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 consider the joint SPX & VIX calibration within a general class of Gaussian polynomial
volatility models in which the volatility of the SPX is assumed to be a polynomial function of a …

We study an extension of the Heston stochastic volatility model that incorporates rough
volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston …

Signature stochastic differential equations (SDEs) constitute a large class of stochastic
processes, here driven by Brownian motions, whose characteristics are entire or real …

In the context of stochastic portfolio theory we introduce a novel class of portfolios which we
call linear path-functional portfolios. These are portfolios which are determined by certain …

We consider a stochastic volatility model where the dynamics of the volatility are given by a
possibly infinite linear combination of the elements of the time extended signature of a …

We introduce a novel discrete-time-continuous-time exact calibration method: we first build
an S&P 500/VIX jointly calibrated discrete-time model that is later extended to continuous …

We regard options on VIX and Realised Variance as solutions to path-dependent PDEs in a
continuous stochastic volatility model. The modeling assumption specifies that the …

We introduce a novel discrete-time-continuous-time exact calibration method: we first build
an S&P 500/VIX jointly calibrated discrete-time model that is later extended to continuous …

Motivated by insurance applications, we propose a new approach for the validation of real-
world economic scenarios. This approach is based on the statistical test developed by …