Optimization of Continuous-Time Financial Models Driven by Machine Learning: A Core Scenario of Option Pricing

DOI

10.2991/978-94-6463-916-2_67How to use a DOI?

Keywords

Continuous-Time Models; Option Pricing; Machine Learning; Black-Scholes Model; Volatility Surface; Neural Networks; Model Calibration

Abstract

The exact price of financial derivatives, especially options, is still a core of quantitative finance and risk management. Traditional continuous-time models, such as the Black-Scholes-Merton (BSM) framework, provide a theoretical foundation but they make simplifying assumptions, mainly constant volatility, vastly different from those in markets. This gives rise to systematic pricing errors in the price model, and ruins the usefulness of the hedge. This paper explores novel approaches that integrate machine learning with traditional quantitative finance methods to improve pricing accuracy. Focusing on the key case of European option pricing, it demonstrates that a Feedforward Neural Network (FNN) can learn the complex, non-linear implied volatility surface directly from market data without the strong assumptions of traditional models. We train our network with a large set of historical S&P 500 index options, taking moneyness and time to maturity as inputs and predicting implied volatility as outputs. The performance of this machine learning-based approach is compared to that of the BSM framework. The model is also compared to more sophisticated alternatives, such as the Heston Stochastic Volatility Model. Empirically, our approach significantly reduces pricing errors, as evidenced by low Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values on out-of-sample test data. It also offers excellent computational speed, it can be calibrated quickly and deployed in real time for high-frequency trading, risk management and more. This research demonstrates the transformative potential of machine learning in quantitative finance: it enables the development of more robust, accurate, and computationally efficient models, which will drive the development of a new generation of more powerful quantitative tools over time.

Copyright

© 2025 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Zhiyan Zhu
PY  - 2025
DA  - 2025/12/22
TI  - Optimization of Continuous-Time Financial Models Driven by Machine Learning: A Core Scenario of Option Pricing
BT  - Proceedings of the 2025 4th International Conference on Public Service, Economic Management and Sustainable Development (PESD 2025)
PB  - Atlantis Press
SP  - 617
EP  - 623
SN  - 2352-5428
UR  - https://doi.org/10.2991/978-94-6463-916-2_67
DO  - 10.2991/978-94-6463-916-2_67
ID  - Zhu2025
ER  -