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| Research on Financial Futures Pricing in a Rational Expectations Equilibrium: Information Driven or Arbitrage Driven？ |
| CHEN Binbin, LIU Shancun, ZHANG Qiang, ZENG Qingduo
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School of Finance, Shandong University of Finance and Economics;
School of Economics and Management, Beihang University;
School of Economics and Management, Beijing University of Chemical Technology;
School of Economics, Guangdong University of Technology |
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Abstract The futures market plays a fundamental role in asset price discovery. Improving the efficiency of asset price discovery would help enhance financial market efficiency, reduce information acquisition costs for investors, and promote finance's positive effects on the real economy. China's Futures and Derivatives Law, which came into effect in 2022, indicates the importance of developing the futures market to raise its price discovery function. The cost-of-carry model, a classical futures pricing model, reveals the relationship between futures and spot prices only when there are infinite arbitrageurs. However, this model is not suitable when dealing with limited arbitrageurs and does not illustrate the micro-mechanism of information aggregation in the futures market. Although empirical research indicates that price discovery efficiency in the financial futures market is higher than that in the spot market, a robust theoretical foundation for this relationship is lacking. Thus, we develop a futures pricing model, where informed traders, cross-market arbitrageurs, and noise traders trade within a rational expectations equilibrium framework, to investigate the pricing outcomes of spot and futures markets, characterize the interactions between different types of investors, and uncover the micro-mechanisms of information aggregation in the futures market, the determinants of the price discovery function of spot and futures markets.
Given that futures delivery is earlier than the liquidation of spot in the real financial world, we assume that the spot is traded in each period and futures are only traded in the first period in a two-period trading model. The spot is liquidated after the end of the second period and the futures contract is delivered at the equilibrium price of spot in the second period. Informed traders and arbitrageurs exist in the spot and futures markets, but only arbitrageurs can trade across markets. Under these assumptions, we first solve the partial market equilibrium without cross-market arbitrageurs. In this equilibrium, we analyze how delivery risk affects informed trading behaviors in the futures markets and how private information is incorporated into futures prices. In addition, we determine how spot-futures spread occurs from the perspective of information structure and inventory risk. Subsequently, we solve the overall market equilibrium by considering the cross-market arbitrageurs' strategy. In the overall equilibrium, we examine the factors determining arbitrage intensity, the impact of the number of arbitrageurs on the spot-futures spread, and the relationship between arbitrage trading and price discovery efficiency. Finally, we empirically test the model's findings by analyzing the impact of COVID-19 on the price discovery of CSI 300 index futures in China.
This study yields the following results. First, the price discovery of futures is determined by informed traders and noise traders rather than by arbitrageurs. The price discovery level of spot is better than that of futures when the precision of private information and noise trading in the two market is equal. Second, the greater the information aggregation efficiency of a spot at the delivery stage of the futures, the higher the price discovery level of futures. Third, when private information in the futures market is more precise than that in the spot market, the liquidity of futures is positively related to its price discovery and the relative impact of arbitrage trading on asset prices is negatively correlated with its price discovery efficiency. Finally, we determine that COVID-19 reduces the price discovery function of stock index futures due to increased investor concerns regarding short-term stock index volatility.
This paper contributes to the futures pricing literature in three aspects. First, by incorporating informed traders and noise traders, we construct a model that is more suitable for analyzing the price discovery function of futures within the framework of the rational expectations equilibrium. This model provides a theoretical basis for previous empirical analyses and suggests avenues for further research. Second, many existing studies assume no-arbitrage exogenously, which limits their ability to analyze the differential impact of arbitrage trading on spot and futures prices and the resulting price discovery efficiency. We address this limitation by endogenizing arbitrage strategies. Third, we empirically examine how investors' expectations about the underlying asset's price volatility affect the price discovery level of futures, providing an empirical basis for our theoretical model. Based on these findings, future research could explore the choices of informed traders between trading in the spot market or futures market and investigate investors' decisions to roll over their positions on the delivery date to further examine futures pricing.
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Published: 02 September 2023
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