Chapter 7
Barrier Options
7.1 Introduction
Barrier options are an important class of exotic options which are traded in the FX and OTC markets. They are our first examples of path dependent options. Such options have payoffs which depend, at least in part, on some aspect of the actual asset path traced out, and not just on the terminal value of the path. Barrier options have payoffs which depend on whether a given barrier level x = b is crossed or otherwise during the life of the option.
For any given payoff f(x) at time T in the future, there are four standard barrier options. These are referred to as the:
1. |
Down-and-out |
(D/O) |
barrier option |
2. |
Up-and-out |
(U/O) |
barrier option |
3. |
Down-and-in |
(D/I) |
barrier option |
4. |
Up-and-in ... |
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