A contingent premium option is a European option whose premium is deferred to expiration and is paid only if the option expires in-the-money. If it expires at-the-money or out-of-the-money, no premium is paid and the option expires worthless.
The expiration value (which equals the payoff) of a contingent premium call is shown in Exhibit 1. Obviously, the holder of the option will lose money if the option expires only slightly in the money. The purchaser is betting that the option will either not expire in the money or that it will expire far in the money.
A derivatives dealer can assemble a contingent premium option from more simple instruments. For example, a contingent premium call can be assembled by selling a cash-or-nothing binary call option and using the proceeds to purchase a vanilla call. The contingent premium option can be priced by valuing the constituent parts.