Cointegration in discrete and continuous time and application to pairs trading

When creating trading strategies, the most usual approach is to suppose simple dynamics such as the Geometric Brownian Motion [2] for the assets and to use aggregate market indicators that condense systematic behavior. These procedures while providing a market view, fail to improve the understanding of single-asset continuous-time behavior. On the other hand, many improvements have been made to better model asset dynamics from the standard GBM to other models, mainly focused on volatility improvements as [5]. However, these approaches do not properly improve the modelling of the drift term. This work focuses on combining a property of co-movement of assets, that is, a systematic factor, while having a continuous-time model for each asset’s dynamics explained by a stochastic differential equation.