"Market making" behaviour in an order book model and its impact on the bid-ask spread

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.Comment: 17 pages, 9 figure

Exact and asymptotic solutions of the call auction problem

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.Comment: 24 pages, 7 figure

Econophysics: empirical facts

This article aims at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since its name was coined in 1995 by merging the words "Economics" and "Physics", this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes. We give a brief introduction in the first part and begin with discussing interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics in the second part. Then the third part is dedicated to empirical studies revealing statistical properties of financial time series. We begin the presentation with the widely acknowledged "stylized facts" describing the distribution of the returns of financial assets: fat-tails, volatility clustering, etc. Then we show that some of these properties are directly linked to the way "time" is taken into account, and present some new remarks on this account. We continue with the statistical properties observed on order books in financial markets. For the sake of illustrations in this review, (nearly) all the stated facts are reproduced using our own high-frequency financial database. Contributions to the study of correlations of assets such as random matrix theory and graph theory are finally presented in this part. The fourth part of our review deals with models in Econophysics through the point of view of agent-based modeling. Using previous work originally presented in the fields of behavioural finance and market microstructure theory, econophysicists have developed agent-based models of orderdriven markets that are extensively reviewed here. We then turn to models of wealth distribution where an agent-based approach also prevails: kinetic theory models, and continue with game theory models and review the now classic minority games. We end this review by providing an outlook on possible directions of research.

Econophysics: agent-based models

This article is the second part of a review of recent empirical and theoretical developments usually grouped under the heading Econophysics. In the first part, we reviewed the statistical properties of financial time series, the statistics exhibited in order books and discussed some studies of correlations of asset prices and returns. This second part deals with models in Econophysics from the point of view of agent-based modeling. Of the large number of multiagent- based models, we have identified three representative areas. First, using previous work originally presented in the fields of behavioral finance and market microstructure theory, econophysicists have developed agent-based models of order-driven markets that we discuss extensively here. Second, kinetic theory models designed to explain certain empirical facts concerning wealth distribution are reviewed. Third, we briefly summarize game theory models by reviewing the now classic minority game and related problems.

Parallel Iterative Linear Solvers on GPU: A Financial Engineering Case

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