Background and Motivation
Accurately pricing American-style options, which allow early exercise at any time before expiry, remains a significant challenge in quantitative finance. This task becomes even more complex under realistic market conditions where asset volatility is not constant but fluctuates randomly, as described by stochastic volatility models like Heston's. Traditional numerical methods, often mesh-based, can be computationally intensive and struggle with high-dimensional problems. With the exponential growth of derivatives trading and the critical need for effective risk management, evidenced by billions of contracts traded annually, there is a pressing demand for more efficient and accurate pricing tools. Furthermore, markets for newer derivatives, such as those linked to real estate indices, lack reliable pricing models, creating a gap that this research aims to fill.
Methodology and Scope
This study pioneers the application of Physics-Informed Neural Networks (PINNs) and a faster variant, Physics-Informed Extreme Learning Machines (PIELMs), to solve the complex partial differential equations governing option prices. The research focuses on two critical, real-world two-factor models: the Heston stochastic volatility model for equity options and an extended Fabozzi-Shiller-Tunaru model with stochastic volatility for real estate index options. For American options, formulated as linear complementarity problems, the authors integrate a penalty method within the neural network framework. The models are trained to minimise a loss function that encodes the governing PDE, initial conditions (option payoff), and boundary conditions, using automatic differentiation to compute crucial hedging sensitivities (Greeks) efficiently.
Key Findings and Contributions
Why It Matters
This research represents a significant step in applying modern AI techniques to solve core, realistic problems in financial engineering. By demonstrating that deep learning frameworks can accurately and efficiently price complex derivatives under stochastic volatility, it opens the door to tackling even higher-dimensional pricing problems that are intractable for traditional grid-based methods (the "curse of dimensionality"). The development of a credible model for real estate index derivatives is particularly impactful, offering investors and institutions a much-needed tool for hedging exposure to property market risks without direct physical investment.
Practical Applications
Discover high-quality academic insights in finance from this article published in China Finance Review International . Click the DOI below to read the full-text!
China Finance Review International
News article
Deep neural networks for the valuation of equity and real-estate index American options under models with stochastic volatility
1-Dec-2025