  We train an LSTM network based on a pooled dataset made of hundreds of liquid
stocks aiming to forecast the next daily realized volatility for all stocks.
Showing the consistent outperformance of this universal LSTM relative to other
asset-specific parametric models, we uncover nonparametric evidences of a
universal volatility formation mechanism across assets relating past market
realizations, including daily returns and volatilities, to current
volatilities. A parsimonious parametric forecasting device combining the rough
fractional stochastic volatility and quadratic rough Heston models with fixed
parameters results in the same level of performance as the universal LSTM,
which confirms the universality of the volatility formation process from a
parametric perspective.
