PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable J\"ackel Operator

The article introduces PIVOT (Price-Implied-Volatility Objective Translator), a differentiable layer that integrates with J\"ackel's LBR solver to efficiently bridge price and implied volatility spaces in option-learning systems. PIVOT maintains the efficiency of the LBR forward pass while enabling accurate gradient computation through implicit differentiation, achieving 1.79 billion IV/s on a single H100 GPU with a maximum relative error of 9.3e-14. The implementation shows significant improvements in price mean absolute error (MAE) and implied volatility MAE across various datasets, indicating its potential to enhance model performance in financial applications.