PPT 4.5 Lognormal Distribution

# PPT 4.5 Lognormal Distribution - McGill University Advanced...

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Unformatted text preview: McGill University Advanced Business Statistics MGSC-272 MGSC 272 Lognormal Distribution The Lognormal Distribution A continuous random variable X follows a lognormal distribution if its natural logarithm, ln(X), follows a normal distribution. The lognormal distribution is an asymmetric distribution with interesting applications for modeling the probability distributions of stock and other asset prices The Lognormal Distribution • Properties of the lognormal distribution – The lognormal distribution is skewed to the right – The lognormal distribution is strictly positive (i.e. bounded below by 0) – The lognormal distribution may be used to model data on asset prices (note that prices are bounded below by 0) The Lognormal Distribution • The lognormal distribution is described by two parameters, its mean and variance, as in the case of a normal distribution • The mean of a lognormal distribution X is given by where μ and σ 2 are the mean and variance of the normal distribution of the ln( X ) variable and e ≈ 2.718 is the natural base for logarithms. ( 29 2 2 1 ) ( σ μ + = e X E The Lognormal Distribution The variance of a lognormal distribution is given by 2 2 (2 ) Var ( ) ( 1) X e e μ σ σ + =- The Lognormal Distribution Observation • Recall that the exponential and logarithmic functions are inverse functions • This implies the following result •...
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PPT 4.5 Lognormal Distribution - McGill University Advanced...

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