  In this paper, a rapid and high accurate numerical method for pricing
discrete single and double barrier knock-out call options is presented.
According to the well-known Black-Scholes framework, the price of option in
each monitoring date could be calculate by computing a recursive integral
formula upon the heat equation solution. We have approximated these recursive
solutions with the aim of Lagrange interpolation on Jacobi polynomials node.
After that, an operational matrix, that makes our computation significantly
fast, has been driven. The most important feature of this method is that its
CPU time dose not increase when the number of monitoring dates increases. The
numerical results confirm the accuracy and efficiency of the presented
numerical algorithm.
