# A simple and efficient numerical method for pricing discretely monitored early-exercise options

## TL;DR

This paper introduces a simple, fast, and accurate quadrature-based numerical method for pricing discretely monitored early-exercise options within the Black-Scholes model, suitable for various structured products and options.

## Contribution

It proposes a novel quadrature technique that uses elementary calculations and a fixed grid, achieving high convergence rate and efficiency for pricing discretely monitored options.

## Key findings

- Convergence rate of $O(1/N^4)$
- Computational complexity of $O(MN ext{log} N)$
- Applicable to a wide range of options including barrier and Bermudan options

## Abstract

We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is $O(1/N^4)$ and the complexity is $O(MN\log N)$, where $N$ is the number of grid points and $M$ is the number of observation dates.