Rex bought a put on Alpha stock with a strike price of $35 when the market price of Alpha stock was $33 a share. Alpha is currently selling at $34 a share. Which of the following statements are true given this information? I. Rex's option is worth at least $100 today. II. Rex's option is worthless today. III. Rex's option has more value today than when he bought it. IV. Rex's option has less value today than when he bought it.