Definition of 'Down-and-In Option'
A form of barrier option that becomes activated only if the price of the underlying asset falls below a pre-determined barrier price level during the life of the option. In a down-and-in option, the barrier level is set at some level below the current spot or prevailing price of the underlying asset. If the asset price falls below the barrier level, it becomes activated and has value; if the asset price does not fall below the barrier level, the option expires worthless.
The opposite of a down-and-in option is a down-and-out option, which becomes null and void if the price falls below a certain barrier price. The biggest benefit of such barrier options is that premiums payable for them are cheaper than for plain-vanilla options.
Investopedia explains 'Down-and-In Option'
For example, consider a one-month down-and-in put option on a stock that is trading at $10, with a strike price of $9.50 and a barrier of $9. If the price of the stock falls below $9 before the one-month expiration of the option contract, the put option is activated and the buyer has the right to sell the stock at the strike price of $9. On the other hand, if the stock does not fall below the $9 barrier, the put option is not activated and will expire worthless.