Arbitrage, speculation and futures price fluctuations with boundedly rational and heterogeneous agents
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Arbitrage, speculation and futures price fluctuations with boundedly rational and heterogeneous agents Qingbin Gong1
· Zhe Yang1,2
Received: 8 April 2019 / Accepted: 17 August 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract This paper proposes a dynamic model for the futures market with three types of investors. The bounded rationality and heterogeneity of investors are taken into consideration. The equilibrium of the system and its stability conditions are derived with mathematical analysis. In the equilibrium, the futures price and the spot price converge to the equilibrium simultaneously. The equilibrium is determined by many factors, including the risk appetite and the rationality of investors, the trading costs, the arbitrage basis price and the fundamental price. When the stability conditions are violated, complex dynamics will emerge in the market. As shown by the simulations, the arbitrage is likely to destabilize the market. Moreover, when investors have the high degree of rationality, the equilibrium will become unstable and the futures market is inefficient. Statistical analysis indicates that the model can reproduce the stylized facts observed in the futures market, such as long memory, volatility clustering and fat tail of returns. Keywords Futures market · Arbitrage · Bounded rationality · Heterogeneous agent model · Chaos
1 Introduction Due to the delivery mechanism, the futures price does not deviate too much from the spot price. They usually converge to each other as the expiration date approaches. The trading activity of arbitrageurs plays an important role in the reversion of the basis (Miller et al. 1994). When the basis widens largely, the arbitrageurs simultaneously
B
Qingbin Gong [email protected] Zhe Yang [email protected]
1
School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China
2
Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China
123
Q. Gong, Z. Yang
buy the futures and sell the spot, pulling the basis back to normal level. When the basis narrows, the arbitrageurs trade in reverse. The dynamics of basis are complicated in the futures market. Dwyer et al. (1996) empirically studied the nonlinear dynamic relationship between S&P 500 futures and cash indexes. Their results indicated that nonlinear dynamics are important and related to arbitrage. Kim et al. (2010) studied the nonlinear dynamics in arbitrage of the S&P 500 index and futures. They verified that the futures price leads the nonlinear mean-reverting behavior of the index but not vice versa. Some researches on commodity futures also suggested the significant impacts of arbitrage on the relationship between the futures price and the spot price (see Tilton et al. 2011; Chen and Chang 2015; Go and Lau 2017; Park and Shi 2017). Tilton et al. (2011) claimed that the futures price and the spot price are closely linked when the market is in strong contango, due to the arbitrage by buying the spot and selling the futures. La
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