An option “paper” is a right but not an obligation, so its holder has no obligation, so this paper is always worth a non-negative value.
if the option holder forgets it, she could get automatically exercised or receive the cash-settlement income. No one would go after her.
In contrast, an obligation requires you to fulfill your duty.
A fwd contract to buy some asset (say oil) is an obligation, so the pre-maturity value can be negative or positive. Example – a contract to “buy oil at $3333” but now the price is below $50. Who wants this obligation? This paper is a liability not an asset, so its value is negative.
