Option pricing using Generative Adversarial Networks
Details
- Authors: Siem Peters
- Title: Option pricing using Generative Adversarial Networks
- Supervisor: Prof. Dr. Laura Spierdijk, Dr. Jörg Osterrieder
- Degree: Master of science
- University: University of Twente
- Year: 2024
- Status: Master thesis
Abstract
This master thesis introduces a novel approach to price financial options, namely a GAN-QMC. It combines a Generative Adversarial Network (GAN) with a Quasi-Monte Carlo (QMC) simula- tion. The main objective is to improve the accuracy and efficiency of option pricing, specifically focusing on overcoming limitations associated with traditional QMC for option pricing. In this research, GANs are used to model the process of the underlying asset, aiming for a realistic representation of financial data as input to the QMC.
This thesis begins by building a theoretical framework, using relevant literature to place the topic within the broader landscape of option pricing, MC simulation, and GANs. The method- ology involves the development of the GAN-QMC framework including option pricing using MC/QMC, neural networks, GANs, and risk-neutral price path construction. Here we discov- ered that the GAN-QMC can only effectively be implemented as a semi-parametric method, relaxing certain distributional assumptions associated with traditional MC/QMC option pric- ing.
The concepts of the GAN-QMC methodology were implemented. The GAN hyper-parameters were determined by using an automated tuning strategy based on perturbation theory. The GAN’s ability to generate financial stock returns was determined by comparing it to real-world data from exchange-listed companies. The Wasserstein GAN with Gradient Penalty was best in capturing the statistical properties exhibited by the real-world data but wasn’t perfect. Afterward, we compared the performance of regular QMC to GAN-QMC. Here we discovered that, despite the GAN’s limitations in capturing the statistical properties of real-world finan- cial data, GAN-QMC demonstrates comparable accuracy to QMC at roughly 3.5%. Moreover, GAN-QMC seems to show potential advantages in computational efficiency, being approxi- mately 20% faster.
In summary, this thesis contributes to the field of option pricing by introducing GAN-QMC as a semi-parametric framework with potential advantages in accuracy and efficiency. While there are challenges and limitations, particularly in training a financial GAN, this study does suggest possibilities for future research to improve GANs and the GAN-QMC method further.