Related papers: Modelling Uncertain Volatility Using Quantum Stoch…
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical…
In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions…
Maximum likelihood estimation applied to high-frequency data allows us to quantify intermittency in the fluctu- ations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency…
The use of factor stochastic volatility models requires choosing the number of latent factors used to describe the dynamics of the financial returns process; however, empirical evidence suggests that the number and makeup of pertinent…