232 Frequently Asked Questions In Quantitative Finance

R

andom variables can be continuous or discrete

(the latter denoted below by∗). Or a combination.

New distributions can also be made up using random

variables from two or more distributions.

Here is a list of distributions seen in finance (mostly),

and some words on each.

Normal or Gaussian This distribution is unbounded below

and above, and is symmetrical about its mean. It has

two parameters:a, location;b>0 scale. Its probability

density function is given by

1

√

2 πb

e

−(x−a)

2

2 b^2.

This distribution is commonly used to model equity

returns, and, indeed, the changes in many financial

quantities. Errors in observations of real phenomena

are often normally distributed. The normal distribution

is also common because of theCentral Limit Theorem.

Mean

a.

Variance

b^2.

Lognormal Bounded below, unbounded above. It has

two parameters:a, location;b>0 scale. Its probability

density function is given by

1

√

2 πbx

exp

(

−

1

2 b^2

(ln(x)−a)^2

)

x≥ 0.

This distribution is commonly used to model equity

prices. Lognormality ofpricesfollows from the assumption

of normally distributedreturns.