# A Numerical Method for Pricing Discrete Double Barrier Option by Legendre Multiwavelet

## TL;DR

This paper introduces a fast, efficient numerical algorithm based on Legendre multiwavelets for pricing discrete double barrier options, maintaining computational speed as monitoring dates increase.

## Contribution

It develops a novel Legendre multiwavelet-based recursive method for option pricing that is computationally efficient and convergent under the Black-Scholes model.

## Key findings

- CPU time remains nearly constant with more monitoring dates
- The method demonstrates high accuracy and efficiency
- Convergence rate of the algorithm is established

## Abstract

In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legendre multiwavelets as orthonormal basis functions and expressed in operational matrix form. The most important feature of this method is that its CPU time is nearly invariant when monitoring dates increase. Besides, the rate of convergence of presented algorithm was obtained. The numerical results verify the validity and efficiency of the numerical method.