An introduction to econophysics: correlations and complexity in finance
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | Digitally print. version, paperback re-issue |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | IX, 148 S. graph. Darst. |
| ISBN: | 9780521620086 9780521039871 0521039878 |
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Record in the Search Index
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| adam_text | Contents
Preface viii
1
Introduction
1
1.1
Motivation
1
1.2
Pioneering approaches
2
1.3
The chaos approach
4
1.4
The present focus
5
2
Efficient market hypothesis
8
2.1
Concepts, paradigms, and variables
8
2.2
Arbitrage
8
2.3
Efficient market hypothesis
9
2.4
Algorithmic complexity theory
11
2.5
Amount of information in a financial time series
12
2.6
Idealized systems in physics and finance
12
3
Random walk
14
3.1
One-dimensional discrete case
14
3.2
The continuous limit
15
3.3
Central limit theorem
17
3.4
The speed of convergence
19
3.4.1
Berry-Esséen
Theorem
1 20
3.4.2
Berry-Esséen
Theorem
2 20
3.5
Basin of attraction
21
4
Levy stochastic processes and limit theorems
23
4.1
Stable distributions
23
4.2
Scaling and self-similarity
26
4.3
Limit theorem for stable distributions
27
4.4
Power-law distributions
28
4.4.1
The St Petersburg paradox
28
4.4.2
Power laws in finite systems
29
VI
Contents
4.5
Price change statistics
29
4.6
Infinitely divisible random processes
31
4.6.1
Stable processes
31
4.6.2
Poisson
process
31
4.6.3
Gamma distributed random variables
32
4.6.4
Uniformly distributed random variables
32
4.7
Summary
33
5
Scales in financial data
34
5.1
Price scales in financial markets
35
5.2
Time scales in financial markets
39
5.3
Summary
43
6
Stationarity and time correlation
44
6.1
Stationary stochastic processes
44
6.2
Correlation
45
6.3
Short-range correlated random processes
49
6.4
Long-range correlated random processes
49
6.5
Short-range compared with long-range correlated noise
51
7
Time correlation in financial time series
53
7.1
Autocorrelation function and spectral density
53
7.2
Higher-order correlations: The volatility
57
7.3
Stationarity of price changes
58
7.4
Summary
59
8
Stochastic models of price dynamics
60
8.1
Levy stable non-Gaussian model
61
8.2
Student s
ŕ-distribution
62
8.3
Mixture of Gaussian distributions
63
8.4
Truncated Levy flight
64
9
Scaling and its breakdown
68
9.1
Empirical analysis of the S&P
500
index
68
9.2
Comparison with the TLF distribution
72
9.3
Statistical properties of rare events
74
10
ARCH and GARCH processes
76
10.1
ARCH processes
77
10.2
GARCH processes
80
10.3
Statistical properties of ARCH/GARCH processes
81
10.4
The
GARCH(U)
and empirical observations
85
10.5
Summary
87
11
Financial markets and turbulence
88
11.1
Turbulence
89
11.2
Parallel analysis of price dynamics and fluid velocity
90
Contents
vii
11.3
Scaling in turbulence and in financial markets
94
11.4
Discussion
96
12
Correlation and anticorrelation between stocks
98
12.1
Simultaneous dynamics of pairs of stocks
98
12.1.1
Dow-Jones Industrial Average portfolio
99
12.1.2
S&P
500
portfolio
101
12.2
Statistical properties of correlation matrices
103
12.3
Discussion
103
13
Taxonomy of a stock portfolio
105
13.1
Distance between stocks
105
13.2
Ultrametric spaces
106
13.3
Subdominant
ultrametric space of a portfolio of stocks 111
13.4
Summary
112
14
Options in idealized markets
113
14.1
Forward contracts
113
14.2
Futures
114
14.3
Options
114
14.4
Speculating and hedging
115
14.4.1
Speculation: An example
116
14.4.2
Hedging: A form of insurance
116
14.4.3
Hedging: The concept of a riskless portfolio
116
14.5
Option pricing in idealized markets
118
14.6
The Black
&
Scholes formula
120
14.7
The complex structure of financial markets
121
14.8
Another option-pricing approach
121
14.9
Discussion
122
15
Options in real markets
123
15.1
Discontinuous stock returns
123
15.2
Volatility in real markets
124
15.2.1
Historical volatility
124
15.2.2
Implied volatility
125
15.3
Hedging in real markets
127
15.4
Extension of the Black
&
Scholes model
127
15.5
Summary
128
Appendix A: Notation guide
130
Appendix B: Martingales
136
References
137
Index
145
Paperback
Re-issue
This book concerns the use of concepts from statistical physics in the
description of financial systems. Specifically, the authors illustrate the
scaling concepts used in probability theory, in critical phenomena, and in
fully developed turbulent fluids. These concepts are then applied to financial
time series to gain insights into the behavior of financial markets. The
authors also present a stochastic model that displays several of the statistical
properties observed in empirical data.
Usually in the study of economic systems it is possible to investigate the
system at different scales. But it is often impossible to write down the
microscopic equation for all the economic entities interacting within a given
system. Statistical physics concepts such as stochastic dynamics, short- and
long-range correlations, self-similarity and scaling permit an understanding
of the global behavior of economic systems without first having to work out a
detailed microscopic description of the same system. This book will be of
interest both to physicists and to economists. Physicists will find the
application of statistical physics concepts to economic systems interesting
and challenging, as economic systems are among the most intriguing and
fascinating complex systems that might be investigated. Economists and
workers in the financial world will find useful the presentation of empirical
analysis methods and well-formulated theoretical tools that might help
describe systems composed of a huge number of interacting subsystems.
This book is intended for students and researchers studying economics or
physics at a graduate level and for professionals in the field of finance.
Undergraduate students possessing some familarity with probability theory or
statistical physics should also be able to learn from the book.
|
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
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| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Digitally print. version, paperback re-issue |
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| spelling | Mantegna, Rosario N. 1960- Verfasser (DE-588)133655857 aut An introduction to econophysics correlations and complexity in finance Rosario N. Mantegna ; H. Eugene Stanley Econophysics Digitally print. version, paperback re-issue Cambridge [u.a.] Cambridge Univ. Press 2007 IX, 148 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Kapitalmarkttheorie (DE-588)4137411-3 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s Statistische Physik (DE-588)4057000-9 s Kapitalmarkttheorie (DE-588)4137411-3 s DE-604 Finanzmathematik (DE-588)4017195-4 s 1\p DE-604 Stanley, H. Eugene 1941- Verfasser (DE-588)124434851 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020143269&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=020143269&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mantegna, Rosario N. 1960- Stanley, H. Eugene 1941- An introduction to econophysics correlations and complexity in finance Finanzmathematik (DE-588)4017195-4 gnd Statistische Physik (DE-588)4057000-9 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4057000-9 (DE-588)4137411-3 (DE-588)4066472-7 |
| title | An introduction to econophysics correlations and complexity in finance |
| title_alt | Econophysics |
| title_auth | An introduction to econophysics correlations and complexity in finance |
| title_exact_search | An introduction to econophysics correlations and complexity in finance |
| title_full | An introduction to econophysics correlations and complexity in finance Rosario N. Mantegna ; H. Eugene Stanley |
| title_fullStr | An introduction to econophysics correlations and complexity in finance Rosario N. Mantegna ; H. Eugene Stanley |
| title_full_unstemmed | An introduction to econophysics correlations and complexity in finance Rosario N. Mantegna ; H. Eugene Stanley |
| title_short | An introduction to econophysics |
| title_sort | an introduction to econophysics correlations and complexity in finance |
| title_sub | correlations and complexity in finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd Statistische Physik (DE-588)4057000-9 gnd Kapitalmarkttheorie (DE-588)4137411-3 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Finanzmathematik Statistische Physik Kapitalmarkttheorie Wirtschaftsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020143269&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=020143269&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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