There is one problem that bothers me:
Let’s say I buy a European put option with a certain maturity date with premium \$1.6 Suppose that the market price of the put option rises before maturity (\$3) and that I sell it to earn the difference in the market prices of the option (\$1.4),
will I become the writer/seller of the option? In other words, will my payoff at maturity be $-\max\{ K-S_T,0 \}$?
But if that is the case, and I sell the put option to buyer $B$, who later re-sells it to another buyer $C$ (who holds until maturity), will buyer $B$ be the new writer of the option, who bears responsibility of the purchase at maturity?