The Black-Scholes model:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Series: | Mastering mathematical finance
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | IX, 168 S. |
| ISBN: | 9781107001695 1107001692 9780521173001 0521173000 |
Staff View
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| 245 | 1 | 0 | |a The Black-Scholes model |c Marek Capiński ; Ekkehard Kopp |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
page vii
Introduction
1
1.1
Asset dynamics
1
1.2
Methods of option pricing
5
Strategies and risk-neutral probability
10
2.1
Finding the risk-neutral probability
10
2.2
Self-financing strategies
16
2.3
The No Arbitrage Principle
19
2.4
Admissible strategies
21
2.5
Proofs
30
Option pricing and hedging
37
3.1
Martingale representation theorem
38
3.2
Completeness of the model
47
3.3
Derivative pricing
51
3.4
The Black-Scholes PDE
61
3.5
The Greeks
68
3.6
Risk and return
73
3.7
Proofs
74
Extensions and applications
79
4.1
Options on foreign currency
79
4.2
Structural model of credit risk
87
4.3
Compound options
90
4.4
American call options
96
4.5
Variable coefficients
98
4.6
Growth optimal portfolios
99
Path-dependent options
107
5.1
Barrier options
107
5.2
Distribution of the maximum
109
5.3
Pricing barrier and
lookback
options
114
5.4
Asian options
126
VI
Contents
General
models
6.1
Two assets
6.2
Many assets
6.3
Ito
formula
6.4
Levy s Theorem
6.5
Girsanov Theorem
6.6
Applications
133
133
145
147
153
158
163
Index
168
The Black-Scholes option pricing model is the
first, and by far the best-known, continuous-
time mathematical model used in mathematical
finance. Here,
ir
provides a sufficiently complex,
yet tractable,
testbed
for exploring the basic
methodology of option pricing.
The discussion of extended markets, the careful
attention paid to the requirements for admissible
trading strategies, the development of pricing
formulae for many widely traded instruments and
the additional complications offered by multi-stock
models will appeal to a wide class of instructors.
Students, practitioners and researchers alike will
benefit from the book s rigorous, but unfussy,
approach to technical issues. It highlights potential
pitfalls, gives clear motivation for results and
techniques, and includes carefully chosen examples
and exercises, all of which makes it suitable for
self-study.
•
Equips students with the tools needed to price
the main options in current markets
•
Detailed proofs are presented in manageable
steps so students can see the wood for the trees
•
Exercises range in difficulty to challenge even
the most able student. Solutions are available
online
Mastering Mathematical
Finance (MMF) is a series of
short books that cover all core
topics and the most common
électives
offered in Master s
programmes in mathematical or
quantitative finance. The books
are closely coordinated and
largely self-contained, and can
be used efficiently in combination
but also individually.
The MMF books start financially
from scratch and mathematically
assume only undergraduate
calculus, linear algebra and
elementary probability theory.
The necessary mathematics
is developed rigorously,
with emphasis on a natural
development of mathematical
ideas and financial intuition, and
the readers quickly see real-life
financial applications, both for
motivation and as the ultimate
end for the theory. All books are
written for both teaching and
self-study, with worked examples,
exercises and solutions.
Marek Ca piński
has published over
50
research
papers and eleven books, and he has been teaching
for over
35
years, mainly in Poland and in the UK.
He is currently Professor of Applied Mathematics
at
AGH
University of Science and Technology in
Kraków,
Poland, where he
established a Master s programme in
mathematica]
finance.
Ekkehard
Kopp
is Emeritus Professor of Mathematics at the University of
Hull. He has published over
50
research papers and five books, on measure
and probability, stochastic analysis and mathematical finance. He has taught
in the UK, Canada and South Africa, and he serves on the editorial board of
the
x ÏMS
Librarv Series.
|
| any_adam_object | 1 |
| author | Capiński, Marek 1951- Kopp, Peter E. 1944- |
| author_GND | (DE-588)172897866 (DE-588)120339889 |
| author_facet | Capiński, Marek 1951- Kopp, Peter E. 1944- |
| author_role | aut aut |
| author_sort | Capiński, Marek 1951- |
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| bvnumber | BV040356778 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-10T00:22:22Z |
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| isbn | 9781107001695 1107001692 9780521173001 0521173000 |
| language | English |
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| physical | IX, 168 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Mastering mathematical finance |
| spelling | Capiński, Marek 1951- Verfasser (DE-588)172897866 aut The Black-Scholes model Marek Capiński ; Ekkehard Kopp 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2012 IX, 168 S. txt rdacontent n rdamedia nc rdacarrier Mastering mathematical finance Options (Finance) / Prices / Mathematical models Mathematisches Modell Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 s DE-604 Kopp, Peter E. 1944- Verfasser (DE-588)120339889 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025210719&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025210719&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Capiński, Marek 1951- Kopp, Peter E. 1944- The Black-Scholes model Options (Finance) / Prices / Mathematical models Mathematisches Modell Black-Scholes-Modell (DE-588)4206283-4 gnd |
| subject_GND | (DE-588)4206283-4 |
| title | The Black-Scholes model |
| title_auth | The Black-Scholes model |
| title_exact_search | The Black-Scholes model |
| title_full | The Black-Scholes model Marek Capiński ; Ekkehard Kopp |
| title_fullStr | The Black-Scholes model Marek Capiński ; Ekkehard Kopp |
| title_full_unstemmed | The Black-Scholes model Marek Capiński ; Ekkehard Kopp |
| title_short | The Black-Scholes model |
| title_sort | the black scholes model |
| topic | Options (Finance) / Prices / Mathematical models Mathematisches Modell Black-Scholes-Modell (DE-588)4206283-4 gnd |
| topic_facet | Options (Finance) / Prices / Mathematical models Mathematisches Modell Black-Scholes-Modell |
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