The binary gap option has a payout that depends on two strikes. One strike (K1) determines if there is goin to be a payout, while the other strike (K2) determines the payout amount.
Some properties
When K2=0 the binary gap call option reduces to a binary asset-or-nothing call, while the put reduces to -1*a binary asset-or-nothing put.
When K2=K1 the binary gap option reduces to a vanilla option.
The binary gap call is equivalent to a vanilla call with strike K1 + a binary cash-or-nothing call with K2. The binary gap put is equivalent to a vanilla put with strike K1 - a binary cash-or-nothing put with K2.
 gap option.png "Binary (digital) gap option equation")
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