Predicting Option Prices Using Graph Neural Networks: A Multi-Relational Approach to Modeling Option Chain Structure

The Black-Scholes-Merton (BSM) framework prices options under assumptions of constant volatility, constant interest rates, and no transaction costs, and, critically, prices each contract independently of every other contract on the same underlying. In practice, options on a common underlying that share an expiry or a strike move together, and the shape of an option chain carries information that a per-contract model discards. This paper proposes a graph neural network (GNN) framework for option price prediction that represents an option chain as a graph in which each node is an individual contract (defined by strike, expiry, and type) and edges connect contracts that share an expiry (sparsified to each contract's k nearest strikes, to keep aggregation local to the relevant part of the smile), share a strike, or are the same contract observed on a prior trading day. Across the full 123-day historical SPX options window collected for this study (Databento, OPRA), a multilayer variant of the proposed GNN improves on a Black-Scholes-Merton baseline (using realized, not implied, volatility to avoid circularity) by mean absolute error (191.5 vs. 201.6) and mean squared error (184,902 vs. 351,512), but does not outperform a plain feedforward neural network trained on the same input features (MAE 151.3); an LSTM baseline using only each contract's own price history performs worse still (MAE 313.8). This gap widens, not narrows, at full scale, and BSM overtakes the multilayer GNN on relative (MAPE) error even as the GNN keeps an edge on absolute error. We report this directly: the graph structure improves on the classical baseline on some metrics but does not outperform a simpler feature-to-price mapping, which we discuss in light of how much pricing-relevant information the BSM inputs already carry.