A contingent premium option in which premium is only paid at expiration date. The amount of the premium depends on how long the option was in the money. In other words, the two parties initially agree on a specific premium level which would be adjusted at maturity by relating the number of days the option was in the money to the number of days in its entire life. No premium would be expected if the option was not in the money on at least one day during its time to expiration. The initial premium of a time discount option is generally larger than that of a regular option with similar features.