Understanding Short-Term Implied Volatility Dynamics: A Model-Independent Approach Beyond Stochastic Volatility

Liexin Cheng and Xue Cheng

Papers from arXiv.org

Abstract: This paper examines the short-term asymptotic behavior of the implied volatility surface, focusing on the at-the-money (ATM) skew and curvature. Rather than committing to a specific stochastic differential equation, we adopt a distribution-based approach by imposing cumulant conditions on the log-return distribution. Under these weak assumptions, we derive a quadratic expansion of implied volatility as a function of moneyness for near-the-money options and asymptotic expressions for ATM skew and curvature as time to maturity approaches zero, treating the decay rates of the third and fourth cumulants as independent parameters and introducing a marginal-type classifier. These results highlight differences in ATM asymptotic properties across different types of log return distributions and yield a unified, model-independent characterization of short-term smile dynamics in terms of the scaling laws of the marginal cumulants, covering regular/rough stochastic volatility and distribution-based ones like scalable gamma/CGMY martingale models alike from simple moment information. We subsequently present a distribution-based calibration method that not only effectively validates the analytical approximations, but also exhibits strong interpretability and consistent performance, and discuss potential connections to model-independent path-dependent applications via martingale optimal transport. Overall, our findings provide model-independent analytical tools for evaluating model performance against market stylized features, accurately approximating short-term option prices, and performing robust calibration.

Date: 2024-01, Revised 2026-08
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2401.03776 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2401.03776

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().