  The existence of time-lagged cross-correlations between the returns of a pair
of assets, which is known as the lead-lag relationship, is a well-known
stylized fact in financial econometrics. Recently some continuous-time models
have been proposed to take account of the lead-lag relationship. Such a model
does not follow a semimartingale as long as the lead-lag relationship is
present, so it admits an arbitrage without market frictions. In this paper we
show that they are free of arbitrage if we take account of market frictions
such as the presence of minimal waiting time on subsequent transactions or
transaction costs.
