Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets

TL;DR

This paper models optimal trading strategies in futures markets considering transaction costs, using a discrete-time Brownian market model, and provides explicit solutions for maximizing expected utility of terminal wealth.

Contribution

It introduces a framework for futures trading with transaction costs, including concepts like margin and slippage, and derives explicit solutions for optimal portfolio strategies.

Findings

Explicit solution for optimal portfolio process.

Framework incorporating margin, gearing, and slippage.

Analysis of utility maximization under transaction costs.

Abstract

We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a fund/agent investing in futures markets. We offer some preliminary remarks about statistical arbitrage strategies and we set the framework for futures markets, and introduce concepts such as margin, gearing and slippage. The setting is of discrete time, and the price evolution of the futures prices is modelled as discrete random sequence involving Ito's sums. We assume the drift and the Brownian motion driving the return process are non-observable and the transaction costs are represented by the bid-ask spread. We provide explicit solution to the optimal portfolio process, and we offer an example using logarithmic utility.