Optimal Futures Trading with Bid-Ask Transaction Costs

Summary

This document formulates expected utility maximization of terminal wealth for an investor trading futures in discrete time. It places the problem in a Brownian market framework and introduces practical futures concepts including margin, gearing, and slippage. Price changes are represented as a discrete random sequence, while the return process is driven by an unobserved drift and Brownian motion.

Transaction costs enter through the bid-ask spread, and the work states that it derives an explicit optimal portfolio process, illustrating the result with logarithmic utility. It also offers preliminary discussion of statistical arbitrage strategies. The supplied description does not give the derivation, assumptions about parameter estimation, numerical example, or performance evidence, so it supports understanding the model’s setup but not judging the solution’s robustness or real-world profitability. In particular, the treatment of unobservable return drivers and spread costs may constrain how directly the result can be applied to live markets.

Key ideas

• The problem is to maximize expected utility of terminal wealth in a discrete-time futures market.
• The model represents futures returns using an unobserved drift and Brownian motion.
• Transaction costs are modeled through the bid-ask spread.
• Margin, gearing, and slippage are introduced as relevant futures-market concepts.
• An explicit portfolio solution is presented with logarithmic utility as an example, though details are absent from the summary.

Tags

# Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets


# Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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