An option whose payoff shows a singularity jumping from zero to a positive value. In other words, this option has a fixed singular payoff that depends on a specific condition being met. Basically, singular payoff options are path independent because the payoff is not a function to the values taken by the underlying price or rate over the option’s life.

Examples of this option include binary options and contingent premium options. The latter can be decomposed into vanilla options and binary options.