Feedback and efficiency in limit order markets

A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the order book are essential to ensure consistency at the smallest time scale. All the stocks investigated in Paris Stock Exchange have consistent price impact functions.Comment: 8 pages, 2 figures. Proceedings of APFA

Regrets, learning and wisdom

This contribution discusses in what respect Econophysics may be able to contribute to the rebuilding of economics theory. It focuses on aggregation, individual vs collective learning and functional wisdom of the crowds.Comment: 9 pages, 1 figure. Opinion paper submitted to European Physical Journal - Special Topics "Can economics be a physical science?

Sharper asset ranking from total drawdown durations

The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities.Comment: 21 pages, 12 figure

One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statistics

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity. A nonparametric two-sample r-statistic is introduced, whose power is very close to that of Welch statistic for Gaussian or uniformly distributed variables.Comment: 12 pages, 13 figure

Inter-pattern speculation: beyond minority, majority and $-games

A new model of financial market is proposed, based on the sequential and inter-temporal nature of trader-trader interaction. In this pattern- based speculation model, the traders open and close their positions explicitely. Information ecology can be precisely characterised, and is strikingly similar to that of the Minority Game. Naive and sophisticated agents are shown to give rise to very different phenomenology.Financial market, agent-based modelling, minority game, majority game, $-game, information, market efficiency

Validation of agent-based models

The automatic collection of customer transaction data, through either online shops or reward cards, is producing very large databases which contain much information about consumer behaviour. What kind of information and how exploitable it is are very relevant questions. Two approaches are being used. Either one concentrates on individual behaviour and tries to apply various theoretical frameworks and results of the literature on discrete choice, or one uses clustering algorithms in order to determine several classes of customers. The very existence of such categories is likely to be the result of social interactions and influences. The literature on discrete choice cannot easily be generalised to networked interactions, which are known to be widely present in various contexts. Another approach is to use toy models of individual behaviour and concentrate on global, aggregate quantities such as market share or demand fluctuations. This raises the question of how to validate such kind of model, hence the request of Unilever. The latter should also be understood with respect to the contribution of ESGI 2004, where a very sophisticated agent-based model of consumer behaviour was proposed (but not much studied)