Related papers: Sig-SDEs model for quantitative finance
We propose a neural network-based approach to calibrating stochastic volatility models, which combines the pioneering grid approach by Horvath et al. (2021) with the pointwise two-stage calibration of Bayer et al. (2018) and Liu et al.…
We propose a new pseudo-Siamese Network for Asset Pricing (SNAP) model, based on deep learning approaches, for conditional asset pricing. Our model allows for the deep alpha, deep beta and deep factor risk premia conditional on high…
We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
Semi-supervised learning (SSL) has demonstrated high performance in image classification tasks by effectively utilizing both labeled and unlabeled data. However, existing SSL methods often suffer from poor calibration, with models yielding…
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…
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 Brownian motion. First, we show that the model is…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…
Stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) are increasingly used to model systems with rough dynamics and long-range dependence, such as those arising in quantitative finance and reliability…
In modern society, the trading methods and strategies used in financial market have gradually changed from traditional on-site trading to electronic remote trading, and even online automatic trading performed by a pre-programmed computer…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
Prediction of stock price movements presents a formidable challenge in financial analytics due to the inherent volatility, non-stationarity, and nonlinear characteristics of market data. This paper introduces SPH-Net (Stock Price Prediction…
Masked Image Modeling (MIM) techniques have redefined the landscape of computer vision, enabling pre-trained models to achieve exceptional performance across a broad spectrum of tasks. Despite their success, the full potential of MIM-based…
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
New products must be formulated rapidly to succeed in the global formulated product market; however, key product indicators (KPIs) can be complex, poorly understood functions of the chemical composition and processing history. Consequently,…