Barrier Option

A barrier option is a type of derivative where the payoff depends on whether or not the underlying asset has reached or exceeded a predetermined price. A barrier option can be a knock-out, meaning it expires worthless if the underlying exceeds a certain price, limiting profits for the holder and limiting losses for the writer. It can also be a knock-in, meaning it has no value until the underlying reaches a certain price. 

Barrier options are considered exotic options because they are more complex than basic American or European options. Barrier options are also considered a type of path-dependent option because their value fluctuates as the underlying's value changes during the option's contract term. In other words, a barrier option's payoff is based on the underlying asset's price path. The option becomes worthless or may be activated upon crossing of a price point barrier. Barrier options are typically classified as either knock-in or knock-out.

A knock-In option is a type of barrier option where the rights associated with that option only come into existence when the price of the underlying security reaches a specified barrier during the option's life. Once a barrier is knocked in, or comes into existence, the option remains in existence until it expires.

Knock-in options may be classified as up-and-in or down-and-in. In an up-and-in barrier option, the option only comes into existence if the price of the underlying asset rises above the pre-specified barrier, which is set above the underlying's initial price. Conversely, a down-and-in barrier option only comes into existence when the underlying asset price moves below a pre-determined barrier that is set below the underlying's initial price.

Contrary to knock-in barrier options, knock-out barrier options cease to exist if the underlying asset reaches a barrier during the life of the option. Knock-out barrier options may be classified as up-and-out or down-and-out. An up-and-out option ceases to exist when the underlying security moves above a barrier that is set above the underlying's initial price. A down-and-out option ceases to exist when the underlying asset moves below a barrier that is set below the underlying's initial price. If an underlying asset reaches the barrier at any time during the option's life, the option is knocked out, or terminated.

Other variants of the barrier options described above are possible. Here are three of them:

1. Rebate Barrier Options: Both knock-out and knock-in barrier options can contain a provision to provide rebates to holders, if the option does not reach the barrier price and becomes worthless. Such options are known as rebate barrier options. Rebates, in such cases, take the form of a percentage of the premium paid by the holder for the option.
2. Turbo Warrant Barrier Options: Mainly traded in Europe and Hong Kong, Turbo warrant are a type of down-and-out option that are highly leveraged and are characterized by low volatility. They are popular in Germany and are used for speculation purposes.
3. Parisian Option: In a Parisian option, reaching the barrier price does not trigger the contract. Instead the underlying asset's price has to spend a pre-defined amount of time beyond the trigger barrier price for the contract to kick in. The amount of time that the underlying asset's price spends outside and inside the barrier price range is measured in this type of option.

Because barrier options have additional conditions built in, they tend to have cheaper premiums than comparable options with no barriers. Therefore, if a trader believes the barrier is unlikely to be reached, then they may opt to buy a knock-out option, for example, since it has a lower premium and the barrier condition is unlikely to affect them. 

Someone who wants to hedge a position, but only if the price of the underlying reaches a specific level, may opt to use knock-in options. The lower premium of the barrier option may make this more appealing than using non-barrier American or European options.

Here are two examples of barrier options described above.

Knock-In Barrier Option

Assume an investor purchases an up-and-in call option with a strike price of $60 and a barrier of $65, when the underlying stock is trading at $55. The option would not come into existence until the underlying stock price moved above $65. While the investor pays for the option, and the potential that it could become valuable, the option only becomes applicable if the underlying reaches $65. If it doesn't, the option is never triggered and the option buyer loses what they paid for the option.

Knock-Out barrier option

Assume a trader purchased an up-and-out put option with a barrier of $25 and a strike price of $20, when the underlying security was trading at $18. The underlying security rises above $25 during the life of the option, and therefore, the option ceases to exist. The option is now worthless, even if it only touched $25 briefly and then dropped back below.