Introduction to Econophysics : Correlations and Complexity in Finance / Rosario N. Mantegna, H. Eugene Stanley.

Format:

Book

Contributor:

Mantegna, Rosario N. (Rosario Nunzio), 1960-

Stanley, H. Eugene (Harry Eugene), 1941-

Series:

Cambridge books online.

Language:

English

Subjects (All):

Finance--Statistical methods.

Finance.

Finance--Mathematical models.

Statistical physics.

Physical Description:

1 online resource (164 pages) : digital, PDF file(s)

Place of Publication:

Cambridge : Cambridge University Press, 1999.

System Details:

Mode of access: World Wide Web.

text file

PDF

Summary:

This pioneering text explores the dynamic new specialty of econophysics, the use of statistical physics concepts in the description of financial systems.

Contents:

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-Esseen Theorem 1 20

3.4.2 Berry-Esseen 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

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

5 Scales in financial data 34

5.1 Price scales in financial markets 35

5.2 Time scales in financial markets 39

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

8 Stochastic models of price dynamics 60

8.1 Levy stable non-Gaussian model 61

8.2 Student's t-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(1,1) and empirical observations 85

11 Financial markets and turbulence 88

11.1 Turbulence 89

11.2 Parallel analysis of price dynamics and fluid velocity 90

11.3 Scaling in turbulence and in financial markets 94

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

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

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 Speculaton: 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

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.

Notes:

Title from publishers bibliographic system (viewed on 02 Mar 2012).

Other Format:

Print version:

ISBN:

9780511755767

9780521620086

Access Restriction:

Restricted for use by site license.