Selective Forgetting in Option Calibration: An Operator-Theoretic Gauss-Newton Framework

TL;DR

This paper introduces a novel operator-theoretic framework for selective forgetting in option calibration models, enabling data removal without full retraining, thus improving efficiency and robustness in dynamic market conditions.

Contribution

It presents a new operator-based approach for machine unlearning in option calibration, with stability guarantees and local exactness under standard assumptions.

Findings

Operators satisfy local exactness under regularity assumptions.

Framework provides stability guarantees and perturbation bounds.

Enables data removal without full model retraining.

Abstract

Calibration of option pricing models is routinely repeated as markets evolve, yet modern systems lack an operator for removing data from a calibrated model without full retraining. When quotes become stale, corrupted, or subject to deletion requirements, existing calibration pipelines must rebuild the entire nonlinear least-squares problem, even if only a small subset of data must be excluded. In this work, we introduce a principled framework for selective forgetting (machine unlearning) in parametric option calibration. We provide stability guarantees, perturbation bounds, and show that the proposed operators satisfy local exactness under standard regularity assumptions.