Optimal Trading of a Basket of Futures Contracts

TL;DR

This paper develops a new model for dynamically trading multiple futures contracts, capturing joint stochastic basis dynamics with a multi-dimensional scaled Brownian bridge, and derives semi-explicit optimal strategies considering market conditions.

Contribution

It introduces a novel multi-dimensional Brownian bridge model for futures basis dynamics and derives semi-explicit solutions for optimal trading strategies.

Findings

Optimal long-short trading strategies depend on market contango or backwardation.

The model quantifies the value of trading futures with or without underlying assets.

Numerical examples demonstrate the impact of model parameters on strategies.

Abstract

We study the problem of dynamically trading multiple futures contracts with different underlying assets. To capture the joint dynamics of stochastic bases for all traded futures, we propose a new model involving a multi-dimensional scaled Brownian bridge that is stopped before price convergence. This leads to the analysis of the corresponding Hamilton-Jacobi-Bellman (HJB) equations, whose solutions are derived in semi-explicit form. The resulting optimal trading strategy is a long-short policy that accounts for whether the futures are in contango or backwardation. Our model also allows us to quantify and compare the values of trading in the futures markets when the underlying assets are traded or not. Numerical examples are provided to illustrate the optimal strategies and the effects of model parameters.