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