Frequently Asked Questions In Quantitative Finance

Chapter 3: The Most Popular Probability Distributions 247

Exponential

0

0.2

0.4

0.6

0.8

1

00.511.522.533.54

a = 0

b = 1

Mean

a+b.

Variance

b^2.

L ́evy Unbounded below and above. It has four param-

eters:μ, a location (mean); 0<α≤2, the peakedness;

− 1 <β<1, the skewness;ν>0, a spread. (Conven-

tional notation is used here.) This distribution has been

saved to last because its probability density function

does not have a simple closed form. Instead it must be

written in terms of its characteristic function. IfP(x)

is the probability density function then the moment

generating function is given by

M(z)=

∫∞

−∞

eizxP(x)dx,