Stable Distributions

Index

α-stable variable, 8

algorithm

Box-Muller, 9

asset return, 16

Black Monday, 18

Chambers-Mallows-Stuck method, 9

characteristic function, 4

distribution

Levy stable, 2

stable,

→ stable distribution

stable Paretian, 2

Dow Jones Industrial Average (DJIA),

18

extreme event, 2

Fourier transform, 5

function

characteristic,

→ characteristic function

goodness-of-fit, 18

Hill estimator, 11

stable distribution, 1

characteristic exponent, 2

density function, 6

direct integration, 6, 16

distribution function, 6

FFT-based approach, 6, 16

index of stability, 2

maximum likelihood method, 15

method of moments, 14

quantile estimation, 13

regression-type method, 14, 15

simulation, 8

skewness parameter, 2

tail exponent, 2

estimation, 11

tail index, 2

stable laws, 16

asset returns, 1

tail exponent, 2, 11

estimation, 11

log-log regression, 11

test statistic

Anderson-Darling, 18

Kolmogorov, 18

Monte Carlo
method, 18

power-law tail, 3

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