A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high‐frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key‐stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside the scope of stochastic volatility models. On the mathematical side, Markovianity and, partially, semimartingality are lost. In this paper, we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provide a new and powerful tool to analyze rough volatility models.

中文翻译：

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波动性大的正则结构

最近在财务建模中出现了一个新的范例：剧烈（随机）波动。首先由Gatheral等人观察到。在高频数据中，随后在市场微观结构模型中得出，粗略的波动率捕获了整个隐含波动率表面的简约风格化事实，包括极端偏斜（如Alòs等人先前所观察到的），这些偏斜被认为超出了范围。随机波动率模型。在数学方面，马尔可夫性和部分半军事性丧失了。在本文中，我们证明了Hairer的正则结构是粗糙路径理论的主要扩展，它引起了随机偏微分方程领域的一场革命，也为分析粗糙波动率模型提供了新的强大工具。