Down-and-In Option

A down-and-in option is a type of knock-in barrier option that only becomes viable when the price of the underlying security falls to a specific price level, called the barrier price. If the price does not drop to the barrier level, the option never becomes active and expires worthless. If the price reaches the barrier, the option becomes active and acts like any other option by giving the holder the right but not the obligation to exercise their call or put option at the strike price on or before the expiration date specified in the contract.

Considered an exotic option, a down-and-in option is one of two types of knock-in barrier options, the other being an up-and-in option. Both kinds come in the put and call varieties. A barrier option is a type of option where the payoff, and the very existence of the option, depends on whether or not the underlying asset reaches a predetermined price. A barrier option can be a knock-out. A knock-out means it expires worthless if the underlying reaches a certain price, limiting profits for the holder and limiting losses for the writer. The barrier option can also be a knock-in. As a knock-in, it has no value until the underlying reaches a certain price.

The critical concept is if the underlying asset reaches the barrier at any time during the option's life, the option is knocked in, or brought into active existence, and will remain that way until expiration. It does not matter if it moves back to pre-knock-in levels.

For example, a down-and-in option has a strike price of 100 and a knock-in price of 80. At the option's inception the price of the stock was 95, but before the option became viable, the price of the stock must dip to 80. If it doesn't then the option automatically expires worthless even if the underlying hits 100 before the exercise date.

A down-and-in option can be a call or put. Both get knocked in if the underlying falls to the barrier price.

For an up-and-in option, if the underlying rises to the barrier price, then the option becomes viable. Both calls and puts will expire worthless if the underlying never rises to its barrier price.

Large institutions or market makers create these options by direct agreement, for the primary reason that valuing them is a complex undertaking. For example, a portfolio manager can use them as a less expensive method to hedge against losses on a long position. The hedge would be less costly than buying vanilla put options. However, it would be imperfect since the buyer would be unprotected if the security price decreased below the barrier price.

Pricing depends on the all regular options metrics with the knock-in feature adding an extra dimension. European style expirations, where the exercise may only happen at the expiration date, are complicated enough. However, an American style option, where the holder may exercise the option at any time on or before expiration, is even more complicated.