A down-and-out barrier option is a barrier option which gives its holder the right to buy or sell an underlying asset if the price of the underlying asset does not reach or fall below a predefined barrier level (the knock-out price in this case) over the option’s lifetime.
Down-and-out barrier options are used by investors who believe that the price of a specific asset will either remain stable or increase within a certain time frame.
When a down-and-out barrier option is created, the buyer of the option and the owner of the underlying assets agree to a strike price. This is the price at which the option buyer will be entitled to purchase the underlying assets if their price does not reach or fall below the barrier level within the option term.
The buyer of the option pays a premium to the asset owner for the option and the rights which it grants. If the price of the underlying asset reaches or falls below the barrier level within the option term, the down-and-out barrier option becomes invalid.
A down-and-out barrier option can be a call option (meaning it grants its holder the right to buy underlying assets if it becomes exercisable) or a put option (meaning it gives its holder the right to buy underlying assets if it becomes exercisable). Put options are held asset owners and grant them the right to sell the underlying assets to an investor if the option becomes exercisable. When a put option is created, the asset owner pays an option premium to the investor who promises to buy their assets at the strike price if the barrier level is reached or surpassed and the option becomes exercisable.
Down-and-out barrier option example 1:
An investor enters into a down-and-out barrier call option contract with the owner of 100,000 shares in a stock which is listed at 2 Swiss francs per share at the time of the option contract’s creation.
The investor and the asset owner agree to a barrier level of 1.70 francs and a strike price of 1.75 francs. The option term of 5 days.
The owner of the shares charges the investor a premium of 0.02 francs per underlying share. The total option premium is 2000 francs.
Over the 5-day term, the price of the underlying stock falls to 1.79 francs at its lowest point.
At the end of the 5-day term, the option is in the money by 0.09 francs. The investor can exercise his right to purchase the shares at the predetermined strike price of 1.75 francs per share, or a total cost of 175,000 francs. The investor can then sell the shares After deducting the amount spent on the option premium (2000 francs), the investor is left with a gain of 2000 francs.
Down-and-out barrier option example 2:
Using the down-and-out barrier option in the above example, if the price of the underlying stock had fallen to 1.70 during the option term, the option would have become invalid, and the investor would have lost their 2000-franc investment in the option premium. The owner of the underlying assets would have made 2000 francs of profit through the option premium.