Paper: arXiv 2401.03776

Authors: Liexin Cheng, Xue Cheng

Abstract

This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely concerned in the option market. Departing from conventional process-based models that rely on explicit stochastic differential equations, our work adopts a model-independent, distribution-based approach by imposing cumulant conditions on the asset’s log return distribution. Under these broad assumptions, we derive a quadratic expansion for the implied volatility as a function of moneyness for near-the-money options, along with asymptotic expressions for the ATM skew and curvature as the time to maturity tends to zero. These results not only highlight the differences in the properties of ATM asymptotics among different types of models, but also offer a versatile framework for model calibration, including regular stochastic volatility, rough volatility, and discrete-time distribution-based models, using simple moment information. Overall, our findings provide robust analytical tools for the accurate approximation of short-term option prices and the evaluation of model performance against market stylized features.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework using cumulant conditions to derive model-independent short-term implied volatility asymptotics. While mathematically strong and innovative in bridging regular and rough volatility models, it relies primarily on theoretical derivations and lacks empirical validation on historical market data.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze short-term Implied Volatility Surface (IVS) dynamics (ATM skew/curvature) via a model-independent approach"] --> B["Inputs: Cumulant conditions on asset log-return distributions (beyond explicit SDEs)"]
    B --> C["Methodology: Derive quadratic IV expansion as a function of moneyness for near-the-money options"]
    C --> D["Asymptotic Analysis: Compute short-term limit behavior (tau -> 0) for ATM skew and curvature"]
    D --> E["Model Calibration & Application: Apply framework to regular SV, rough volatility, and discrete-time models"]
    E --> F["Key Outcomes: Unified analytical tools for short-term option pricing, model evaluation, and IVS feature matching"]

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