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# Functional central limit theorems for rough volatility

## Author

Listed:
• Blanka Horvath
• Antoine Jacquier
• Aitor Muguruza

## Abstract

We extend Donsker's approximation of Brownian motion to fractional Brownian motion with Hurst exponent $H \in (0,1)$ and to Volterra-like processes. Some of the most relevant consequences of our rough Donsker (rDonsker) Theorem' are convergence results for discrete approximations of a large class of rough models. This justifies the validity of simple and easy-to-implement Monte-Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark Hybrid scheme \cite{BLP15} and find remarkable agreement (for a large range of values of~$H$). This rDonsker Theorem further provides a weak convergence proof for the Hybrid scheme itself, and allows to construct binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan.

## Suggested Citation

• Blanka Horvath & Antoine Jacquier & Aitor Muguruza, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2017.
• Handle: RePEc:arx:papers:1711.03078
as

File URL: http://arxiv.org/pdf/1711.03078

## References listed on IDEAS

as
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## Citations

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Cited by:

1. Elisa Alos & David Garc'ia-Lorite & Aitor Muguruza, 2018. "On smile properties of volatility derivatives and exotic products: understanding the VIX skew," Papers 1808.03610, arXiv.org.
2. Blanka Horvath & Antoine Jacquier & Peter Tankov, 2018. "Volatility options in rough volatility models," Papers 1802.01641, arXiv.org.

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