Determine the probability that a normally distributed random variable lies inside a given confidence interval.
If the natural logarithms lnX of a random variable X are normally distributed, we say that the random variable X is lognormally distributed. See fig. 7 for details.
A lognormal distribution
- is bounded below by zero and
- is skewed to the right, i.e. it has a long right tail.
Therefore, observe the following.
- The lognormal distribution is an accurate description of the distribution of prices.
- The normal distribution is useful for approximating returns.
Memorize the expected mean and variance of a lognormal distribution:
Normal distribution X ~ N(μ, σ2)
Standard normal distribution N(0,1)
Lognormal distribution lnX
e2μ + σ∙σ∙(eσ∙σ - 1)
Tab. 9: Expected value and variance