arXiv subjects

Roberto Mota Navarro

Publications and source records attributed to Roberto Mota Navarro.

4 recordsLinked to original sources

arXiv2025

Scaling and shape of financial returns distributions modeled as conditionally independent random variables

We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S\&P 500 index, Apple and Paramount stocks; and Bitcoin.

q-fin.ST↗

arXiv2023

Dynamical properties of volume at the spread in the Bitcoin/USD market

The study of order volumes in financial markets has shown that these display several non-trivial statistical properties. Most studies have been focused on the bulk properties of volume of incoming orders or of realized transactions rather than the dynamical aspects. The present work is a study of the dynamical properties of volume. Unlike previous works, we studied the volume available at the spread rather than the volume of incoming orders or of realized transactions. We found evidence that suggests mean reverting volume changes and strong asymmetries in the equilibrium of sell and buy orders as well as the presence of clustering.

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arXiv2021

Time-dependent relations between gaps and returns in a Bitcoin order book

Several studies have shown that large changes in the returns of an asset are associated with the sized of the gaps present in the order book In general, these associations have been studied without explicitly considering the dynamics of either gaps or returns. Here we present a study of these relationships. Our results suggest that the causal relationship between gaps and returns is limited to instantaneous causation.

q-fin.ST↗

arXiv2016

A detailed heterogeneous agent model for a single asset financial market with trading via an order book

We present an agent based model of a single asset financial market that is capable of replicating several non-trivial statistical properties observed in real financial markets, generically referred to as stylized facts. While previous models reported in the literature are also capable of replicating some of these statistical properties, in general, they tend to oversimplify either the trading mechanisms or the behavior of the agents. In our model, we strived to capture the most important characteristics of both aspects to create agents that employ strategies inspired on those used in real markets, and, at the same time, a more realistic trade mechanism based on a double auction order book. We study the role of the distinct types of trader on the return statistics: specifically, correlation properties (or lack thereof), volatilty clustering, heavy tails, and the degree to which the distribution can be described by a log-normal. Further, by introducing the practice of profit taking, our model is also capable of replicating the stylized fact related to an asymmetry in the distribution of losses and gains.

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