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Fabrizio Lillo

Publications and source records attributed to Fabrizio Lillo.

5 recordsLinked to original sources
PubMed2005

Scaling and data collapse for the mean exit time of asset prices.

We study theoretical and empirical aspects of the mean exit time (MET) of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a prefactor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both two-state and three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

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PubMed2005

Theory for long memory in supply and demand.

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [J.-P. Bouchaud, Y. Gefen, M. Potters, and M. Wyart, Quant. Finance 4, 176 (2004); F. Lillo and J. D. Farmer Dyn. Syst. Appl. 8, 3 (2004)]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power-law distributed, this gives rise to power-law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v(-alpha) and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau(-(alpha-1)). This is a long-memory process when alpha < 2. With a few caveats, this gives a good match to the data. A version of the model also shows long-memory fluctuations in order execution rates, which may be relevant for explaining the long memory of price diffusion rates.

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PubMed2003

Topology of correlation-based minimal spanning trees in real and model markets.

We compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period with the one obtained from surrogated data simulated by using simple market models. We find that the empirical tree has features of a complex network that cannot be reproduced, even as a first approximation, by a random market model and by the widespread one-factor model.

Journal Article↗
PubMed2002

Comparative genomics study of inverted repeats in bacteria.

MOTIVATION: Comparative genomics provides a powerful way to investigate regularities and differences observed at DNA level across species. Here we study the number and location of inverted repeats occurring in complete genomes of bacteria. Inverted repeats are compatible with the formation of hairpin structures in the messenger RNA. Some of these structures are known to be rho-independent intrinsic terminators. RESULTS: We investigate the number of inverted repeats observed in 37 complete genomes of bacteria. The number of inverted repeats observed is much higher than expected using Markovian models of DNA sequences in most of the eubacteria. By using the information annotated in the genomes we discover that in most of the eubacteria the inverted repeats of stem length longer than 8 nucleotides preferentially locate near the 3' end of the nearest coding regions. We also show that IRs characterized by large values of the stem length locate preferentially in short non-coding regions bounded by two 3' ends of convergent genes. By using the program TransTerm recently introduced to predict transcription terminators in bacterial genomes, we conclude that only a part of the observed inverted repeats fullfils the model requirements characterizing rho-independent termination in several genomes. AVAILABILITY: http://lagash.dft.unipa.it/IR.html

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