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# Binary Options

Last week, we went through the basics of traditional options including their terminology and payoff structure. Today we're going to talk about another, more complex, type of option: the binary (or 'digital') option. This type of option pays either one thing (for example a stock or cash) or nothing depending on the price of an asset relative to the strike price of the option.

Binary options are considered 'exotic' options because they are not traded on major exchanges the way traditional options are. However, they bear certain resemblances: they have a strike price, they are linked to an underlying asset, and they come in 'call' and 'put' varieties. Also, an investor can both buy ('long') and sell ('short') binary options. Unlike traditional options, binary options deliver either the underlying asset (in an asset-or-nothing binary option) or an amount of cash (in a cash-or-nothing binary option).

An asset-or-nothing call increases in value as the underlying asset appreciates relative to the strike price. The price an investor pays to buy the option is the option premium. However, it only pays off if the asset is worth more than the strike price.

A cash-or-nothing call is similar except it pays out a prespecified amount of cash instead of the asset itself.

Asset-or-nothing puts are a bit more confusing. Because they are puts, they pay out only if the underlying asset has decreased below the strike price. But because they deliver the underlying asset, the value of that payout declines as the value of the asset declines, leading to a somewhat unusual payoff structure.

Cash-or-nothing puts are more straightforward because they deliver a fixed cash amount.

Traditional call options can be decomposed as a long asset-or-nothing call and short K cash-or-nothing call options where K is the strike price of the options. Similarly, put options can be decomposed as long K cash-or-nothing puts and short an asset-or-nothing put where K is the strike price of the options. Binary options can be replicated to a certain approximation (and hedged) with traditional options, particularly a call spread strategy.

While binary options are unlikely to be purchased directly by retail investors, binary options are embedded in several types of retail investments, such as dual directional structured products and some structured CDs. We have created a spreadsheet (Excel format) that graphs and values binary options given certain user inputs. We encourage you to play around with these values to get a sense for the complexity of these options.