Estimation of the lead-lag parameter from non-synchronous data

Abstract

We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process (Xt,Y t ) reproduces a lead-lag effect if, for some time shift v σ R, the process (Xt,Yt+v ) is a semi-martingale with respect to a certain filtration. The value of the time shift v is the lead-lag parameter. Depending on the underlying filtration, the standard no-arbitrage case is obtained for v= 0. We study the problem of estimating the unknown parameter v σ R, given randomly sampled nonsynchronous data from (X t ) and (Yt). By applying a certain contrast optimization based on a modified version of the Hayashi-Yoshida covariation estimator, we obtain a consistent estimator of the lead-lag parameter, together with an explicit rate of convergence governed by the sparsity of the sampling design. © 2013 ISI/BS.