Improving the speed and stability of derivatives pricing is crucial for the multi-trillion-dollar OTC market, where even small gains in accuracy can significantly enhance risk management and operational efficiency. We introduce two flagship quantum-inspired deep learning methods using tensor neural networks (TNNs) for derivatives pricing:
1. High-Dimensional Bermudan Pricing: This method improves deep learning solutions for forward-backward SDEs by incorporating TNNs. It delivers faster training, improved stability, and more accurate pricing than industry-standard Monte Carlo, which tends to underestimate Bermudan options and scale poorly with model complexity. TNNs also reduce variance in loss functions and model size while improving convergence. However, this approach requires retraining when market parameters shift.
2. Parameterized Deep Pricing Framework: To address retraining limitations, we developed a TNN-based model that encapsulates full market parameter ranges, eliminating the need for retraining. Applied to Heston models for European, Barrier, and Basket options, our method achieved 90–95% accuracy within a 5% error tolerance, and was 1,000–5,000× more efficient than Monte Carlo. Tensor compression further boosted efficiency, reaching up to 15,000× gains with minimal accuracy loss. These results demonstrate the method's potential to disrupt traditional pricing workflows.
For macroeconomic stability, we extended quantum algorithms for financial network analysis by scaling QUBO-based crash propagation models to realistic scenarios. Our method avoids exponential scaling by exactly encoding crash dynamics with only quadratic overhead. Benchmarking across static, dynamic, and uncertain models showed robust performance for complex networks, enabling analyses previously intractable on quantum hardware.
In transaction networks, our quantum-inspired optimization outperformed the Guntzner Liquidity Saving Mechanism (GLSM) in large, interconnected systems where GLSM's cycle detection faltered. We introduced a netted maximization method to improve settlement quality and reduce systemic risk. Tensor network optimization was also more cost-effective and scalable than quantum solvers in specific scenarios.
The Singularity QMC framework advanced probabilistic methods for financial risk analysis. We benchmarked MPS-based state preparation and quantum Monte Carlo on IBM QPUs, finding MPS methods to be the most scalable and accurate, though noisy hardware remains a challenge. Compared to qGANs and deep direct encoding, MPS offered superior performance in simulation.
Finally, tensor network integration emerged as a powerful classical alternative to quantum Monte Carlo. By leveraging Tensor Cross Approximation, we achieved near-linear scaling in high-dimensional settings, outperforming classical Monte Carlo and QMC in efficiency and precision.
Our results highlight the potential of combining quantum and quantum-inspired technologies for real-world finance. While pure quantum methods await further hardware advances, quantum-inspired approaches offer immediate, high-impact benefits today.
