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Quantitative Methods - Lognormal distribution

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Quantitative Methods

Lognormal distribution

{*LOSnr43*}

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{*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.

image
Lognormal distribution

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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

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  • 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