Volatility Calibration via Automatic Local Regression

ArXiv ID: 2509.16334 “View on arXiv”

Authors: Ruozhong Yang, Hao Qin, Charlie Che, Liming Feng

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.

Keywords: local volatility model, Greeks, hedging, calibration, finite difference method, Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper involves advanced mathematical concepts like solving ill-posed inverse problems, automatic parameter selection via asymptotic MSE, and numerical PDE methods, giving high math complexity. However, the empirical section focuses on numerical experiments rather than real-market backtests, with no mention of code, live data, or out-of-sample validation, leading to moderate empirical rigor.

  flowchart TD
    A["Research Goal<br>Stable Greeks &<br>Accurate LV Calibration"] --> B["Key Methodology<br>Pre-calibration Smoothing"]
    
    B --> C["Input Data<br>Market Observables<br>Finite Strikes/Maturities"]
    
    C --> D["Computational Process<br>Automatic Local Regression"]
    
    D --> E["Outcome 1<br>Denoised Market Inputs<br>Reduced High-Frequency Noise"]
    
    D --> F["Outcome 2<br>Smoother LV Surface<br>Preventing Spiky Artifacts"]
    
    E --> G["Final Finding<br>Exotic Options Valuation<br>Stable Greeks &<br>Preserved Market Fit"]
    F --> G