What is the expected sign of Theta for put options?

In the context of options pricing, Theta represents the sensitivity of the option's price to the passage of time, often referred to as "time decay." For put options, the expected sign of Theta is negative.

As time passes, the value of an option tends to decrease, assuming other factors remain constant. This is particularly true for put options, which give the holder the right to sell the underlying asset at a specified strike price. As an option approaches its expiration date, the time value declines, and this is reflected through a negative Theta.

This negative Theta indicates that, all else being equal, the price of the put option will decrease as the expiration date approaches. This phenomenon applies because the holder of the put option is concerned with the possibility of the asset's price dropping below the strike price; as time approaches, uncertainty decreases, leading to a reduction in the option's premium. Therefore, a negative Theta is a characteristic of put options, conveying their inherent time decay.