Related papers: Modelling Uncertain Volatility Using Quantum Stoch…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…
Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…
In this paper, we focus on the estimation of historical volatility of asset prices from high-frequency data. Stochastic volatility models pose a major statistical challenge: since in reality historical volatility is not observable, its…
The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity.…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to…
This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…
Accurate and efficient pricing of multi-asset basket options poses a significant challenge, especially when dealing with complex real-world data. In this work, we investigate the role of quantum-enhanced uncertainty modeling in financial…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…
We propose how to quantify high-frequency market sentiment using high-frequency news from NASDAQ news platform and support vector machine classifiers. News arrive at markets randomly and the resulting news sentiment behaves like a…