Put options at a given strike price cost less (or more) in a rising (or falling) market because the the put option gives the right to have sold Dec’22 futures at a specified level ($1.20 in this example). This option has intrinsic value only when the underlying futures is below $1.20. Therefore, put option premiums move opposite of the direction of the underlying futures price. This is important because an increasing put option premium can act as an insurance payment against falling futures and (assuming a stable cash basis) falling cash prices.
In the chart below, as Dec’22 cotton futures (the blue line) plunged in June after trending higher for the preceding year. Dec’22 futures settled at 96.21 cents per pound on July 28.
Back when Dec’22 was trading at 120.10 cents per pound, the associated premium for a $1.20 put option was 10.41 cents per pound. Buying it at that level was essentially buying the right to a 109.59 cent short futures position. This implied a minimum cash price around 105 per pound with upside potential and no margin call exposure. Since the plunge in Dec’22 futures, the $1.20 put was worth 27.15 cents per pound on August 4.