Numerical method of pricing discretely monitored Barrier option

A Barrier option is an option whose payoff depends on the underlying asset prices during the life of the option. Most Barrier option pricing usually assumes the continuous monitoring of the barrier. However, Barrier options traded in markets are discretely monitored and in this discretely monitoring case there are no closed form solutions available. In this paper we use four different recombining quadrature methods, which are a kind of recombining multinomial tree, to price a discretely monitored Single Barrier option. We compare these recombining multinomial tree methods with the existing trapezoidal, Simpson and Milev–Tagliani (2010) methods. We find that all four recombining methods outperform the classical trapezoidal and Simpson methods, while Clenshaw–Curtis (CC), Gauss–Legendre–Lobatto (GLL) and Milev–Tagliani methods are comparable in convergence speed. More interestingly, among the four recombining methods, Fejér and Gauss–Legendre methods, which do not use the barrier as an end point, outperform Clenshaw–Curtis and Gauss–Legendre–Lobatto methods, which do use the barrier as an end point.