Catálogo de publicaciones - libros

The Foreign Exchange Market is a market for the trade of currencies and it defines their relative values. The study of the interdependence and correlation between price fluctuations of currencies is important to understand this market. For this purpose, in this work we search for the dependence between the time series of prices for pairs of currencies using a mutual information approach. By applying time shifts we are able to detect time delay in the dependence, what enable us to construct a directed network showing the influence structure of the market. Finally, we obtain a dynamic description of this structure by analyzing the time evolution of the network. Since the period of analysis includes the great earthquake in Japan in 2011, we can observe how such big events affect the network.

Entropy measures in their various incarnations play an important role in the study of stochastic time series providing important insights into both the and the structure of the stochastic relationships between the individual components of a system. Recent applications of entropic techniques and their linear progenitors such as Pearson correlations and Granger causality have included both as well as periods in a system’s dynamical evolution. Here I measure the entropy, Pearson correlation and transfer entropy of the intra-day price changes of the Dow Jones Industrial Average (DJIA) in the period immediately leading up to and including the Asian financial crisis and subsequent mini-crash of the DJIA on the 27th October 1997. I use a novel variation of transfer entropy that dynamically adjusts to the arrival rate of individual prices and does not require the binning of data to show that quite different relationships emerge from those given by the conventional Pearson correlations between equities. These preliminary results illustrate how this modified form of the TE compares to results using Pearson correlation.

We analyze mechanisms of foreign currency market order’s annihilation with a focus on the lifetime of these orders. Limit orders submitted in this market are approximately executed according to the random walk theory. In consequence, the distribution of execution lifetime can be approximated by a power law with exponent 1/2. Alternatively, limit orders submitted in foreign currency markets are roughly cancelled according to a mixed distribution; as a random walk with a tail following a power law. The cancellation lifetime distribution can be approximated by using a scaling relationship between the distance from mid-price and the random walk theory. In addition, we introduce the concept that market participants cancel orders depending on the market price’s movement which is represented as the movement of the mid-price. Taking into consideration market conditions when orders have been injected, market participants do not have symmetric decision rules. This behavior could at least partially explain the shape of price change distribution.

A time series of signs of market orders was found to exhibit long memory. There are several proposed explanations for the origin of this phenomenon. A cogent one is that investors tend to strategically split their large hidden orders into small pieces before execution to prevent the increase in the trading costs. Several mathematical models have been proposed under this explanation.In this paper, taking the bursty nature of the human activity patterns into account, we present a new mathematical model of order signs that have a long memory property. In addition, the power law exponent of distribution of a time interval between order executions is supposed to depend on the size of hidden order. More precisely, we introduce a discrete time stochastic process for polymer model, and show it’s scaled process converges to a superposition of a Brownian motion and countably infinite number of fractional Brownian motions with Hurst exponents greater than one-half.

This article reviews a recent finding on the properties of stock market indices (Wu, Europhys Lett 97:48009, 2012). A stock market index is an average of a group of stock prices with equal or unequal weights. Different stock market indices derived from various combinations of stocks are not expected to have fixed relations among them. From analyzing the daily index ratios of Dow Jones Industry Average (DJIA), NASDAQ, and S&P500 from 1971/02/05 to 2011/06/30 using the empirical mode decomposition, we found that the ratios NASDAQ/DJIA and S&P500/DJIA, normalized to 1971/02/05, approached and then retained the values of 2 and 1, respectively. The temporal variations of the ratios consist of global trends and oscillatory components including a damped oscillation in 8-year cycle and damping factors of 7183 days (NASDAQ/DJIA) and 138,471 days (S&P500/DJIA). Anomalies in the ratios, corresponding to significant increases and decreases of indices, are local events appearing only in the time scale less than 8-year cycle. The converge of the dominant damped oscillatory component implies that representative stocks in the pair-markets become more coherent as time evolves.

This paper utilizes agent-based simulation to explore market making strategy for high frequency traders (HFTs) and tests its performance under competition environments. After proposing a model representing HFTs’ activities in financial market when they act as market makers, we carry out simulations to explore how order price and order quantity affect HFTs’ profits and risks. As the result, we find that offering prices around last trading price, as well as taking advantage of order imbalance, increases HFTs’ returns. On the other hand, our results show utilizing adaptive order size based on previous order execution rate and setting a net threshold based on average trading volume helps to control the risks of end-of-day inventory. In addition, we introduce the competition environments of increased competitors and decreased latency, so as to see how these factors affect the performance of market making strategy.

We investigate the effect of the order canceling rule in the trading model of financial exchanges. This study employs a stochastic order-book model. Such models are widely used to study the relation between price fluctuation and price formation in continuous double auction. The model herein incorporates simple mechanisms such as limit order and trading rules without considering investors’ strategies. It captures the transaction structure used in financial exchanges. Using three simple stochastic order-book models, we indicate the comparative analysis of the effectiveness of the cancel order.

Throughout the past decade, there has been a significant advance in understanding the structure and function of networks, and mathematical models of networks are now widely used to describe a broad range of complex systems, such as socio-economic systems. However, the significant majority of methods have dealt almost exclusively with individual networks treated as isolated systems. In reality an individual network is often just one component in a much larger complex multi-level network (network of networks, NON). The NON framework provides critical new insights into the structure and function of real-world complex systems. One such insight is that NON system is significantly more vulnerable to shocks and damages, which has lead to the development of the theory of cascading failures in interdependent networks. Here we provide an overview of this theory, and one example of its application to economic systems.

Whether interactions among the elements make the system robust or fragile has been a central issue in broad range of field. Here we introduce a novel type of mechanism which governs the robustness of open and dynamical systems such as social and economical systems, based on a very simple mathematical model. This mechanism suggest a moderate number ( ∼ 10) of interactions per element is optimal to make the system against successive and unpredictable disturbances. The relation between this very simple model and more detailed nonlinear dynamical models is discussed, to emphasize the relevance of this newly reported mechanism to the real phenomena.

In this study, we introduce a model to simulate gross domestic product (GDP) for international trade network data. By applying a linear gravity transportation model, we confirm that estimated values approximately agree with the real values of GDP by tuning the model parameters. An exception is the estimated GDP of China that is about two times bigger than the real value. This discrepancy might imply that China’s GDP is not saturated and it is on the way of growing.