Lognormal dististbution

A random variable is lognormally distributed if the natural log of the random variable follows a normal distribution. It is usually used to model asset prices.

Y=e^x

Properties of lognormal dististbution :

• Y is never be zero or negatve
• Y is not symmetrical, skewed to the right
  

Notes:

• E(Y)≠e^E(X), E(Y)>^eE(X) , Var(Y)≠e^var(X) but not clear which is greater
• Increase in E(X) leads to increase in E(Y) & var(Y)
• Increase in Var(X) leads to increase E(Y) & Var(Y)
• (Y)=e^{E(X)+Var(x)/2}, Var(Y)=e^2E(X)+Var(X) - (e^Var(X)-1)

My tips:

• No need to memorize the above ugly formula, but need to understand the indication of the direction of change.