Estimating volatility from recent high frequency data, we revisit the question of the
smoothness of the volatility process. Our main result is that log-volatility behaves essentially …

We learn from data that volatility is mostly path-dependent: up to 90% of the variance of the
implied volatility of equity indexes is explained endogenously by past index returns, and up …

In this paper, we present a comprehensive survey of continuous stochastic volatility models,
discussing their historical development and the key stylized facts that have driven the field …

We investigate the statistical evidence for the use of 'rough'fractional processes with Hurst
exponent H< 0.5 for modeling the volatility of financial assets, using a model-free approach …

The log realized volatility (RV) is often modeled as an autoregressive fractionally integrated
moving average model ARFIMA (1, d, 0). Two conflicting empirical results have been found …

Statistical inference for rough volatility: Minimax theory Page 1 The Annals of Statistics 2024,
Vol. 52, No. 4, 1277–1306 https://doi.org/10.1214/23-AOS2343 © Institute of Mathematical …

We investigate the performance of the Deep Hedging framework under training paths
beyond the (finite dimensional) Markovian setup. In particular, we analyse the hedging …

In recent years, there has been a substantive interest in rough volatility models. In this class
of models, the local behavior of stochastic volatility is much more irregular than …

In the setting of stochastic Volterra equations, and in particular rough volatility models, we
show that conditional expectations are the unique classical solutions to path-dependent …

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 …