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Saddle-Point Approach to Large-Time Volatility Smile

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  • Chun Yat Yeung
  • Ali Hirsa

Abstract

We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function fulfills a L\'evy-type scaling behavior in large time, the approach allows us to study analytically the large-time smile behaviors under specific models, and moreover, to reach a very wide class of arbitrage-free model-inspired parametrizations, in the same manner as stochastic-volatility-inspired (SVI).

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  • Chun Yat Yeung & Ali Hirsa, 2022. "Saddle-Point Approach to Large-Time Volatility Smile," Papers 2212.05671, arXiv.org.
    • Handle: RePEc:arx:papers:2212.05671
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    References listed on IDEAS

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    4. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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