Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating portfolios of highly liquid stocks, we find that there are a large number of high-frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one-factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets

Recent years have seen an unprecedented rise of the role that technology plays in all aspects of human activities. Unavoidably, technology has heavily entered the Capital Markets trading space, to the extent that all major exchanges are now trading exclusively using electronic platforms. The ultra fast speed of information processing, order placement, and cancelling generates new dynamics which is still not completely deciphered.Analyzing a large dataset of stocks traded on the US markets, our study evidences that since 2001 the level of synchronization of large price movements across assets has significantly increased. Even though the total number of over-threshold events has diminished 1 www.quantlab.it 1 arXiv:1505.00704v1 [q-fin.ST] 4 May 2015 in recent years, when an event occurs, the average number of assets swinging together has increased. Quite unexpectedly, only a minor fraction of these events -regularly less than 40% along all years -can be connected with the release of pre-announced macroeconomic news. We also document that the larger is the level of sistemicity of an event, the larger is the probability -and degree of sistemicity -that a new event will occur in the near future. This opens the way to the intriguing idea that systemic events emerge as an effect of a purely endogenous mechanism. Consistently, we present a high-dimensional, yet parsimonious, model based on a class of self-and cross-exciting processes, termed Hawkes processes, which reconciles the modeling effort with the empirical evidence.

We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return times, Lyapunov exponent). We considered as a benchmark for the methods several systems with different statistical properties: renewal processes, dynamical systems provided and not provided with a Markov partition, slow or fast decay of correlations. Most experiments are supported by rigorous mathematical results, which are explained in the paper.

We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate true inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure.

No abstract