# Trading strategies for stock pairs regarding to the cross-impact cost

## TL;DR

This paper develops an extended trading strategy framework for stock pairs that minimizes cross-impact costs by optimizing trading rates and periods, supported by empirical data analysis.

## Contribution

It introduces a novel extension of Gatheral's single-stock trading model to pairs of stocks, incorporating cross-impact effects and empirical cost quantification.

## Key findings

- Optimal trading strategies reduce cross-impact costs.
- Empirical analysis quantifies cross-impacts of volume and time lag.
- Model demonstrates influence of cross-impacts on trading decisions.

## Abstract

We extend the framework of trading strategies of Gatheral [2010] from single stocks to a pair of stocks. Our trading strategy with the executions of two round-trip trades can be described by the trading rates of the paired stocks and the ratio of their trading periods. By minimizing the potential cost arising from cross-impacts, i.e., the price change of one stock due to the trades of another stock, we can find out an optimal strategy for executing a sequence of trades from different stocks. We further apply the model of the strategy to a specific case, where we quantify the cross-impacts of traded volumes and of time lag with empirical data for the computation of costs. We thus picture the influence of cross-impacts on the trading strategy.