How do high-frequency traders under different option market regulations affect the quality and co-movement of the stock market and option market?

Using an agent-based model as a framework, this study explores the mechanisms of high-frequency trading (HFT) in the stock and options markets and its impact on market quality and trader profitability. By simulating market performance under various regulatory policies (including minimum price levels, make/take fees, delay mechanisms, minimum order durations, and a financial transaction tax), the study systematically analyses market liquidity, volatility, price efficiency, and profit distribution.The results show that HFT has a typical dual effect: on the one hand, it significantly narrows bid-ask spreads, reduces price errors, and improves price discovery efficiency; on the other hand, its entry reduces order book depth, compresses the profit margins of slow traders, and, under certain conditions, may amplify market instability. Furthermore, HFT's own profits exhibit diminishing returns, demonstrating the dilution of internal returns caused by speed competition. Regulatory experiments further demonstrate significant differences and trade-offs in the effectiveness of different policy tools: Tick size and make/take mechanisms improve market depth but compromise efficiency; delay mechanisms and minimum order durations have limited impact on stability; and transaction taxes are effective in curbing speculation and improving price precision, but at the expense of liquidity. Options markets are more sensitive to regulatory tools, reflecting the derivatives market's high sensitivity to volatility and the regulatory environment.The main contributions of this study are: first, it constructs a simulation framework covering both stock and options markets, revealing the cross-market impact of HFT; second, it systematically compares the advantages and disadvantages of different regulatory tools, revealing the trade-offs between efficiency, fairness, and stability; and third, it provides new quantitative evidence for understanding the complex role of HFT in different market structures and policymaking. The conclusions of this article suggest that HFT is a double-edged sword: while promoting market efficiency, it also carries the risk of undermining stability and fairness. Therefore, future regulation should adopt contextualised and differentiated strategies to achieve a balance between efficiency and stability.