Stochastic processes are random variables with values in some space of paths. However,
reducing a stochastic process to a path-valued random variable ignores its filtration, ie the …

Since we will never really know why the prices of financial assets move, we should at least
make a faithful model of how they move. This was the motivation of Bachelier in 1900, when …

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 …

Full article: Volatility has to be rough Skip to Main Content Taylor and Francis Online homepage
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The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and
it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide …

We provide a unified treatment of pathwise large and moderate deviations principles for a
general class of multidimensional stochastic Volterra equations with singular kernels, not …

We introduce the notion of rough local stochastic volatility models, extending the classical
concept to the case where volatility is driven by some Volterra process. In this setting, we …

We present a new methodology to analyze large classes of (classical and rough) stochastic
volatility models, with special regard to short-time and small noise formulae for option prices …

In this paper, we study the option pricing problems for rough volatility models. As the
framework is non-Markovian, the value function for a European option is not deterministic; …