long, 93
short, 93
Positive excess kurtosis. See
Leptokurtosis
Present value, 8–9
Present-value pricing model. See Discounted-
cash-flow pricing model
Price
exercise, 94
option, 96
spot, 94
strike, 94
Price-demand relations, 138–139, 138f,
139f
Pricing model
discounted-cash-flow, 8–9
future value, 9
given future value, 9
present-value, 8
Probability density function, 16
Process
anti-persistent, 63
autoregressive, 43
compound stochastic, 92
homoskedastic, 51–54
independently and identically distributed
(IID), 33
Markov, 29–32
mean-reverting, 42
multiplicative, 64
persistent, 62
scale-free, 26
standard Wiener, 31–32, 34–35
stationary, 49
stochastic, 29–42
Profits and losses (P/L), 122, 123f, 124f
Put-call parity, 96
Q
Quasi-periodic attractors, 78
Quasi-periodicity, 83
R
Random walk, 12–13, 44
continuous-time, 34
with drifts, 45
Rate of return, 139
Rates
firm, 141
foreign exchange, 141
indicative, 141
Rational bubble, 9
Rational investors, 12–13
Rescaled range (R/S) analysis, 63, 88
Return
compounded, 8
log, 8
required rate of, 10
simple, 7
Return on Equity (ROE), 117
Rho, 104
Riemann integral, 36
Riemann-Stieltjes integral, 36–37
Risk
cash-flow, 121
coherent, measures, 124
credit, 121
liquidity, 121
market, 121
operational, 121
Risk-free asset, 130–131. See also Bond
Risk-neutral valuation, 99
Risk-return trade off line, 112
Risky asset, 130–131
ROE. See Return on Equity
R/S. See Rescaled range analysis
S
Santa Fe artificial market, 133
Scale-free process, 26
Scaling function, 66–67
Seasonal effects, 45–46
166 Index
Security market line, 115
Self-affine object, 59
Self-affinity, 59
Sharpe ratio, 115
Short
position, 93
selling, 6
Simple return, 7
Simultaneous equation, 54
Skewness, 19
S&P 500 index, 24f, 87
returns of, 89
Stable distribution, 25
Standard deviation, 18
Standard Wiener process, 31–32, 34–35
Stationary process, 49
non-, 49
Statistical arbitrage, 14
Stieltjes integral, 37
Stochastic
compound, process, 92
differential equation, 35
integral, 36–39
Ito’s integral, 38–39
process, 29–42
trend, 49–50, 50f
Stochastic trend v. deterministic trend, 49–50,
50f
Stop orders, 6
Stratonovich’s integral, 39
Strict stationarity, 49
Submartingale, 40
Super-efficient portfolio, 114
Supermartingale, 40
T
Technical analysis, 12
Term structure, 104–105
Theta, 103
Tick, 6
Tick-by-tick data, 6–7
Traders
regular, 139–141
technical, 139–141, 140f
Trajectory, 71, 76f, 77–79, 78f, 79f
Trend
deterministic, 49–50, 50f
stochastic, 49–50
Truncated Levy flight, 26–27, 88–89
U
Uniform distribution, 20
standard, 20
Unit root, 45
Univariate time series, 43
V
Value at risk (VaR), 122–124, 123f
conditional, 141
Van der Pol
equation, 77–78
oscillator, 78f
VAR. See Vector autoregressive model
VaR. See Value at risk
Variance, 18
matrix, 19
Variate, 16
Vector autoregressive model (VAR), 55–56
Vega, 104
Volatility, 19
implied, 103
smile, 104
Volatility smile, 104–105
W
Weak stationarity, 49
White noise, 33, 43
non-, 39
Wiener process
standard, 31–32, 34–35
Z
Zipf’s law, 89
Index 167
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