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Cover Mantegna Rosario N., Stanley H. Eugene An Introduction to Econophysics: Correlations and Complexity in Finance
Id: 112544
39.9 EUR

An Introduction to Econophysics: Correlations and Complexity in Finance

160 pp. (English). Hardcover. ISBN 0-521-62008-2.
Second hand. The state is rated 8 (out of 10)



1 Introduction

1.1 Motivation

1.2 Pioneering approaches

1.3 The chaos approach

1.4 The present focus

2 Efficient market hypothesis

2.1 Concepts, paradigms, and variables

2.2 Arbitrage

2.3 Efficient market hypothesis

2.4 Algorithmic complexity theory

2.5 Amount of information in a financial time series

2.6 Idealized systems in physics and finance

3 Random walk

3.1 One-dimensional discrete case

3.2 The continuous limit

3.3 Central limit theorem

3.4 The speed of convergence

3.4.1 Berry-Esseen Theorem 1

3.4.2 Berry-Esseen Theorem 2

3.5 Basin of attraction

4 Levy stochastic processes and limit theorems

4.1 Stable distributions

4.2 Scaling and self-similarity

4.3 Limit theorem for stable distributions

4.4 Power-law distributions

4.4.1 The St Petersburg paradox

4.4.2 Power laws in finite systems

4.5 Price change statistics

4.6 Infinitely divisible random processes

4.6.1 Stable processes

4.6.2 Poisson process

4.6.3 Gamma distributed random variables

4.6.4 Uniformly distributed random variables

4.7 Summary Scales in financial data

5.1 Price scales in financial markets

5.2 Time scales in financial markets

5.3 Summary

Stationarity and time correlation

6.1 Stationary stochastic processes

6.2 Correlation

6.3 Short-range correlated random processes

6.4 Long-range correlated random processes

6.5 Short-range compared with long-range correlated noise Time correlation in financial time series

7.1 Autocorrelation function and spectral density

7.2 Higher-order correlations: The volatility

7.3 Stationarity of price changes

7.4 Summary

Stochastic models of price dynamics

8.1 Levy stable non-Gaussian model

8.2 Student's -distribution

8.3 Mixture of Gaussian distributions

8.4 Truncated Levy flight Scaling and its breakdown

9.1 Empirical analysis of the SP 500 index

9.2 Comparison with the TLF distribution

9.3 Statistical properties of rare events ARCH and GARCH processes

10.1 ARCH processes

10.2 GARCH processes

10.3 Statistical properties of ARCH/GARCH processes

10.4 The GARCH(1,1) and empirical observations

10.5 Summary

Financial markets and turbulence

11.1 Turbulence

11.2 Parallel analysis of price dynamics and fluid velocity

11.3 Scaling in turbulence and in financial markets

11.4 Discussion

12 Correlation and anticorrelation between stocks

12.1 Simultaneous dynamics of pairs of stocks

12.1.1 Dow-Jones Industrial Average portfolio

12.1.2 SP 500 portfolio

12.2 Statistical properties of correlation matrices

12.3 Discussion

13 Taxonomy of a stock portfolio

13.1 Distance between stocks

13.2 Ultrametric spaces

13.3 Subdominant ultrametric space of a portfolio of stocks

13.4 Summary

14 Options in idealized markets

14.1 Forward contracts

14.2 Futures

14.3 Options

14.4 Speculating and hedging

14.4.1 Speculation: An example

14.4.2 Hedging: A form of insurance

14.4.3 Hedging: The concept of a riskless portfolio

14.5 Option pricing in idealized markets

14.6 The Black Scholes formula

14.7 The complex structure of financial markets

14.8 Another option-pricing approach

14.9 Discussion

15 Options in real markets

15.1 Discontinuous stock returns

15.2 Volatility in real markets

15.2.1 Historical volatility

15.2.2 Implied volatility

15.3 Hedging in real markets

15.4 Extension of the Black Scholes model

15.5 Summary Appendix A: Notation guide Appendix B: Martingales References


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