The Black-Scholes-Merton model assumes that the prices of the underlying asset at maturity are log-normally distributed. I understand that this assumes that the prices can never go below zero.
However, there are cases where the underlying asset's price can be negative. For example:
- With (hypothetical) unlimited liability companies, the stock price can go below zero.
- With commodity futures, the futures price can go below zero.
In these cases, is a normal distribution a better assumption than a log-normal distribution?