10. The Lognormal Distribution

o. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;

What is a lognormal distribution?
A random variable, Y, follows a lognormal distribution if its natural logarithm, lnY, is normally distributed. You can think of the term lognormal as "the log is normal." For example, suppose X is a normal random variable, and Y = e^X. Therefore, Ln(Y) = Ln(e^X) = X. Because X is normally distributed, Y follows a lognormal distribution.

Just like the normal distribution, what two parameters completely describe a lognormal distribution?
Mean and variance can completely describe both a normal and lognormal distribution. However, unlike a normal distribution the mean and variance for a lognormal distribution are not identical.

What is the lower bound of a lognormal distribution?
Zero

Which direction does a lognormal distribution skew?
Always to the right. It is bounded at 0 and skews to the right

Source:

• CFA