Grasping asymmetric information in market impacts

The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify the asymmetries of the distributions and of the market structures of cross-impacts, and find that the impacts across the market are asymmetric and non-random. Using spectral statistics and Shannon entropy, we visualize the asymmetric information in price impacts. Also, we introduce an entropy of impacts to estimate the randomness between stocks. We show that the useful information is encoded in the impacts corresponding to small entropy. The stocks with large number of trades are more likely to impact others, while the less traded stocks have higher probability to be impacted by others

Time scales involved in market emergence

In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or minutes up to two days, we compare magnitude of the largest eigenvalue of the correlation matrix for the same set of securities but for different time scales. For various sets of stocks of different capitalization (and the average trading frequency), we observe a significant elevation of the largest eigenvalue with increasing time scale. Our results from the correlation matrix study go in parallel with the so-called Epps effect. There is no unique explanation of this effect and it seems that many different factors play a role here. One of such factors is randomness in transaction moments for different stocks. Another interesting conclusion to be drawn from our results is that in the contemporary markets the emergence of significant correlations occurs on time scales much smaller than in the more distant history.Comment: 13 page

"Decentralized Trade, Random Utility and the Evolution of Social Welfare"

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are subject to persistent random shocks stemming from agents' maximization of random utility. By imposing structure on the utility noise term -logit distribution-, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizer of several social welfare functions in different variants of the model.

Decentralized Trade, Random Utility and the Evolution of Social Welfare

We study decentralized trade processes in general exchange economies and house allocation problems with and without money. Such processes are subject to persistent random shocks stemming from agents’ maximization of random utility. By imposing structure on the utility noise term —logit distribution—, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizer of several social welfare functions in different variants of the model.Decentralized Trade, Exchange Economies, Housing Markets, Stochastic Stability, Logit Model, Social Welfare Functions