# Random Neural Networks for Rough Volatility

## TL;DR

This paper introduces a deep learning algorithm to solve complex financial equations related to rough volatility using a special type of neural network.

## Contribution

A novel deep learning algorithm using reservoir neural networks is proposed for solving path-dependent PDEs in rough volatility.

## Key findings

- The reservoir neural network approach simplifies the optimization problem to a least-square regression.
- Theoretical convergence properties of the proposed method are proven.

## Abstract

We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an BSDE, building upon recent insights by Bayer, Qiu and Yao, and on constructing a neural network of reservoir type as originally developed by Gonon, Grigoryeva, Ortega. The reservoir approach allows us to formulate the optimisation problem as a simple least-square regression for which we prove theoretical convergence properties.