A Sentiment-Based Model for the Bitcoin: Theory, Estimation and Option Pricing

Bitcoin is a decentralised digital currency which attracts growing interest over recent years. Much research from different subjects emerged as bitcoin is a multidisciplinary product. Among all these studies, the interpretation of the drastic fluctuation of bitcoin price attracts a great attention. Many influence factors of bitcoin price were found. However, seldom research reveals the dependence structure between price and its influence factors. By selecting ten interpretable influence factors from the bitcoin network and using copula theory, we find that the bitcoin price has different correlation structures with its influence factors. These findings provide new insights into the behaviour of miners, users, and coins in the bitcoin system, thus leading to meaningful implications for policymakers, investors and risk managers dealing with bitcoin and other cryptocurrencies.

Bitcoin, the first decentralized cryptocurrency, has attracted significant attention from investors and researchers alike due to its volatile and unpredictable price movements. However, predicting the price of Bitcoin remains a challenging task. This paper presents a detailed literature review on previous studies that have attempted to predict the price of Bitcoin. It discusses the main drivers of Bitcoin prices, including its attractiveness, macroeconomic and financial factors with a particular focus on the use of Blockchain information. We apply time series to daily data for the period from 28/04/2013 to 28/01/2023. We used Python and TensorFlow library version 2.11.0 and propose a deep multimodal reinforcement learning policy combining Convolutional Neural Network (CNN) and Long ShortTerm Memory (LSTM) neural network for cryptocurrencies’ prices prediction. Also, this study attempts to predict the price of Bitcoin using a special type of deep neural networks, a Deep Autoencoders. Two results are worth noting: Autoencoders turns out to be the best method of predicting Bitcoin prices, and Bitcoin-specific Blockchain information is the most important variable in predicting Bitcoin prices. This study highlights the potential utility of incorporating Blockchain factors in price prediction models. Also, our findings show that sentiment indicator, Ethereum, XRP and Doge Coin prices, global currency ratio, macroeconomic factors, and Blockchain information of Ethereum did not contribute significantly toward predicting Bitcoin prices. These conclusions provide decision support for investors and a reference for the governments to design better regulatory policies.

With the continuous development of capital market, quantitative investment emerges as a new investment method. Traders often buy and sell volatile assets to maximize profits in capital markets. We use the ARIMA-GARCH time series model to make accurate predictions on the market prices of gold and Bitcoin. We creatively propose an "iterative" neural network in order to give the optimal decision based on prediction. The "iterative" neural network is different from the traditional in two main aspects: Firstly, the training set is updated daily, so as to ensure the accuracy and advancement of the neural network. Secondly, we also add confidence parameters to ensure that the neural network can be used in the case of insufficient training set. Finally, we use this neural network to give the optimal portfolio. The application of the model helps market traders to make quantitative investment decisions and maximize profits

In early 2018 Bitcoin prices peaked at US$ 20,000 and, almost two years later, we still continue debating if cryptocurrencies can actually become a currency for the everyday life or not. From the economic point of view, and playing in the field of behavioral finance, this paper analyses the relation between Bitcoin price and the search interest on Bitcoin since 2014. We questioned the forecasting ability of Google Bitcoin Trends for the behavior of Bitcoin price by performing linear and nonlinear dependency tests, and exploring performance of ARIMA and Neural Network models enhanced with this social sentiment indicator. Our analyses and models are founded upon a set of statistical properties common to financial returns that we establish for Bitcoin, Ethereum, Ripple and Litecoin.

Summary We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to compute numerically the maximum likelihood parameter estimate via the well known expectation maximization (EM) algorithm. Therefore in this paper, we propose a method of moments based parameter estimator. The moments of the observed process are computed explicitly as a function of the time discretization interval of the discrete time observation process. We then propose two algorithms for parameter estimation of the MSM. The first algorithm is based on a least-squares fit to the exact moments over different time lags, while the second algorithm is based on estimating the coefficients of the expansion (with respect to time) of the moments. Extensive numerical results comparing the algorithm with the EM algorithm for the discretized model are presented.

This article examines the influence of the major stock indices' value on Bitcoin price fluctuations. The study focuses on the correlation between the absolute value of Bitcoin and the daily closing prices of leading stock market indices — namely, the S&P 500, Nasdaq Composite, and Dow Jones Industrial Average — based on daily time series data from 2020 to 2025. The paper spotlights the correlation analysis between the dynamics of daily changes (increases or decreases) in the closing prices of these indices and the corresponding changes in the price of Bitcoin over the same time frame. The Pearson correlation coefficient was employed to quantify the strength and direction of linear relationships between Bitcoin and each stock market index for each year within selected timeframe. Furthermore, the correlation results were interpreted using Chaddock’s scale to assess their practical significance and to identify the stock asset with the highest correlation to Bitcoin. The methodological framework of the study includes quantitative analysis methods, observation, and comparative analysis. The findings reveal the presence of a variable, time-dependent correlation between Bitcoin and the selected stock indices, with stronger interconnections observed during periods of global financial turmoil. This may reflect a growing integration of the cryptocurrency market into the broader financial system. At the same time, during relatively stable periods, both the cryptocurrency and traditional stock markets tend to show a degree of independence from each other. These results support the hypothesis of Bitcoin's complex and hybrid nature as a financial asset, which may simultaneously serve speculative purposes and display certain hedging characteristics. The results obtained may be of practical importance for the development of investment strategies, portfolio diversification, cryptocurrency price forecasting, and risk assessment in conditions of increasing financial market uncertainty. Consequently, the research contributes to a deeper understanding of Bitcoin’s role within the global financial landscape and its potential responsiveness to systemic risks.

Orthonormal basis functions for modelling continuous-time systems

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.

Bivariate cumulative damage models are proposed where the responses given the damages are independent random variables. The bivariate damage process can be either bivariate Poisson or bivariate gamma. A bivariate continuous cumulative damage model is investigated in which the responses given the damages have gamma distributions. In this case evaluation of the joint density function and bivariate tail probability function is facilitated by expanding the gamma distributions of the conditional responses by Laguerre polynomials. This approach also leads to evaluation of associated survival models. Moments and estimating equations are discussed. In addition, a bivariate discrete cumulative damage model is investigated in which the responses given the damages have a distribution chosen from a class that includes the negative binomial, the Neyman Type-A, the Polya-Aeppli, and the Lagrangian Poisson. Probabilities are obtained from recursive formulas which do not involve cancellation error as all quantities are non-negative. Moments and estimating equations are presented for these models also. The continuous and the discrete models are applied to describe the rise of systolic and diastolic blood pressure with age.

Multivariate Jacobi process with application to smooth transitions

A Hybrid Model for Equity Indices and Stochastic Interest Rates

Long-term swings and seasonality in energy markets

High frequency trading and standard asset pricing models

Accelerated longitudinal designs (ALDs) provide an opportunity to capture long developmental periods in a shorter time framework using a relatively small number of assessments. Prior literature has investigated whether univariate developmental processes can be characterized with data obtained from ALDs. However, many important questions in psychology and related sciences imply working with several variables that are intercorrelated as they unfold over time, such as cognitive and cortical development. Therefore, bivariate developmental models are required. This study aimed to assess the effectiveness of continuous-time bivariate Latent Change Score (CT-BLCS) models for recovering the trajectories of two interdependent developmental processes using data from diverse ALDs. Through a Monte Carlo simulation study, the efficacy of different sampling designs and sample sizes was examined. The study fills a gap in the literature by examining the performance of ALDs in bivariate systems, providing specific recommendations for future application of ALDs for studying interrelated developmental variables.

Consistency analysis of the Simplified Refined Instrumental Variable method for Continuous-time systems