We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

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We present a simple model of a stock market where a random communication structure between agents generically gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to distributions observed in recent empirical studies of high frequency market data. Our model provides a link between two well-known market phenomena: the heavy tails observed in the distribution of stock market returns on one hand and 'herding' behavior in financial markets on the other hand. In particular, our study suggests a relation between the excess kurtosis observed in asset returns, the market order flow and the tendency of market participants to imitate each other.

We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Itô formula to pathdependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space of square-integrable martingales. This extension defines a weak derivative which is shown to be the inverse of the Itô integral and which may be viewed as a nonanticipative "lifting" of the Malliavin derivative.These results lead to a constructive martingale representation formula for Itô processes. By contrast with the Clark-Haussmann-Ocone formula, this representation only involves nonanticipative quantities which may be computed pathwise.

31 pages, 3 figures. First version: 2007. Revised: 2009.International audienceMeasuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ``risk measure" which summarizes the risk of the portfolio. We define the notion of ``risk measurement procedure", which includes both of these steps and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate in particular that using recently proposed risk measures like CVaR/ expected shortfall lead to a less robust risk measurement procedure than historical Value at Risk. We also propose alternative risk measurement procedures which possess the robustness property

We study the price impact of order book events -limit orders, market orders and cancelations -using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask prices. Our study reveals a linear relation between order flow imbalance and price changes, with a slope inversely proportional to the market depth. These results are shown to be robust to seasonality effects, and stable across time scales and across stocks. We argue that this linear price impact model, together with a scaling argument, implies the empirically observed "square-root" relation between price changes and trading volume. However, the relation between price changes and trade volume is found to be noisy and less robust than the one based on order flow imbalance.

20.02.13 KB. Elsevier says okd for accepted version ok to add while mandate not enforced. Elsevie

We present a quantitative methodology for analyzing the potential for contagion and systemic risk in a network of interlinked financial institutions, using a metric for the systemic importance of institutions: the Contagion Index.We apply this methodology to a data set of mutual exposures and capital levels of financial institutions in Brazil in 2007 and 2008, and analyze the role of balance sheet size and network structure in each institution's contribution to systemic risk. Our results emphasize the contribution of heterogeneity in network structure and concentration of counterparty exposures to a given institution in explaining its systemic importance. These observations plead for capital requirements which depend on exposures, rather than aggregate balance sheet size, and which target systemically important institutions.