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arXiv · 2212.05671

Saddle-Point Approach to Large-Time Volatility Smile

Chun Yat Yeung·Ali Hirsa
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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. 2022-12-12. Saddle-Point Approach to Large-Time Volatility Smile. https://arxiv.org/abs/2212.05671

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