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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