Preface1 Introduction1．1 Motivation1．2 Pioneering approaches1．3 The chaos approach1．4 The present focus2 Efficient market hypothesis2．1 Concepts， paradigms， and variables2．2 Arbitrage2．3 Efficient market hypothesis2．4 Algorithmic complexity theory2．5 Amount ofinformation in a financial time series2．6 Idealized systems in physics and finance3 Random walk3．1 One-dimensional discrete case3．2 The continuous limit3．3 Central limit theorem3．4 The speed of convergence3．4．1 Berry-Esseen Theorem 13．4．2 Berry-Esseen Theorem 23．5 Basin of attraction4 Levy stochastic processes and limit theorems4．1 Stable distributions4．2 Scaling and self-similarity4．3 Limit theorem for stable distributions4．4 Power-law distributions4．4．1 The St Petersburg paradox4．4．2 Power laws in finite systems4．5 Price change statistics4．6 Infinitely divisible random processes4．6．1 Stable processes4．6．2 Poisson process4．6．3 Gamma distributed random variables4．6．4 Uniformly distributed random variables4．7 Summary5 Scales in financial data5．1 Price scales in financial markets5．2 Time scales in financial markets5．3 Summary6 Stationarity and time correlation6．1 Stationary stochastic processes6．2 Correlation6．3 Short-range correlated random processes6．4 Long-range correlated random processes6．5 Short-range compared with long-range correlated noise7 Time correlation in financial time series7．1 Autocorrelation function and spectral density7．2 Higher-order correlations： The volatility7．3 Stationarity of price changes7．4 Summary8 Stochastic models of price dynamics8．1 Levy stable non-Gaussian model8．2 Student's t-distribution8．3 Mixture of Gaussian distributions8．4 Truncated Levy fiight9 Scaling and its breakdown9．1 Empirical analysis of the S&P 500 index9．2 Comparison with the TLF distribution9．3 Statistical properties of rare events10 ARCH and GARCH processes10．1 ARCH processes10．2 GARCH processes10．3 Statistical properties of ARCH／GARCH processes10．4 The GARCH（1，1） and empirical observatins10．5 Summary11 Financial markets and turbulence11．1 Turbulence11．2 Parallel analysis of price dynamics and fiuld velocity11．3 Scaling in turbulence and in financial markets11．4 Discussion12 Correlation and anticorrelation between stocks12．1 Simultaneous dynamics of pairs of stocks12．1．1 Dow-Jones Industrial Average portfolio12．1．2 S&P 500 portfolio12．2 Statistical properties of correlation matrices12．3 Discussion13 Taxonomy of a stock portfolio13．1 Distance between stocks13．2 Ultrametric spaces13．3 Subdominant ultrametric space of a portfolio of stocks13．4 Summary14 Options in idealized markets14．1 Forward contracts14．2 Futures14．3 Options14．4 Speculating and hedging14．4．1 Speculation： An example14．4．2 Hedging： A form ofinsurance14．4．3 Hedging： The concept of a riskless portfolio14．5 Option pricing in idealized markets14．6 The Black & Scholes formula14．7 The complex structure of financial markets14．8 Another option-pricing approach14．9 Discussion15 Options in real markets15．1 Discontinuous stock returns15．2 Volatility in real markets15．2．1 Historical volatility15．2．2 Implied volatility15．3 Hedging in real markets15．4 Extension of the Black & Scholes model15．5 SummaryAppendix A： Notation guideAppendix B： MartingalesReferencesIndex