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

By Marc Hoffmann, Mathieu Rosenbaum, Nakahiro Yoshida. 2013

66 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/7da377fa19f5a8bdb1468785b1635e4ad26772f7

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In Economics and Econometrics

1. Tristan Froidure
2. Yves Choueifaty
3. Julien Reynier

In Finance

1. Tristan Froidure
2. Julien Reynier
3. Yves Choueifaty

Citations in the corpus

• Properties of the Most Diversified Portfolio (2013, background): “See also Hoffmann et al (2009) for further references.”