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Mean, 18 exercise price of, 94
reversion, 44 exotic, 141
squared error, 48 expiration date of, 94
Mean squared error (MSE), 48 long call, 95, 97f
Mean-reverting process, 42 long put, 95, 97f
Mean-square limit, 38 maturity of, 93“94
Mean-variance efficient portfolio, 108 premium of, 96
Median, 18 put, 94
Microsoft Excel, 4, 25 short call, 95, 97f
Mimetic contagion, 134 short put, 95“96, 97f
Minority game, 129“130 strike price of, 94
MLE. See Maximum likelihood estimate Orders
Mortgage-backed securities (MBS) limit, 6
arbitrage, 119 market, 6
Moving average model, 45“47 stop, 6
autoregressive, 45“46 Ordinary least squares (OLS), 48
invertible, 46“47 Ornstein-Uhlenbeck equation, 42
MSE. See Mean squared error
Multifractal, 63“64. See also Fractal
binomial measure, 64
P
cascade, 63“64
spectrum, 64
Multipliers, 64 Pair trading, 118
Multivariate time series, 54“57 Pareto distribution, 24, 26
Partition function, 67
Partly forcastable prices, 70
N Period-doubling, 82
Persistent process, 62
Noise anti-, 63
non-white, 38 P/L. See Profits and losses
white, 33, 43 Poisson distribution, 21
Nonanticipating function, 39 Portfolio
Non-equilibrium price models, 130, 134“136 delta-neutral, 106
Non-integrable system, 75 rebalancing, 106
Normal distribution, 21“22 well-diversified, 117
standard, 22, 24f Portfolio selection, 111“115
Notations, 4 Position
166 Index


R
long, 93
short, 93
Positive excess kurtosis. See Random walk, 12“13, 44
Leptokurtosis continuous-time, 34
Present value, 8“9 with drifts, 45
Present-value pricing model. See Discounted- Rate of return, 139
cash-flow pricing model Rates
Price firm, 141
exercise, 94 foreign exchange, 141
option, 96 indicative, 141
spot, 94 Rational bubble, 9
strike, 94 Rational investors, 12“13
Price-demand relations, 138“139, 138f, Rescaled range (R/S) analysis, 63, 88
139f Return
Pricing model compounded, 8
discounted-cash-flow, 8“9 log, 8
future value, 9 required rate of, 10
given future value, 9 simple, 7
present-value, 8 Return on Equity (ROE), 117
Probability density function, 16 Rho, 104
Process Riemann integral, 36
anti-persistent, 63 Riemann-Stieltjes integral, 36“37
autoregressive, 43 Risk
compound stochastic, 92 cash-flow, 121
homoskedastic, 51“54 coherent, measures, 124
independently and identically distributed credit, 121
(IID), 33 liquidity, 121
Markov, 29“32 market, 121
mean-reverting, 42 operational, 121
multiplicative, 64 Risk-free asset, 130“131. See also Bond
persistent, 62 Risk-neutral valuation, 99
scale-free, 26 Risk-return trade off line, 112
standard Wiener, 31“32, 34“35 Risky asset, 130“131
stationary, 49 ROE. See Return on Equity
stochastic, 29“42 R/S. See Rescaled range analysis
Profits and losses (P/L), 122, 123f, 124f
Put-call parity, 96

S
Q Santa Fe artificial market, 133
Scale-free process, 26
Quasi-periodic attractors, 78 Scaling function, 66“67
Quasi-periodicity, 83 Seasonal effects, 45“46
167
Index


Security market line, 115 deterministic, 49“50, 50f
Self-affine object, 59 stochastic, 49“50
Self-affinity, 59 Truncated Levy flight, 26“27, 88“89
Sharpe ratio, 115
Short
U
position, 93
selling, 6
Simple return, 7
Uniform distribution, 20
Simultaneous equation, 54
standard, 20
Skewness, 19
Unit root, 45
S&P 500 index, 24f, 87
Univariate time series, 43
returns of, 89
Stable distribution, 25
Standard deviation, 18
V
Standard Wiener process, 31“32, 34“35
Stationary process, 49
non-, 49 Value at risk (VaR), 122“124, 123f
Statistical arbitrage, 14 conditional, 141
Stieltjes integral, 37 Van der Pol
Stochastic equation, 77“78
compound, process, 92 oscillator, 78f
differential equation, 35 VAR. See Vector autoregressive model
integral, 36“39 VaR. See Value at risk
Ito™s integral, 38“39 Variance, 18
process, 29“42 matrix, 19
trend, 49“50, 50f Variate, 16
Stochastic trend v. deterministic trend, 49“50, Vector autoregressive model (VAR), 55“56
50f Vega, 104
Stop orders, 6 Volatility, 19
Stratonovich™s integral, 39 implied, 103
Strict stationarity, 49 smile, 104
Submartingale, 40 Volatility smile, 104“105
Super-efficient portfolio, 114
Supermartingale, 40

W
T Weak stationarity, 49
White noise, 33, 43
Technical analysis, 12 non-, 39
Term structure, 104“105 Wiener process
Theta, 103 standard, 31“32, 34“35
Tick, 6
Tick-by-tick data, 6“7

Z
Traders
regular, 139“141
technical, 139“141, 140f
Zipf™s law, 89
Trajectory, 71, 76f, 77“79, 78f, 79f
Trend

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