PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable J\"ackel Operator
arXiv:2606.17065v1 Announce Type: cross Abstract: Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) space, where volatility surfaces are smoothed, regularized, and evaluated. The bottleneck is interface, not approximation: J\"ackel's seminal "Let's Be Rational" (LBR) solver already inverts the Black-Scholes price to machine precision efficiently. What is missing is a differentiable layer that preserves LBR in the forward pass and avoids backpropagating through its bra
This development addresses a critical interface bottleneck in financial modeling and machine learning, leveraging existing efficient solvers with a novel differentiable layer.
It significantly improves the efficiency and accuracy of option pricing models by enabling direct integration of Black-Scholes implied volatility into differentiable learning systems, enhancing risk management and hedging strategies.
The ability to backpropagate through the Jäckel solver within option learning systems means more robust and adaptable models for financial derivatives, fostering innovation in quantitative finance.
- · Quantitative Funds
- · High-Frequency Trading Firms
- · Financial AI/ML Developers
- · Derivatives Market Participants
- · Traditional Option Pricing Modelers
More accurate and rapid option pricing and risk assessment models become widely deployable.
Increased efficiency in derivatives trading and hedging, potentially compressing margins for some market makers.
Enhanced financial stability due to better risk management and a shift towards more dynamic, AI-driven derivative strategies impacting market liquidity and discovery.
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Read at arXiv cs.AI