European High-Dimensional Option Pricing using Backward Stochastic Differential Equation-Based Convolutional Neural Network

Aldi Eka Wahyu Widianto, Endah Rokhmati Merdika Putri, Imam Mukhlash, Mohammad Iqbal

Abstract: Options, as financial derivatives, play a crucial role in hedging against financial risks in global markets. The pricing of options has been a topic of extensive research, particularly for high-dimensional options. Traditional methods such as the binomial tree and finite difference methods are impractical for solving high-dimensional options due to the curse of dimensionality. Additionally, simulation-based methods like Monte Carlo is highly dependent on variance, posing challenges in accurately pricing high-dimensional options. In recent years, a method with a backward stochastic differential equation (BSDE) -based deep neural networks (DNNs) approach called the Deep BSDE method has shown a promising result on solving a 100-dimensional European option. This approach addresses the limitations of traditional methods. However, the Deep BSDE method utilizes a sequence of feedforward networks (FNNs) that neglects the temporal information of underlying assets price dynamics, and the number of parameters depends on the number of discretization time steps. In this paper, we propose an alternative network, namely the convolutional neural network (CNN) to overcome these problems. We demonstrate that by employing this network, we can price high-dimensional options with higher accuracy and reduced computational time. Our results show that our network performs up to 2.9 times faster than the sequence of FNNs used in the Deep BSDE method.