6
Barrier Options

6.1 A TAXONOMY OF BARRIER OPTIONS

Barrier options are the most commonly traded kind of exotic options in the FX market. They are employed in structures devised to hedge the FX risk of the cash flows of a corporate, and to take exposures to sophisticated views on the FX spot rates by speculators. As such they engender the most relevant risks of the book of a typical market maker. We will start with the taxonomy of a different kind of barrier option, including also the touch-type exotic products in this broad category.
Let us start with barrier options. The main feature, common to all these kinds of exotic contracts, is the presence of a barrier whose breaching triggers a given event.
 
Definition 6.1.1. Barrier FX option contract. An XXXYYY barrier option is a contract in all respects equal to an otherwise identical plain vanilla option, the only difference being that the terminal payoff is contingent on the knocking of a predefined level by the underlying FX spot rate.77
 
More specifically, knock-in options pay the terminal value only if, during the life of the contract, the barrier is breached at least once, whereas knock-out options pay their value at expiry only if the barrier level is never touched. If the barrier is set at a level with respect to which the terminal value of the option is out-of-the-money, the contract is considered a standard barrier; on the contrary, if the terminal value is in-the-money then the contract is denominated as a reverse

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