Multi-Fidelity Convolutional Neural Network for Efficient SABR Stochastic Volatility Modeling

The stochastic alpha-beta-rho (SABR) model is a widely used stochastic volatility model for capturing the volatility smile in derivatives markets. Accurate and efficient option pricing under this framework remains challenging. Monte Carlo simulation offers high accuracy at a high computational cost during calibration, while cheaper asymptotic approximations, such as Hagan's formula, lose accuracy for long-maturity or high-volatility options. Together, these two approaches represent two fidelity levels of the same system. Hagan's asymptotic expansion serves as a low-fidelity approximation, while MC simulation serves as a high-fidelity ground truth. Recent studies have proposed multi-fidelity approaches that utilize both high-fidelity Monte Carlo data and low-fidelity asymptotic expansion data to get a high accuracy estimation at low computational cost. This study extends these efforts by proposing a generalized multi-fidelity convolutional architecture for surrogate modeling of implied volatility surfaces. Our method combines residual learning with the Multi-Fidelity Data Aggregation Convolutional Neural Network (MDA-CNN) framework, originally applied to engineering simulations, and adapts it to the higher-dimensional space of financial modeling. Instead of learning a point-to-point mapping as seen in other approaches, the network learns a point-to-domain mapping through convolutional receptive fields, which allows it to extract spatial correlations across the volatility surface and utilize more low-fidelity information. Our design allows for a richer high-fidelity representation to be captured, resulting in a more accurate prediction.