Functional central limit theorems for rough volatility

We extend Donsker’s approximation of Brownian motion to fractional Brownian motion with Hurst exponent H∈(0,1) and related processes. Some of the most relevant consequences of our ‘rough Donsker (rDonsker) Theorem’... [ view full abstract ]

We extend Donsker’s approximation of Brownian motion to fractional Brownian motion with Hurst exponent H∈(0,1) and related 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 Monte-Carlo methods, for which we provide numerical recipes. We find remarkable agreement with the current benchmark Hybrid scheme. In addition we provide a weak convergence proof for the Hybrid scheme itself, and construct binomial trees, the first available scheme (in the rough volatility context) for early exercise options such as American.