Optimal Dynamic Basis Trading

Abstract

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters. Keywords: futures stochastic basis cash and carry scaled Brownian bridge risk aversion JEL Classification C41 G11 G12 IntroductionBasis trading, also known as cash-and-carry trading in the context of futures contracts, is a core strategy for many speculative traders who seek to profit from anticipated convergence of spot and futures prices.The practice usually involves taking a long position in the under-priced asset and a short position in the over-priced one, and closing the positions when convergence occurs. In reality, however, basis trading is far from a riskless arbitrage. Unexpected changes in market factors such as interest rate, cost of carry, or dividends can diminish profitability. Moreover, market frictions, such as transaction costs and collateral payments, can turn seemingly certain arbitrage opportunities into disastrous trades. It is also possible that the basis does not converge at maturity. This non-convergence phenomenon was commonly observed in the grains markets. As reported in Irwin et al. (2011), Adjemian et al. (2013), and Garcia et al. (2015, for most of 2005-2010 futures contracts expired up to 35% above the spot price. As a result, some cash-and-carry traders may choose to close their positions prior to maturity to limit risk exposure.Early works on pricing of futures contracts, such as Cox et al. (1981) and Modest and Sundaresan (1983), established no-arbitrage relationships between the spot price and associated futures prices. Assuming imperfections, such as transaction cost, these relationships take the form of pricing bounds, which can be

Optimal trading of a basket of futures contracts

“…The plots shows that the CE values approach infinity for certain level of risk-aversion in the range (0, 1). As we have mentioned already, this behavior is consistent with the findings of Angoshtari and Leung (2019) and indicates the existence of the so-called nirvana strategies.…”

“…In particular, under this assumption, an argument similar to the proof of Proposition 1 of Angoshtari and Leung (2019) shows that the market model has a risk-neutral measure and, thus, is arbitrage free.…”

“…(3.1) and (3.2) directly follow from (2.1)-(2.3) by applying Itô's lemma. The rest of the proof is similar to the proof of Lemma 1 in Angoshtari and Leung (2019) and is, thus, omitted.…”

“…We briefly discuss nirvana solutions in Figure 6 below. For a more complete treatment of the subject, we refer the reader to Angoshtari and Leung (2019) for a detailed analysis of nirvana solutions in a special case of our market model where there is only one pair of futures and underlying assets. To keep the discussion less technical, however, we have decided to focus on the well-posed case γ > 1.…”

“…Among the authors' recent related studies, Leung and Yan (2018) and Leung and Yan (2019) applied utility maximization approach to derive dynamic pairs trading strategies for futures under two-factor spot models. Most recently and relevantly, Angoshtari and Leung (2019) analyzed the problem of dynamically trading a futures contract and its underlying asset. The associated basis is modeled by a Brownian bridge, but the process is stopped early to capture the non-convergence of prices at the end of trading horizon.…”