Black-Scholes-Merton model assumptions (underlying return)


just a quick question, are the underlying returns distributed normally or lognormally?

I was sure that underlying RETURNS are distributed normally where underlying PRICES are distributed lognormally, but I found some inconsistency between Schweser readings and Schweser questions.


Asset price are lognormal.

So price reltives must also be lognormal Pt/Pt-1 can’t go below zero.

So that’s why we take the natural log Ln(Pt/Pt-1) this is normally distributed.

So if you said returns are normally distributed you’d be incorrect but if you say the log of the returns are normally distributed you’d be correct.

I think you may have missed this nuance from the Schweser books.