Volatility Calibration via Automatic Local Regression

2025-09-19

AI Summary

Local volatility (LV) model calibration is inherently ill-posed: finite market data cannot uniquely determine the infinite-dimensional continuous volatility surface, often leading to spurious spikes and high-frequency oscillations that destabilize Greeks in finite-difference pricing. This paper proposes an automated, local-regression-based pre-calibration smoothing method as a generic preprocessing module seamlessly integrated into any LV calibration pipeline. Guided by asymptotic mean-squared error minimization, the method adaptively balances noise suppression and market-data fidelity. Numerical experiments demonstrate substantial improvements in surface smoothness and Greeks stability, while preserving high-fidelity calibration to market quotes and incurring negligible computational overhead. The key contribution lies in the first systematic integration of adaptive local regression smoothing at the front end of LV calibration—achieving a principled trade-off among robustness, accuracy, and practicality.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Local Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Managing exotic derivatives requires accurate mark-to-market pricing and stable Greeks for reliable hedging. The Local Volatility (LV) model distinguishes itself from other pricing models by its ability to match observable market prices across all strikes and maturities with high accuracy. However, LV calibration is fundamentally ill-posed: finite market observables must determine a continuously-defined surface with infinite local volatility parameters. This ill-posed nature often causes spiky LV surfaces that are particularly problematic for finite-difference-based valuation, and induces high-frequency oscillations in solutions, thus leading to unstable Greeks. To address this challenge, we propose a pre-calibration smoothing method that can be integrated seamlessly into any LV calibration workflow. Our method pre-processes market observables using local regression that automatically minimizes asymptotic conditional mean squared error to generate denoised inputs for subsequent LV calibration. Numerical experiments demonstrate that the proposed pre-calibration smoothing yields significantly smoother LV surfaces and greatly improves Greek stability for exotic options with negligible additional computational cost, while preserving the LV model's ability to fit market observables with high fidelity.

Problem

• Calibrating local volatility surfaces from finite market observables is ill-posed
• Ill-posed calibration causes spiky volatility surfaces and unstable Greeks
• Finite-difference valuation suffers from high-frequency oscillations in solutions

Innovation

• Pre-calibration smoothing using local regression
• Automatically minimizes asymptotic conditional mean squared error
• Generates denoised inputs for Local Volatility calibration