Catálogo de publicaciones - libros

The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996–2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, C, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.

This paper uses the Subbotin power exponential family of probability densities to statistically characterize the distribution of price returns in some European day-ahead electricity markets (NordPool, APX, Powernext). We implement a generic non-parametric method, known as Cholesky factor algorithm, in order to remove the strong seasonality and the linear autocorrelation structure observed in power prices. The filtered NordPool and Powernext data are characterized by an inverse relationship between the returns volatility and the price level - approximately a linear functional dependence in log-log space, which properly applied to the Cholesky residuals yields a homoskedastic sample. Finally, we use Maximum Likelihood estimation of the Subbotin family on the rescaled residuals and compare the results obtained for different markets. All empirical densities, irrespectively of the time of the day and of the market considered, are well described by a heavy-tailed member of the Subbotin family, the Laplace distribution.

We analyze the variations in S&P CNX NSE daily closing index stock values through discrete wavelets. Transients and random high frequency components are effectively isolated from the time series. Subsequently, small scale variations as captured by Daubechies level 3 and 4 wavelet coefficients and modelled by genetic programming. We have smoothened the variations using Spline interpolation method, after which it is found that genetic programming captures the dynamical variations quite well through Padē type of map equations. The low-pass coefficients representing the smooth part of the data has also been modelled. We further study the nature of the temporal variations in the returns.

Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount of data available, either for free in the Internet or commercially. Financial time-series analysis is of great interest to practitioners as well as to theoreticians, for making inferences and predictions. Furthermore, the stochastic uncertainties inherent in financial time-series and the theory needed to deal with them make the subject especially interesting not only to economists, but also to statisticians and physicists [ 1 ]. While it would be a formidable task to make an exhaustive review on the topic, with this review we try to give a flavor of some of its aspects.

We study the returns of stock prices and show that in the context of data from Bombay stock exchange there are groups of stocks that remain moderately correlated for up to 3 days. We use the delay correlations to identify these groups of stocks. In contrast to the results of same-time correlation matrix analysis, the groups in this case do not appear to come from any industry segments. We present our results using the closing prices of 326 significant stocks of Bombay stock exchange for the period 1995 to 2005.

We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $$ \underline{\underline E} $$ onto a non-random vector. The scaling index $$ \underline{\underline E} $$ models prices of the individual financial assets (stocks, mutual funds, etc.). We find the functional form of the characteristic function of real powers of the price returns and we compute the expectation value of these real powers and we speculate on the utility of these results for statistical inference. Finally we consider a portfolio composed of an asset and an option on that asset. We derive the characteristic function of the deviation of the portfolio, $$ \mathfrak{D}_t^{(\mathfrak{t})} $$ , defined as a temporal change of the portfolio diminished by the the compound interest earned. We derive pseudo-differential equations for the option as a function of the log-stock-price and time and we find exact closed-form solutions to that equation. These results were not known before. Finally we discuss how our solutions correspond to other approximate results known from literature,in particular to the well known Black & Scholes equation.

There has been an explosion in the number of models proposed for understanding and interpreting the dynamics of financial markets. Broadly speaking, all such models can be classified into two categories: (a) models which characterize the macroscopic dynamics of financial prices using time-series methods, and (b) models which mimic the microscopic behavior of the trader population in order to capture the general macroscopic behavior of prices. Recently, many econophysicists have trended towards the latter by using multi-agent models of trader populations. One particularly popular example is the so-called Minority Game [ 1 ], a conceptually simple multi-player game which can show non-trivial behavior reminiscent of real markets. Subsequent work has shown that - at least in principle - it is possible to train such multi-agent games on real market data in order to make useful predictions [ 2 – 5 ]. However, anyone attempting to model a financial market using such multi-agent trader games, with the objective of then using the model to make predictions of real financial time-series, faces two problems: (a) How to choose an appropriate multi-agent model? (b) How to infer the level of heterogeneity within the associated multi-agent population?

The financial markets started to be computerized due to development and spread of the Information and Communication Technology (ICT) in early 1990s. As the result rapid development and spread of electrical trading systems occurred all over the world. Moreover advance of processing speed of computers and capacity of storages leads to accumulation of activity records of market participants, high frequency financial data. By utilizing the high frequency financial data one can observe behavior of the market participants with high resolutions and analyze a large amount of data enough to quantify them in the statistically significant.

During the last few years various models of networks [ 1 , 2 ] have become a powerful tool for analysis of complex systems in such distant fields as Internet [ 3 ], biology [ 4 ], social groups [ 5 ], ecology [ 6 ] and public transport [ 7 ]. Modeling behavior of economical agents is a challenging issue that has also been studied from a network point of view. The examples of such studies are models of financial networks [ 8 ], supply chains [ 9 , 10 ], production networks [ 11 ], investment networks [ 12 ] or collective bank bankrupcies [ 13 , 14 ]. Relations between different companies have been already analyzed using several methods: as networks of shareholders [ 15 ], networks of correlations between stock prices [ 16 ] or networks of board directors [ 17 ]. In several cases scaling laws for network characteristics have been observed.

Bilateral trade relationships in the international level between pairs of countries in the world give rise to the notion of the International Trade Network (ITN). This network has attracted the attention of network researchers as it serves as an excellent example of the weighted networks, the link weight being defined as a measure of the volume of trade between two countries. In this paper we analyzed the international trade data for 53 years and studied in detail the variations of different network related quantities associated with the ITN. Our observation is that the ITN has also a scale invariant structure like many other real-world networks.