We explore the NYSE Trades and Quotes (TAQ) database that contains tick-by-tick transaction information of stocks traded in the New York Stock Exchange and NASDAQ stock markets. Consistent with asymmetric information models of market infrastructure, we analyze the role of trading intensity, as a proxy for latent information, on the value of financial assets. We consider the interval-valued time series (ITS) of low/high returns. We assume that the returns (or prices) are generated by a latent process with some unknown conditional density. From this density, at each period of time, we have some random draws (trades) and the lowest and highest returns are the realized extreme observations of the latent process over the sample of draws. In this context, we propose a semiparametric model of extreme returns that exploits the results provided by extreme value theory. If properly centered and standardized extremes have well-defined limiting distributions, the conditional mean of extreme returns is a highly nonlinear function of conditional moments of the latent process and of the conditional intensity of the process that governs the number of draws. We implement a two-step estimation procedure. In a first step, we estimate parametrically the regressors that will enter into the nonlinear function. In a second step, we estimate nonparametrically the conditional mean of extreme returns as a function of the generated regressors. Unlike current models for ITS, the proposed semiparametric model is robust to misspecification of the conditional density of the latent process. We fit several nonlinear and linear models to the 5-min and 1-min low/high returns to seven major banks and technology stocks, and find that the nonlinear specification is superior to the current linear models and that the conditional volatility of the latent process and the conditional intensity of the trading process are major drivers of the dynamics of extreme returns.

Prof. Gloria Gonzalez-Rivera