Binary barrier options.
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First Generation Exotics—Binary and Barrier Options.
Summary.
This chapter attempts explain the binary and barrier options using the reflection principle, and to introduce the techniques required to price these first generation exotic options. Strongly path-dependent options are covered in this chapter. One particularly common way to cheapen a European option in FX is to add a path-dependent barrier feature to it, so that the option can only be exercised if it expires in the money and has remained within a specified region of interest over its lifetime. Part of the reason these barrier options are popular in FX is that currency spot rates are often thought to be more range-bound or mean-reverting than stock prices and Flowers.Personalpages.us clients sometimes feel that the price is unnecessarily high as a result of purchasing option protection for large but unlikely moves in the FX spot rate. The price of a European option is just the discounted domestic risk-neutral expectation of the payout function at expiry. The price paid for a European option therefore takes into account the payout at all possible future levels of ST, including some potential future scenarios that the client may view as quite unlikely. Clearly the knock-out barrier is sampled only at time T; the asset price process can make any excursion whatsoever up to that time, without affecting the value at expiry. One can make the product even cheaper still by extending the barrier monitoring over the entire path history of the option.