Binary options, sometimes referred to as digital options, are options that pay out either a fixed amount or nothing.
Cash-or-nothing binary is like a standard vanilla option except that it pays a fixed cash amount if it expires in the money and nothing otherwise. For example, a cash-or-nothing call makes a fixed payment if the option expires with the underlying asset above the strike price. If the option expires with the underlying asset equal to or less than the strike price, then it pays nothing.
Asset-or-nothing binary, is like a Cash-or-nothing binary except that it pays the value of the underlying asset (as it was at expiration) if the option expires in the money. Like a Cash-or-nothing option the Asset-or-nothing option will pay nothing if the underlying asset is not greater than the strike price.
Binary barrier options are a cross between barrier options and binary options. In the case of an "up and in" or a "down and in" barrier, if the barrier is touched then a payout occurs, however if the barrier is not touched then no pay out occurs. In the case of an "up and out" or a "down and out" barrier, if the barrier is touched then no payout occurs. Binary barrier option can either be cash or asset, meaning that either the option pays out a fixed amount, as per Cash-or-nothing binary options, or the value of the underlying asset, as per Asset-or-nothing binary options.
Gap options are like standard vanilla options, in that the spot price must be above the strike price in order for there to be a pay out. The nature of the pay out is however different. A "payoff" strike price is subtracted from the spot to give the amount paid. This can cause the option to have a negative pay out (such options are sometimes referred to as pay-later options).
Supershare options, first introduced in November of 1976 by Nils Hakansson, pay out a proportion of the assets underlying a portfolio if the value of the portfolio lies between a lower and an upper bound at the expiry of the option. If the value is outside the bounds then the supershare option expires worthless.
Two-asset-cash-or-nothing options are cash or nothing options over two assets. There are four types of Two-asset-cash-or-nothing options, based on the relationship between the spot price, and the strike of the assets. For example in an "up and up" Two-asset-cash-or-nothing option the spot of both assets must be above the strike price of both assets, for a pay out to occur. If this is not the case then the option expires worthless. In an "up and down", the spot of the first asset must be above the first assets strike price and the spot of the second must be below the strike price of the second asset for a pay out to occur.
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