Consider three at-the-money (ATM) European PUT options (i.e., S = X for each of them) written on the same underlying asset, with the following common parameter values: r = 0% p.a. and sigma = 100% p.a. However, one of the options matures in T = 12 months, another in T = 24 months, and the last one matures in 36 months. Based on the premiums of these three put options, what do you conclude regarding the relationship between the put premium and time to maturity?

The put option premium decreases as time to maturity increases.

There is no relationship between the put option's premium and its time to maturity.

The put option premium remains the same as time to maturity increases.

The put option premium increases as time to maturity increases.

The relationship between the put option's premium and its time to maturity is U-shaped.