A perpetual option is a non-standard, exotic financial option without any pre-determined maturity date. It is a form of an American option. While the life of a standard option can range from a few days to several years, a perpetual option can be exercised at any time and without any expiration. They are also called non-expiring option and expireless option.
Perpetual option gives its holder the right, but not the obligation, to purchase (for a call option) or sell (for a put option) a specific amount of the underlying security for a predetermined (strike) price without expiration. For some investors these could represent an advantage over other types of options because the strike price on a perpetual option enables the holder to choose the moment for buy or sell underlying asset and their potential to buy/sell at that price doesn’t expire.
Also perpetual option can be preferable because they eliminate the expiration risk. For the American option, an optimal exercise strategy is a stopping time for which the maximum value of the expected discounted payoff is attained. For perpetual options, the optimization problem can be simplified as the problem of determining the optimal values of one or two parameters. In order to price these options, the conditions for when to optimally exercise must be established, which could be defined as when the underlying asset reaches the optimal price.
Perpetual options are not listed on exchanges. They are therefore only traded over-the-counter (OTC).