I believe the correct answer is the final option - The narrator is unreliable because even though he denies he is mad, his actions say otherwise.
An unreliable narrator is a type of a narrator whom you cannot trust. This is because often this narrator says things that are nonsensical, or paradoxical, or just plain ambiguous so you don't know what he or she is talking about. In this case, the narrator claims he is not mad, even though everything he does proves him otherwise.