## Introduction to Econophysics: Correlations and Complexity in FinanceThis book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. 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. |

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### Contents

1 Introduction | 1 |

2 Efficient market hypothesis | 8 |

3 Random walk | 14 |

4 Lévy stochastic processes and limit theorems | 23 |

5 Scales in financial data | 34 |

6 Stationarity and time correlation | 44 |

7 Time correlation in financial time series | 53 |

8 Stochastic models of price dynamics | 60 |

11 Financial markets and turbulence | 88 |

12 Correlation and anticorrelation between stocks | 98 |

13 Taxonomy of a stock portfolio | 105 |

14 Options in idealized markets | 113 |

15 Options in real markets | 123 |

Notation guide | 130 |

Martingales | 136 |

137 | |

### Other editions - View all

Introduction to Econophysics: Correlations and Complexity in Finance Rosario N. Mantegna,H. Eugene Stanley No preview available - 2007 |

Introduction to Econophysics: Correlations and Complexity in Finance Rosario N. Mantegna,H. Eugene Stanley No preview available - 2000 |

### Common terms and phrases

Algorithmic complexity theory arbitrage opportunities assumption asymptotic attractor autocorrelation function autocovariance behavior Black & Scholes chapter characteristic function concept conditional probability density consider control parameters convergence describe DJIA economic efficient market hypothesis empirical equation evolution example financial asset financial markets finite variance fluctuations Gaussian distribution geometric Brownian motion high-frequency data i.i.d. random variables increments interval investigated L´evy distribution L´evy stable leptokurtic limit theorem logarithm of price long-range correlated Lorentzian observed obtained option P(Sn pair of stocks physicists physics power spectrum power-law distributions price changes price dynamics probability density function probability of return process characterized random process random variables random variables xi random walk rational price real markets scaling properties spectral density stable distribution stable non-Gaussian standard deviation stationary statistical properties stochastic process stock price strike price trading turbulence ultrametric space velocity Wiener process