A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

Table 1

Payoff functions for different types of discretely monitored knock-out barrier options.

Option type	Payoff
Up-and-out call
Up-and-out put
Down-and-out call
Down-and-out put

is the observation date.