Related papers: Price predictability at ultra-high frequency: Entr…
With the increasing integration of power plants into the frequency-regulation markets, the importance of optimal trading has grown substantially. This paper conducts an in-depth analysis of their optimal trading behavior in sequential…
We study the impact of volatility on intraday serial correlation, at time scales of less than 20 minutes, exploiting a data set with all transaction on SPX500 futures from 1993 to 2001. We show that, while realized volatility and intraday…
Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…
This paper assumes that the randomness of market trade values and volumes determines the properties of stochastic market prices. We derive the direct dependence of the first two price statistical moments and price volatility on statistical…
Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropy must typically be estimated from observed data because researchers do not have access to the underlying…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or…
This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…
We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity,…
Building on Shannon's lead, let's consider a more malleable expression for tracking uncertainty, and states of "knowledge available" vs. "knowledge missing," to better practice innovation, improve risk management, and successfully measure…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices…
We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition…
This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…
Misclassification detection is an important problem in machine learning, as it allows for the identification of instances where the model's predictions are unreliable. However, conventional uncertainty measures such as Shannon entropy do…
This work aims to analyse the predictability of price movements of cryptocurrencies on both hourly and daily data observed from January 2017 to January 2021, using deep learning algorithms. For our experiments, we used three sets of…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011)…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…