This article develops theoretical insight into the effect in expected volatility, which means that large shocks are less persistent in volatility than small shocks. The model uses the Kyle-Admati-Pfleiderer setup with liquidity traders, informed traders, and a market maker. Information is modeled as a GARCH process. It is shown that the GARCH process for information is transformed into a TARCH process (for threshold GARCH) for the market price changes. Working with information flows allows one to derive implications for trading volume and market liquidity which provide the basis for a more complete test of the model. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

This article presents an application of extreme value theory to compute the value at risk of a market position. In statistics, extremes of a random process refer to the lowest observation (the minimum) and to the highest observation (the maximum) over a given time-period. Extreme value theory gives some interesting results about the distribution of extreme returns. In particular, the limiting distribution of extreme returns observed over a long time-period is largely independent of the distribution of returns itself. In financial markets, extreme price movements correspond to market corrections during ordinary periods, and also to stock market crashes, bond market collapses or foreign exchange crises during extraordinary periods. An approach based on extreme values to compute the VaR thus covers market conditions ranging from the usual environment considered by the existing VaR methods to the financial crises which are the focus of stress testing. Univariate extreme value theory is used to compute the VaR of a fully aggregated position while multivariate extreme value theory is used to compute the VaR of a position decomposed on risk factors.