Paper: arXiv 2511.14980

Authors: Ahmet Umur Özsoy

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly original theoretical framework applying machine unlearning concepts to option calibration via Gauss-Newton normal equations. While mathematically well-formulated with clear local exactness ideas, the provided excerpt lacks detailed empirical backtesting on real-world market datasets.

Research Flowchart

  flowchart TD
    A["Research Question: How to efficiently remove stale/corrupted market data from calibrated option pricing models without full retraining?"] --> B["Inputs: Initial Option Market Data, Calibrated Model Parameters, Target Deletion Subset"]
    B --> C["Methodology: Operator-Theoretic Gauss-Newton Framework"]
    C --> D["Computational Process: Local Sensitivity Analysis & Low-Rank Unlearning Updates"]
    D --> E["Outcomes & Key Findings: Fast Selective Forgetting, Local Exactness Guarantees, Rigorous Perturbation Bounds"]

Cited References (17)

  1. Making ai forget you: Data deletion in machine learning (2019)
  2. A review on machine unlearning (2023)
  3. A survey of machine unlearning (2025)
  4. Remember what you want to forget: Algorithms for machine unlearning (2021)
  5. Learn to unlearn: Insights into machine unlearning (2024)
  6. Machine unlearning (2021)
  7. Certified data removal from machine learning models (2019) — link
  8. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
and 9 more
  1. Implied volatility functions: Empirical tests (1998)
  2. Implied volatility surfaces: a comprehensive analysis using half a billion option prices (2023)
  3. Implied volatility surface: Construction methodologies and characteristics (2011) — link
  4. Some Economically Meaningful Option Model Calibration Performance Measures (2014)
  5. Nonparametric estimation of state-price densities implicit in financial asset prices (1998)
  6. Linear and non-linear filtering in mathematical finance: a review (2011)
  7. Estimation methods for stochastic volatility models: a survey (2004)
  8. Empirical performance of alternative option pricing models (1997)
  9. Model specification and risk premia: Evidence from futures options (2007)

0 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.