Unlike standard bivariate diffusion models, the rough Bergomi model by Bayer, Friz, and Gatheral (2016) allows to parsimoniously recover key stylized facts of market implied volatility surfaces such as the exploding power-law behaviour of the at-the-money volatility skew as time to maturity goes to zero. However, falling into the class of so-called rough stochastic volatility models sparked by Alo`s, Leo ́n, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), its non-Markovianity poses serious mathematical and computational challenges. To date, calibrating rough Bergomi remained prohibitively expensive since standard calibration routines rely on the repetitive evaluation of the map from model parameters to Black-Scholes implied volatility, which in the case of rough Bergomi involves a costly Monte Carlo simulation (Bennedsen, Lunde, & Pakkanen, 2017; McCrickerd & Pakkanen, 2018; Bayer et al., 2016; Horvath, Jacquier, & Muguruza, 2017). In this paper, we resolve the issue by combining a standard Levenberg-Marquardt calibration routine with a neural network regression, replacing expensive MC simulations with cheap forward runs of a network trained to approximate the implied volatility map. Some numerical results show the prowess of this approach.
- Stochastic Analysis Seminar