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This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent…
Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric…
The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We study two complementary methodologies for calibrating implied volatility surfaces: analytical approximations and data-driven models based on rough path theory. On the analytical side, we revisit a second-order asymptotic expansion for…
This paper shows a novel machine learning model for realized volatility (RV) prediction using a normalizing flow, an invertible neural network. Since RV is known to be skewed and have a fat tail, previous methods transform RV into values…
We introduce a heterogeneous spatiotemporal GARCH model for geostatistical data or processes on networks, e.g., for modelling and predicting financial return volatility across firms in a latent spatial framework. The model combines…
Amortized optimization accelerates the solution of related optimization problems by learning mappings that exploit shared structure across problem instances. We explore the use of Scale Equivariant Graph Metanetworks (ScaleGMNs) for this…
Accurate forecasting of the Volatility-Covariance Matrix (VCV) is central to regulatory capital adequacy processes such as the Internal Capital Adequacy Assessment Process (ICAAP) and the Comprehensive Capital Analysis and Review (CCAR).…
Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…
Realised volatility has become increasingly prominent in volatility forecasting due to its ability to capture intraday price fluctuations. With a growing variety of realised volatility estimators, each with unique advantages and…
We construct a statistical indicator for the detection of short-term asset price bubbles based on the information content of bid and ask market quotes for plain vanilla put and call options. Our construction makes use of the martingale…
Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…
Accurate forecasting in the e-commerce finance domain is particularly challenging due to irregular invoice schedules, payment deferrals, and user-specific behavioral variability. These factors, combined with sparse datasets and short…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
In traditional Graph Neural Networks (GNNs), the assumption of a fixed embedding manifold often limits their adaptability to diverse graph geometries. Recently, Hamiltonian system-inspired GNNs have been proposed to address the dynamic…
This paper introduces one new multivariate volatility model that can accommodate an appropriately defined network structure based on low-frequency and high-frequency data. The model reduces the number of unknown parameters and the…