In order to disentangle the internal dynamics from exogenous factors within the Autoregressive Conditional Duration (ACD) model, we present an effective measure of endogeneity. Inspired from the Hawkes model, this measure is defined as the average fraction of events that are triggered due to...

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting...

We investigate the distributions of epsilon-drawdowns and epsilon-drawups of the most liquid futures financial contracts of the world at time scales of 30 seconds. The epsilon-drawdowns (resp. epsilon- drawups) generalise the notion of runs of negative (resp. positive) returns so as to capture...

We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of...

We propose a “reflexivity” index that quantifies the relative importance of short-term endogeneity for several commodity futures markets (corn, oil, soybean, sugar, and wheat) and a benchmark equity futures market (E-mini S&P 500), from mid-2000s to October 2012. Our reflexivity index is...

We present a new theory of homogeneous volatility (and variance) estimators for arbitrary stochastic processes. The main tool of our theory is the parsimonious encoding of all the information contained in the OHLC prices for a given time interval by the joint distributions of the high-minusopen,...

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes...

This paper offers a new class of models for the term structure of forward interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, but constrain the shocks so that the forward rate curve is kept continuous. We term the shocks to the forward curve...

This paper offers a new class of models for the term structure of forward interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, but constrain the shocks so that the forward rate curve is kept continuous. We term the shocks to the forward curve...

We propose a “reflexivity” index that quantifies the relative importance of short-term endogeneity/reflexivity for several commodity futures markets (corn, oil, soybeans, sugar, and wheat) and a benchmark equity futures market (E-mini S&P 500). Our reflexivity index is defined as the average...