Papers › Estimation of the lead-lag parameter from non-synchronous data
Estimation of the lead-lag parameter from non-synchronous data
M. Hoffmann, M. Rosenbaum, N. Yoshida
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We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process (Xₜ,Yₜ) reproduces a lead-lag effect if, for some time shift ϑ∈ℝ, the process (Xₜ,Y_(t+ϑ)) is a semi-martingale with respect to a certain filtration. The value of the time shift ϑ is the lead-lag parameter. Depending on the underlying filtration, the standard no-arbitrage case is obtained for ϑ=0. We study the problem of estimating the unknown parameter ϑ∈ℝ, given randomly sampled non-synchronous data from (Xₜ) 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.
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