Inference for time-varying lead–lag relationships from ultra-high-frequency data

Abstract

A new approach for modeling lead–lag relationships in high-frequency financial markets is proposed. The model accommodates non-synchronous trading and market microstructure noise as well as intraday variations of lead–lag relationships, which are essential for empirical applications. A simple statistical methodology for analyzing the proposed model is presented, as well. The methodology is illustrated by an empirical study to detect lead–lag relationships between the S&P 500 index and its two derivative products.

No arbitrage and lead–lag relationships

“…Rather recently, Hoffmann et al [26] have proposed a lead-lag model in continuous-time (see also Robert and Rosenbaum [45]), which is based on Brownian motion driven modeling and contains traditional Itô processes as a special case, hence it is readily compatible with the traditional mathematical finance theory. Related models have been subsequently studied by several authors such as [1,5,7,27] for empirical work and [6,11,23,24,34,35] from a statistical point of view, but there is no work in the context of mathematical finance. We intend to bridge the gap between those two areas in this work.…”