Lognormal distribution

From WilmottWiki

Jump to: navigation, search

The Lognormal distribution is a continuous probability distribution which is bounded below, unbounded above. It has two parameters: a, location; b>0 scale. Its probability density function is given by

\frac{1}{\sqrt{2\pi}\;b x}\exp\left(-\frac{1}{2b^2}\left(\ln(x)-a\right)^2\right)\;\;\;x \geq 0.

This distribution is commonly used to model equity prices. Lognormality of prices follows from the assumption of normally distributed returns.

Mean = e^{a+\frac{1}{2} b^2} and Variance = e^{2a+b^2} (e^{b^2}-1).

References

  • Spiegel, MR, Schiller, JJ, Srinivasan, RA 2000 Schaum's Outline of Probability and Statistics. McGraw-Hill
Personal tools

Certificate in Quantitative Finance - Sponsors of Wilmott Wiki