主管:中国科学院
主办:中国优选法统筹法与经济数学研究会
   中国科学院科技战略咨询研究院

Strategic Trading and Market Quality under Ambiguous Volatility

  • Jingzhou Yan ,
  • Zhongfei Li ,
  • Jie Mao ,
  • Xingyi Li
Expand
  • 1.School of Economics,Sichuan University,Chengdu 610065,China
    2.Department of Finance,Southern University of Science and Technology,Shenzhen 518055,China
    3.School of Economics,Shanghai University,Shanghai 200444,China
    4.Centre for Financial Research,Fudan University,Shanghai 200433,China
    5.College of Economics,Shenzhen University,Shenzhen 518060,China

Received date: 2022-12-06

  Revised date: 2023-08-12

  Online published: 2025-09-10

Abstract

Since the outbreak of COVID-19, financial markets worldwide have experienced frequent significant fluctuations, occasionally triggering circuit breaker mechanisms, leading to numerous instances of stocks plummeting. The vast changes in market volatility and its uncertain distribution have made it challenging for investors to accurately predict market dynamics, a phenomenon referred to as ambiguous volatility. Consequently, how ambiguous volatility affects market liquidity is asked. How does it impact investors' trading intensity, expected wealth, and trading volume? These questions are not only important but also intriguing for policymakers and investors alike. In light of this, a continuous-time market microstructure model incorporating ambiguous volatility within a strategic trading framework is constructed and stochastic optimal control theory is applied to solve the corresponding Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, thereby explicitly revealing the impact of ambiguous volatility on informed traders' trading strategies and market quality. The findings indicate that an increase in ambiguous volatility leads to a decrease in the optimal trading intensity of informed traders, worsened market liquidity, a reduction in the expected total trading volume of risky assets, and a decrease in informed traders' expected wealth and overall profits. These effects contrast sharply with those observed under constant volatility. It not only deepens our existing understanding of the differences between ambiguous and constant volatility but also provides theoretical guidance for designing market mechanisms under conditions of uncertain volatility in this paper. It emphasizes the importance of reducing market ambiguity to maintain normal and healthy market operations and to prevent systemic financial risks, highlighting the need for further empirical research to accurately measure ambiguous volatility.

Cite this article

Jingzhou Yan , Zhongfei Li , Jie Mao , Xingyi Li . Strategic Trading and Market Quality under Ambiguous Volatility[J]. Chinese Journal of Management Science, 2025 , 33(8) : 26 -36 . DOI: 10.16381/j.cnki.issn1003-207x.2022.2628

References

[1] Epstein L G, Ji S. Ambiguous volatility and asset pricing in continuous time[J]. The Review of Financial Studies201326(7): 1740-1786.
[2] 毛杰, 刘红忠. 股市信息不对称对股价暴跌的影响——基于不确定性的新视角[J]. 管理科学学报202326(8): 117-132.
  Mao J, Liu H Z. The impact of stock market information asymmetry on stock price crash: A new perspective of uncertainty[J]. Journal of Management Sciences in China202326(8): 117-132.
[3] Hansen P G. New formulations of ambiguous volatility with an application to optimal dynamic contracting[J]. Journal of Economic Theory2022199: 105205.
[4] Peng S. G-expectation, G-Brownian motion and related stochastic calculus of it? type[M]. Berlin, Heidelberg:Springer Berlin Heidelberg,2007.
[5] Epstein L G, Ji S. Ambiguous volatility, possibility and utility in continuous time[J]. Journal of Mathematical Economics201450: 269-282.
[6] Hansen L P, Sargent T J. Robust control and model uncertainty[J]. American Economic Review200191(2): 60-66.
[7] Anderson E W, Hansen L P, Sargent T J. A quartet of semigroups for model specification, robustness, prices of risk, and model detection[J]. Journal of the European Economic Association20031(1): 68-123.
[8] Hansen L P, Sargent T J, Turmuhambetova G, et al. Robust control and model misspecification[J]. Journal of Economic Theory2006128(1): 45-90.
[9] Yi B, Li Z, Viens F G, et al. Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model[J]. Insurance: Mathematics and Economics201353(3): 601-614.
[10] Yi B, Viens F, Li Z, et al. Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria[J]. Scandinavian Actuarial Journal2015, 2015(8): 725-751.
[11] Zeng Y, Li D, Gu A. Robust equilibrium reinsurance-investment strategy for a mean-variance insurer in a model with jumps[J]. Insurance: Mathematics and Economics201666: 138-152.
[12] Wang P, Li Z. Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility[J]. Insurance: Mathematics and Economics201880: 67-83.
[13] 高金窑, 李仲飞. 模型不确定性条件下的Robust投资组合有效前沿与CAPM[J]. 中国管理科学201018(6): 1-8.
  Gao J Y, Li Z F. On the robust portfolio frontier and CAPM under model uncertainty[J]. Chinese Journal of Management Science201018(6): 1-8.
[14] 李仲飞, 高金窑.模型不确定性条件下的一般均衡定价[J].系统工程理论与实践201131(12): 2272-2280.
  Li Z F, Gao J Y. General equilibrium asset pricing under model uncertainty[J]. Systems Engineering-Theory & Practice201131(12): 2272-2280.
[15] 高金窑. 奈特不确定性与非流动资产定价: 理论与实证[J]. 经济研究201348(10): 82-97.
  Gao J Y. Illiquid asset pricing under knightian uncertainty: Theory and evidence[J]. Economic Research Journal201348(10): 82-97.
[16] Chen Z, Epstein L. Ambiguity, risk, and asset returns in continuous time[J]. Econometrica200270(4): 1403-1443.
[17] Nishimura K G, Ozaki H. Irreversible investment and knightian uncertainty[J]. Journal of Economic Theory2007136(1): 668-694.
[18] Liu H. Dynamic portfolio choice under ambiguity and regime switching mean returns[J]. Journal of Economic Dynamics and Control201135(4): 623-640.
[19] Epstein L G, Miao J. A two-person dynamic equilibrium under ambiguity[J]. Journal of Economic Dynamics and Control200327(7): 1253-1288.
[20] Mao J, Shen G, Yan J. A continuous-time macro-finance model with Knightian uncertainty[J]. Pacific-Basin Finance Journal202377: 101929.
[21] 费为银,夏登峰,唐仕冰.Knight不确定与随机汇率下外商投资决策[J].管理科学学报201619(6): 125-135.
  Fei W Y, Xia D F, Tang S B. On study of a foreign investor’s investment with random exchange rate under Knightian uncertainty[J]. Journal of Management Sciences in China201619(6): 125-135.
[22] 陈强, 许万紫. 奈特不确定、汇率波动与外商直接投资[J]. 中国管理科学202331(6): 12-24.
  Chen Q, Xu W Z. Knight uncertainty, exchange rate volatility and foreign direct investment[J]. Chinese Journal of Management Science202331(6): 12-24.
[23] Kyle A S. Continuous auctions and insider trading[J]. Econometrica198553(6): 1315.
[24] Back K. Insider trading in continuous time[J]. The Review of Financial Studies19925(3): 387-409.
[25] Back K, Pedersen H. Long-lived information and intraday patterns[J]. Journal of Financial Markets19981(3-4): 385-402.
[26] Chau M, Vayanos D. Strong-form efficiency with monopolistic insiders[J]. The Review of Financial Studies200821(5): 2275-2306.
[27] Caldentey R, Stacchetti E. Insider trading with a random deadline[J].Econometrica201078(1): 245-283.
[28] Guo M, Ou-Yang H. Feedback trading between fundamental and nonfundamental information[J]. The Review of Financial Studies201528(1): 247-296.
[29] Bolandnazar M, Jackson Jr R J, Jiang W, et al. Trading against the random expiration of private information: A natural experiment[J].The Journal of Finance202075(1): 5-44.
[30] Banerjee S, Breon-Drish B. Strategic trading and unobservable information acquisition[J].Journal of Financial Economics2020138(2): 458-482.
[31] Collin-Dufresne P, Fos V. Insider trading, stochastic liquidity, and equilibrium prices[J]. Econometrica201684(4): 1441-1475.
[32] Banerjee S, Breon-Drish B. Dynamics of research and strategic trading[J]. The Review of Financial Studies202235(2): 908-961.
[33] 刘霞, 刘善存, 张强. 信息认知偏差、有限竞争与资产定价[J]. 中国管理科学202331(2): 9-17.
  Liu X, Liu S C, Zhang Q. Cognitive biases, limited competition and asset pricing[J]. Chinese Journal of Management Science202331(2): 9-17.
[34] Mu C, Yan J, Yang J. Robust risk choice under high-water mark contract[J].Review of Quantitative Finance and Accounting202361(1): 295-322.
[35] 李昊骅, 张晓强, 罗鹏飞, 等.模糊厌恶下关系型借贷定价和最优贷款利率[J].中国管理科学202028(10): 36-42.
  Li H H, Zhang X Q, Luo P F, et al. The pricing of relationship loan and optimal loan interest rate under ambiguity aversion[J]. Chinese Journal of Management Science202028(10): 36-42.
[36] Easley D, O’Hara M, Yang L. Opaque trading, disclosure, and asset prices: Implications for hedge fund regulation[J]. The Review of Financial Studies201427(4): 1190-1237.
[37] Huang H H, Zhang S, Zhu W. Limited participation under ambiguity of correlation[J]. Journal of Financial Markets201732: 97-143.
[38] 何俊勇, 张顺明. 在相关系数暧昧环境下的市场微观结构研究[J].中国管理科学201826(4): 139-154.
  He J Y, Zhang S M. Market microstructure under ambiguity of correlation[J]. Chinese Journal of Management Science201826(4): 139-154.
[39] Easley D, O’Hara M. Ambiguity and nonparticipation: The role of regulation[J]. The Review of Financial Studies200922(5): 1817-1843.
[40] Easley D, O’Hara M. Microstructure and ambiguity[J]. The Journal of Finance201065(5):1817-1846.
[41] 胡志军, 凌爱凡, 杨超. 我国A股市场的模糊性溢价——基于日内高频数据的分析[J]. 中国管理科学202230(1): 42-53.
  Hu Z J, Ling A F, Yang C. The ambiguity premium in China’s A-shares market: The analysis from intra-day high frequency data[J]. Chinese Journal of Management Science202230(1): 42-53.
[42] Lipcer R ?, Liptser R S, ?iraev A N, et al. Statistics of Random Processes II:II. Applications[M]. Berlin, Heidelberg:Springer Berlin Heidelberg,2001.
[43] Maccheroni F, Marinacci M, Rustichini A. Dynamic variational preferences[J].Journal of Economic Theory2006128(1): 4-44.
[44] Maccheroni F, Marinacci M, Rustichini A. Ambiguity aversion, robustness, and the variational representation of preferences[J]. Econometrica200674(6): 1447-1498.
[45] Back K, Collin-Dufresne P, Fos V, et al. Activism, strategic trading, and liquidity[J]. Econometrica201886(4): 1431-1463.
[46] Routledge B R, Zin S E. Model uncertainty and liquidity[J]. Review of Economic Dynamics200912(4): 543-566.
[47] DeMarzo P M, Sannikov Y. Optimal security design and dynamic capital structure in a continuous-time agency model[J]. The Journal of Finance200661(6): 2681-2724.
Outlines

/