SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 437-469, January 2020.
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where log volatility follows a Gaussian Volterra process. While providing a good fit for European options, these models are unable to reproduce the VIX option smile observed in the market and are thus not suitable for VIX products. To accommodate these, we introduce the class of modulated Volterra processes and show that they successfully capture the VIX smile.

中文翻译：

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粗糙波动率模型中的波动率选项

《 SIAM金融数学杂志》，第11卷，第2期，第437-469页，2020年1月。
我们在一些粗糙的波动率模型中讨论了波动率期权的定价和对冲。首先，我们开发了有效的蒙特卡洛方法和渐近逼近法，用于在对数波动遵循高斯Volterra过程的模型中计算期权价格和套期比率。这些型号虽然很适合欧洲选件，但无法重现市场上观察到的VIX选件笑容，因此不适用于VIX产品。为了适应这些情况，我们介绍了Volterra调制过程的类别，并表明它们成功捕获了VIX微笑。