A European put option is a financial derivative that gives the person who holds it the ability to sell some amount of an underlying asset. There are several different characteristics outlined in every option contract that define the ways in which a holder may use the option. The designations of European and put describe the ability that holding the option confers to the holder: "put" means that he may sell the underlying asset, while "European" means that, if an exercise occurs, it must be on a specific date.
Options all have certain characteristics: an underlying asset, which is what the holder may buy or sell; an expiration date, after which the option is invalid; and a strike or exercise price, at which the holder may trade the underlying. The two principle kinds of options are puts and calls. A put guarantees the holder the ability to sell the underlying, while a call is an option to buy. The holder of an option does not have to exercise it, but the issuer, or writer, of the option has the obligation to follow through with the trade if the holder does decide to exercise the option.
A European put option is one that the holder may only choose to exercise at its expiration date. In contrast, American options may be exercised at any point from the time they are purchased until the time at which they expire. American options have greater flexibility. This means that an American put option will have a higher value than an otherwise identical European put option because investors are willing to pay a premium to have the ability to create a wider range of strategies in response to changes in market conditions.
Analysts are interested in the way the values of options change in response to certain market variables because this helps them create trading strategies. They use the derivatives of the option value functions from options pricing models to determine the rate of change of the option value with respect to market variables. Each has a name; theta is the name for the rate of change of the option value over time. Theta is also called time decay because, generally, options lose value over time — in other words, theta is negative. A European put option that is in the money, which means that its strike price is above the market price, is the only kind of option whose value may rise over time, indicating a positive theta.