Quantification of the High Level of Endogeneity and of Structural Regime Shifts in Commodity Markets

Abstract

We propose a novel index of short-term endogeneity (or reflexivity) derived by calibrating the Hawkes self-excited conditional Poisson model on empirical time series of trades. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact of news and the endogenous mechanism 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 quantified for several commodity futures markets (corn, oil, soybean, sugar, and wheat) and also for a benchmark equity futures market (E-mini S&P 500). Specifically, the reflexivity index is the 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. We find an overall increase of the level of short-term endogeneity since the mid-2000s to October 2012, with a typical value nowadays around 0.6-0.7, implying that at least 60-70 per cent of commodity price changes are now due to self-generated activities rather than novel information. Our robustness tests show that the branching ratio provides a 'pure' measure of endogeneity that is independent of the rate of activity, order size, volume or volatility.Email addresses: vfilimonov@ethz.ch (Vladimir Filimonov), david.bicchetti@unctad.org (David Bicchetti), nicolas.maystre@unctad.org (Nicolas Maystre), dsornette@ethz.ch (Didier Sornette) Preprint submitted to The Journal of International Money and Finance (JIMF)March 21, 2013We complement our analysis by relating the endogeneity dynamics of these futures markets to their price dynamics, particularly around the commodity bubble that developed since 2006 and culminated in mid-2008. While our index does not have a long-term memory, interestingly, we find that it can still provide some interesting insights when the mechanisms working at longer time scales cascade down to shorter terms.

Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

“…This result has important implications concerning the efficient market hypothesis and the stability of financial markets in the presence of increasing trading frequency and volume. Our motivation is further increased by the recent claim based also on the calibration of the Hawkes process that financial market have been continuously functioning at or close to criticality (n ≃ 1) over the last decades [4], a result in contradiction with our other studies [2,3].…”

“…The methodology for estimating the endogeneity (or reflexivity) present in the dynamics of a given point process, developed in [2] and later exploited in [3,4,5], is based on the self-excited conditional Poisson model introduced by [6,7]. Being a point process, the linear Hawkes model is defined with the conditional intensity λ(t|F t− ) = lim h↓0 1 h Pr N(t + h) − N(t) > 0|F t− ,…”

“…The shape of the kernel function h(t) defines the correlation properties of the process. Financial applications traditionally use an exponential kernel [8,9,10,2,3] h(t) = 1 τ exp − t τ χ(t) .…”

“…In our original work [2], we have calibrated the Hawkes process within short intervals of 10 to 30 minutes that we scanned over the whole history of E-mini S&P 500 Futures Contracts. Then, we collected the estimates within Regular Trading Hours (RTH, 9:30 to 16:15 CDT) in each month and averaged them to construct the "reflexivity index" for the given month [2,3]. In contrast, [4] considered long intervals of two months, where data was concatenate from the Regular Trading Hours of each day to construct one single continuous point process.…”

“…The motivation of our study stems from the meaning of n as a direct measure of endogeneity (or reflexivity), since n is exactly equal to the fraction of the average number of endogenously generated events among all events [1,2] for stationary time series. Concretely, the measure n = 0.7 − 0.8 reported in our recent studies [2,3] means that 70 to 80% of all trades in the E-mini S&P 500 Futures Contracts and in major commodity future contracts are due in recent years to past trades rather than to external effects or exogenous news. This result has important implications concerning the efficient market hypothesis and the stability of financial markets in the presence of increasing trading frequency and volume.…”