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This paper defines fractional Heston-type (fHt) model as an arbitrage-free financial market model with the infinitesimal return volatility described by the square of a single stochastic equation with respect to fractional Brownian motion…
Predicting stock prices from textual information is a challenging task due to the uncertainty of the market and the difficulty understanding the natural language from a machine's perspective. Previous researches focus mostly on sentiment…
Standard quantitative models of the stock market predict a log-normal distribution for stock returns (Bachelier 1900, Osborne 1959), but it is recognised (Fama 1965) that empirical data, in comparison with a Gaussian, exhibit leptokurtosis…
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an…
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is…
In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…
The prediction of stock prices is an important task in economics, investment and making financial decisions. This has, for decades, spurred the interest of many researchers to make focused contributions to the design of accurate stock price…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
Technical and fundamental analysis are traditional tools used to analyze individual stocks; however, the finance literature has shown that the price movement of each individual stock correlates heavily with other stocks, especially those…
Human motion prediction is an important and challenging topic that has promising prospects in efficient and safe human-robot-interaction systems. Currently, the majority of the human motion prediction algorithms are based on deterministic…
This paper presents a novel hybrid model that integrates long-short-term memory (LSTM) networks and Graph Neural Networks (GNNs) to significantly enhance the accuracy of stock market predictions. The LSTM component adeptly captures temporal…
Predicting financial markets and stock price movements requires analyzing a company's performance, historic price movements, industry-specific events alongside the influence of human factors such as social media and press coverage. We…
A new concept, called balanced estimator of diffusion entropy, is proposed to detect scalings in short time series. The effectiveness of the method is verified by means of a large number of artificial fractional Brownian motions. It is used…
This paper introduces a novel approach to stock data analysis by employing a Hierarchical Graph Neural Network (HGNN) model that captures multi-level information and relational structures in the stock market. The HGNN model integrates stock…
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional…
We obtain a lower asymptotic bound on the decay rate of the probability of a portfolio's underperformance against a benchmark over a large time horizon. It is assumed that the prices of the securities are governed by geometric Brownian…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
Prediction of stock prices has been a crucial and challenging task, especially in the case of highly volatile digital currencies such as Bitcoin. This research examineS the potential of using neural network models, namely LSTMs and GRUs, to…
The importance of predicting stock market prices cannot be overstated. It is a pivotal task for investors and financial institutions as it enables them to make informed investment decisions, manage risks, and ensure the stability of the…
It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and…