A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Node

TL;DR

This paper introduces a fast and accurate numerical method for pricing discrete double barrier options using Lagrange interpolation on Jacobi nodes, with CPU time unaffected by the number of monitoring dates.

Contribution

The paper develops a novel recursive integral approach combined with Lagrange interpolation on Jacobi nodes, significantly improving computational efficiency for barrier option pricing.

Findings

Method achieves high accuracy in pricing

CPU time remains constant regardless of monitoring dates

Numerical results confirm efficiency and precision

Abstract

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.