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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationICoMS 2023 - 2023 6th International Conference on Mathematics and Statistics
PublisherAssociation for Computing Machinery
Pages120-125
Number of pages6
ISBN (Electronic)9798400700187
DOIs
Publication statusPublished - 14 Jul 2023
Event6th International Conference on Mathematics and Statistics, ICoMS 2023 - Hybrid, Leipzig, Germany
Duration: 14 Jul 202316 Jul 2023

Publication series

NameACM International Conference Proceeding Series

Conference

Conference6th International Conference on Mathematics and Statistics, ICoMS 2023
Country/TerritoryGermany
CityHybrid, Leipzig
Period14/07/2316/07/23

Keywords

  • BSDE
  • CNN
  • Deep BSDE
  • Option pricing
  • deep neural network

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