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Approximating Smiles: A Time Change Approach

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  • Liexin Cheng
  • Xue Cheng

Abstract

We present a new method for analyzing the shape of implied volatility smiles The method is applicable to common semimartingale models, such as jump-diffusion, rough volatility, and infinite activity models. We use a moment-based formula to approximate the at-the-money skew and curvature. Additionally, we explicitly approximate the volatility skew and curvature under a time change framework. We derive characteristics of skewness and curvature and explain their implications for model selection based on the approximation. The accuracy of the short-term approximation results on models is tested via numerical methods and on empirical data. The method is then applied to the calibration problem.

Suggested Citation

  • Liexin Cheng & Xue Cheng, 2024. "Approximating Smiles: A Time Change Approach," Papers 2401.03776, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2401.03776
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    References listed on IDEAS

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