbitrage pricing theory shbe Arbitrage shbe Arbitrageverksamhet - matematiska modeller sao Mathematisches Modell Arbitrage Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier (DE-588)4381572-8 gnd Ökonometrie (DE-588)4132280-0 gnd Arbitrage (DE-588)4002820-3 gnd Arbitrage-Pricing-Theorie (DE-588)4112584-8 gnd |
| topic_facet | Arbitrage pricing theory Arbitrage Arbitrageverksamhet - matematiska modeller Mathematisches Modell Arbitrage Problems, exercises, etc Arbitrage Mathematical models Arbitrage Mathematical models Problems, exercises, etc Derivat Wertpapier Ökonometrie Arbitrage-Pricing-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012045701&sequence=000003&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=012045701&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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