Statistical Finance
In this paper we explore the specific role of randomness in financial markets, inspired by the beneficial role of noise in many physical systems and in previous applications to complex socio- economic systems. After a short introduction, we…
Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an…
Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail…
As described in this paper, we study market-wide price co-movements around crashes by analyzing a dataset of high-frequency stock returns of the constituent issues of Nikkei 225 Index listed on the Tokyo Stock Exchange for the three years…
In this paper we perform a statistical analysis of the high-frequency returns of the IBEX35 Madrid stock exchange index. We find that its probability distribution seems to be stable over different time scales, a stylized fact observed in…
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient {\rho} as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence…
Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces…
Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which…
We investigate the use of the Hurst exponent, dynamically computed over a moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2010 credit crisis show…
This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…
We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the…
This paper presents performance analysis of hybrid model comprise of concordance and Genetic Programming (GP) to forecast financial market with some existing models. This scheme can be used for in depth analysis of stock market. Different…
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is…
The paper presents new machine learning methods: signal composition, which classifies time-series regardless of length, type, and quantity; and self-labeling, a supervised-learning enhancement. The paper describes further the implementation…
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete…
We have analyzed the Indices of Industrial Production (Seasonal Adjustment Index) for a long period of 240 months (January 1988 to December 2007) to develop a deeper understanding of the economic shocks. The angular frequencies estimated…
In this paper we propose a bivariate generalization of a weighted indexed semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that financial returns are described by a weighted indexed semi-Markov chain…
Employing a recent technique which allows the representation of nonstationary data by means of a juxtaposition of locally stationary patches of different length, we introduce a comprehensive analysis of the key observables in a financial…
The cross-correlations between the exchange rate fluctuations of 74 currencies over the period 1995-2012 are analyzed in this paper. The eigenvalue distribution of the cross-correlation matrix exhibits a bulk which approximately matches the…
Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…