Selective Forgetting in Option Calibration: An Operator-Theoretic Gauss-Newton Framework
This addresses a practical issue for financial practitioners by enabling efficient data removal in calibration pipelines, though it is incremental as it builds on existing nonlinear least-squares methods.
The paper tackles the problem of removing stale or corrupted data from calibrated option pricing models without full retraining, introducing a selective forgetting framework that provides stability guarantees and local exactness under standard assumptions.
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.