  We propose a simple continuous time model for modeling the lead-lag effect
between two financial assets. A two-dimensional process $(X_t,Y_t)$ reproduces
a lead-lag effect if, for some time shift $\vartheta\in \mathbb{R}$, the
process $(X_t,Y_{t+\vartheta})$ is a semi-martingale with respect to a certain
filtration. The value of the time shift $\vartheta$ is the lead-lag parameter.
Depending on the underlying filtration, the standard no-arbitrage case is
obtained for $\vartheta=0$. We study the problem of estimating the unknown
parameter $\vartheta\in \mathbb{R}$, given randomly sampled non-synchronous
data from $(X_t)$ and $(Y_t)$. 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.
