Valueing binary options
Where F i is the forward value of the interbank rate, X is the cut off rate, σ is the volatility of F i , zc t is the t- period spot rate / zero coupon rate and t i is the time from the valuation date to time i.
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Other possibilities exist, for example an Asian option , but we will not consider these in this document (nor are the functions relevant for any other cases).
It appears, based on a recent article , that regulators in different countries do not know whether to classify binary options as a financial instrument or gambling. This statement shows a shallow understanding of binary options as well as financial instruments. There are a number of types of binary options and this article appears to imply that there is only one. For example, there are fully regulated binary options that trade on the NYSE and NADEX . There is also a Binary Options Exchange where you can be the writer and seller of binary options.
In single barrier options, it is easy to show that barrier options with a knock-in feature can be priced by buying an option without any knock-out feature and selling a knockout option. The same approach can be used in one-touch double barrier binary options. For example, an American binary option with a knock-in barrier H, the option premium is equal to buying an American binary option and selling an American binary knock-out option with a barrier at H. All the options have the same payment barrier (Hui, 1996, p 347).