Paolo Pigato

Understanding how intrinsic brain dynamics are organized is critical for explaining cognition and sensory processing. Theoretical frameworks propose a hierarchical architecture in which some neural systems behave as orchestrators, broadcasting information across the brain, whereas others serve as net receivers (integrators), transforming incoming signals. Here, we test whether this orchestration–integration framework is embedded in intrinsic brain activity, that is, in the absence of cognitive/sensorial tasks. We adopt a multivariate fractional modeling framework originally developed in financial mathematics to characterize how volatility propagates across interacting markets, thereby identifying systems that act as orchestrators or integrators. We then test whether this integrator–orchestrator axis is related to human intelligence. To this end, using 7T resting-state functional magnetic resonance imaging data from 173 healthy young adults, we model spontaneous brain fluctuations with a multivariate fractional Ornstein–Uhlenbeck process to derive directional influence indices. Consistent with our predictions, we identified a bipartite organization, stable across modeling choices. At the subcortical level, the anterior thalamus, putamen, and caudate emerged as orchestrating transmitters, whereas the posterior thalamus, globus pallidus, hippocampus, amygdala, and nucleus accumbens acted as integrating receivers. At the cortical level, attentional and sensory networks functioned as orchestrating transmitters, while higher-order cognitive networks served as integrating receivers. These findings provide support for a theoretically grounded integration–orchestration framework, showing that directional asymmetries in brain spontaneous fluctuations are organized along this axis, with a moderate association with intelligence scores. The proposed fractional framework offers a principled tool to investigate how disruptions of this balance may contribute to brain disorders.

The Gasoil options market is illiquid, making it difficult to construct its implied volatility surface directly. However, it is closely linked to the highly liquid Brent options market. In this paper, we jointly model Brent and Gasoil futures prices through a correlated Bachelier local volatility model: the Brent factor is described by a normal mixture diffusion model, while the Gasoil-Brent spot volatility spread is estimated using a data-driven procedure that identifies clusters of historical crack-spread levels and Gasoil-Brent volatility spreads. The resulting bivariate model allows us to compute an implied volatility correction that maps Brent implied volatilities to Gasoil implied volatilities without using illiquid Gasoil option prices as inputs. Monte Carlo simulations demonstrate that the resulting implied volatilities closely match observed Gasoil implied volatilities when benchmarked against more direct approaches. These results suggest that the proposed framework is well suited for modeling refined products and pricing the corresponding financial derivatives.

1. We consider the log-normal fractional model proposed in Comte and Renault (1998) and Gatheral et al. (2018) for volatility time series and introduce a multivariate extension in which the dynamic...

Understanding how intrinsic brain dynamics are organized is critical for explaining human cognition and sensory processing. Theoretical frameworks propose a hierarchical architecture in which some neural systems act as orchestrators, broadcasting information across the brain, whereas others serve as integrators, transforming incoming signals. Here, we quantitatively test whether this orchestration-integration framework is embedded in intrinsic brain activity, that is, in the absence of explicit cognitive/sensorial tasks. We adopt a multivariate fractional modeling framework originally developed in financial mathematics to characterize how volatility propagates across interacting markets, thereby identifying systems that act as orchestrators or integrators. We then test whether this integrator-orchestrator axis is related to human intelligence. To this end, using 7T resting-state functional magnetic resonance imaging data from 173 healthy young adults, we model spontaneous brain fluctuations with a multivariate fractional Ornstein-Uhlenbeck process to derive directional influence indices. Consistent with our predictions, we identified a bipartite organization, stable across modeling choices. At the subcortical level, the anterior thalamus, putamen, and caudate emerged as orchestrating transmitters, whereas the posterior thalamus, globus pallidus, hippocampus, amygdala, and nucleus accumbens acted as integrating receivers. At the cortical level, attentional and sensory networks functioned as orchestrating transmitters, while higher-order cognitive networks served as integrating receivers. These findings provide support for a theoretically grounded integration-orchestration framework, demonstrating that brain signaling is organized along this axis even at rest, relevant for intelligence scores. The proposed fractional framework offers a principled tool to investigate how disruptions of this balance may contribute to brain disorders. Competing Interest Statement: None.

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the process, with a generalized moment estimator and a maximum likelihood estimator. We develop the asymptotic theory of the estimators when the time horizon of the observations goes to infinity, considering both cases of a fixed time lag (low frequency) and a vanishing time lag (high frequency) between consecutive observations. In the setting of low frequency observations and infinite time horizon we also study the convergence of three local time estimators, that are already known to converge to the local time in the setting of high frequency observations and fixed time horizon. We find that these estimators can behave differently, depending on the assumptions on the time lag between observations.

We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold.We discuss estimation of drift and diffusion parameters from discrete observations of the process, with a generalized moment estimator and a maximum likelihood estimator. We develop the asymptotic theory of the estimators when the time horizon of the observations goes to infinity, considering both cases of a fixed time lag (low frequency) and a vanishing time lag (high frequency) between consecutive observations. In the setting of low frequency observations and infinite time horizon we also study the convergence of three local time estimators, that are already known to converge to the local time in the setting of high frequency observations and fixed time horizon. We find that these estimators can behave differently, depending on the assumptions on the time lag between observations.

Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate version of the Rough Fractional Stochastic Volatility model proposed in Gatheral, Jaisson, and Rosenbaum, Quant. Finance, 2018. It allows for different Hurst exponents in the different marginal components and non trivial interdependencies. We discuss the main features of the model and propose an estimator that jointly identifies its parameters. We derive the asymptotic theory of the estimator and perform a simulation study that confirms the asymptotic theory in finite sample. We carry out an extensive empirical investigation on all realized volatility time series covering the entire span of about two decades in the Oxford-Man realized library. Our analysis shows that these time series are strongly correlated and can exhibit asymmetries in their cross-covariance structure, accurately captured by our model. These asymmetries lead to spillover effects that we analyse theoretically within the model and then using our empirical estimates. Moreover, in accordance with the existing literature, we observe behaviors close to non-stationarity and rough trajectories.

We propose an algorithm, based on Reinforcement Learning, to hedge the payoff on a European call option. The algorithm is first tested in a model where the problem has a well known analytic solution, so that we can compare the strategy obtained by the algorithm to the theoretical optimal one. In a more realistic case, considering transaction costs, the algorithm outperforms the standard delta hedging strategy.

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra process. For this reason, we are able to apply such an LDP to two notable examples of non self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J. Financ. Math, 2021, 12(3), 1257-1284], and models where it is given as a function of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al., Volatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases we derive consequences for short-maturity European option prices, implied volatility surfaces and implied volatility skew. In the fOU case we also discuss moderate deviations pricing and simulation results.