A fractal market perspective on improving futures pricing and optimizing cash-and-carry arbitrage strategies

Traditional futures pricing models, based on the efficient market hypothesis, often fail in today's complex financial markets, leading to significant pricing errors and unreliable arbitrage strategies. This study posits that the fractal market hypothesis (FMH) offers a superior framework by accounting for long memory and multi-scale dynamics. Methodologically, we developed a fractal futures pricing model by incorporating the Hurst exponent and constructed a novel cash-futures arbitrage strategy using trend fractal dimensions and momentum lifecycle logic to generate dynamic trading signals. Empirical analysis using CSI 300 data demonstrates that our fractal pricing model significantly reduces pricing errors compared to the traditional cost-of-carry model. Furthermore, the proposed fractal-based arbitrage strategy achieves substantially higher returns, superior risk-adjusted performance, and lower drawdowns than conventional threshold-based approaches, showing robustness across diverse market conditions. This research validates the practical value of FMH for developing more accurate pricing tools and more adaptive, profitable arbitrage strategies, offering valuable insights for investors and risk managers in nonlinear markets.