Lognormal distribution

{*LOSnr43*}

Merke

Hier klicken zum Ausklappen

{*LOSnr44*}
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.

Lognormal distribution

Merke

Hier klicken zum Ausklappen

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.

Methode

Hier klicken zum Ausklappen
• 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:

 Distribution Mean Variance Normal distribution X ~ N(μ, σ2) μ σ2 Standard normal distribution N(0,1) 0 1 Lognormal distribution lnX μ0.5∙σ∙σ e2μ + σ∙σ∙(eσ∙σ - 1)

Tab. 9: Expected value and variance