Preface |
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viii | |
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1 | (7) |
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1 | (1) |
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2 | (2) |
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4 | (1) |
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5 | (3) |
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Efficient market hypothesis |
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8 | (6) |
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Concepts, paradigms, and variables |
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8 | (1) |
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8 | (1) |
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Efficient market hypothesis |
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9 | (2) |
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Algorithmic complexity theory |
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11 | (1) |
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Amount of information in a financial time series |
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12 | (1) |
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Idealized systems in physics and finance |
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12 | (2) |
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14 | (9) |
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One-dimensional discrete case |
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14 | (1) |
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15 | (2) |
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17 | (2) |
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19 | (2) |
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20 | (1) |
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20 | (1) |
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21 | (2) |
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Levy stochastic processes and limit theorems |
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23 | (11) |
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23 | (3) |
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Scaling and self-similarity |
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26 | (1) |
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Limit theorem for stable distributions |
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27 | (1) |
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28 | (1) |
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The St Petersburg paradox |
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28 | (1) |
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Power laws in finite systems |
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29 | (1) |
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29 | (2) |
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Infinitely divisible random processes |
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31 | (2) |
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31 | (1) |
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31 | (1) |
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Gamma distributed random variables |
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32 | (1) |
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Uniformly distributed random variables |
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32 | (1) |
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33 | (1) |
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34 | (10) |
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Price scales in financial markets |
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35 | (4) |
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Time scales in financial markets |
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39 | (4) |
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43 | (1) |
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Stationarity and time correlation |
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44 | (9) |
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Stationary stochastic processes |
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44 | (1) |
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45 | (4) |
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Short-range correlated random processes |
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49 | (1) |
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Long-range correlated random processes |
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49 | (2) |
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Short-range compared with long-range correlated noise |
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51 | (2) |
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Time correlation in financial time series |
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53 | (7) |
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Autocorrelation function and spectral density |
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53 | (4) |
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Higher-order correlations: The volatility |
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57 | (1) |
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Stationarity of price changes |
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58 | (1) |
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59 | (1) |
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Stochastic models of price dynamics |
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60 | (8) |
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Levy stable non-Gaussian model |
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61 | (1) |
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62 | (1) |
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Mixture of Gaussian distributions |
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63 | (1) |
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64 | (4) |
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Scaling and its breakdown |
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68 | (8) |
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Empirical analysis of the S&P 500 index |
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68 | (4) |
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Comparison with the TLF distribution |
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72 | (2) |
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Statistical properties of rare events |
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74 | (2) |
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76 | (12) |
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77 | (3) |
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80 | (1) |
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Statistical properties of ARCH/GARCH processes |
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81 | (4) |
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The GARCH (1,1) and empirical observations |
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85 | (2) |
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87 | (1) |
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Financial markets and turbulence |
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88 | (10) |
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89 | (1) |
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Parallel analysis of price dynamics and fluid velocity |
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90 | (4) |
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Scaling in turbulence and in financial markets |
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94 | (2) |
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96 | (2) |
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Correlation and anticorrelation between stocks |
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98 | (7) |
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Simultaneous dynamics of pairs of stocks |
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98 | (5) |
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Dow--Jones Industrial Average portfolio |
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99 | (2) |
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101 | (2) |
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Statistical properties of correlation matrices |
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103 | (1) |
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103 | (2) |
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Taxonomy of a stock portfolio |
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105 | (8) |
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105 | (1) |
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106 | (5) |
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Subdominant ultrametric space of a portfolio of stocks |
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111 | (1) |
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112 | (1) |
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Options in idealized markets |
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113 | (10) |
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113 | (1) |
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114 | (1) |
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114 | (1) |
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115 | (3) |
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116 | (1) |
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Hedging: A form of insurance |
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116 | (1) |
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Hedging: The concept of a riskless portfolio |
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116 | (2) |
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Option pricing in idealized markets |
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118 | (2) |
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The Black & Scholes formula |
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120 | (1) |
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The complex structure of financial markets |
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121 | (1) |
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Another option-pricing approach |
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121 | (1) |
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122 | (1) |
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123 | (7) |
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Discontinuous stock returns |
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123 | (1) |
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Volatility in real markets |
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124 | (3) |
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124 | (1) |
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125 | (2) |
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127 | (1) |
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Extension of the Black & Scholes model |
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127 | (1) |
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128 | (2) |
Appendix A: Notation guide |
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130 | (6) |
Appendix B: Martingales |
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136 | (1) |
References |
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137 | (8) |
Index |
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145 | |