Exogenous versus endogenous dynamics in the price discovery process

The talk discusses feedback mechanisms in the price discovery process: from high-frequency marketmaking and algorithmic trading to long-term behavioral mechanisms. In order to quantify short-term endogeneity we propose an index derived by calibrating the self-excited Hawkes model on empirical time series of trades. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact and the the feedback look by which past trading activity may influence future trading activity. Technically known in the mathematical literature on branching processes as the branching ratio, the reflexivity index is defined as an average ratio of the number of price moves that are due to endogenous interactions to the total number of all price changes, which also include exogenous events. This index quantifies at the same time both "criticality" of the system (stability and susceptibility to large shocks) and its "efficiency" (in sense of the Efficient Market Hypothesis). We calibrate our measure on several financial and commodity futures markets and documented presence of "micro" regime shifts that coincided with "macro" changes in trading methods or sentiments of investors. Finally we relate our analysis to recent evidences of an intrinsic "criticality" of price discovery and make a bridge between short- and long-memory models.