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A continuous-time Kyle model with price-responsive traders

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  • Eunjung Noh

Abstract

Classical Kyle-type models of informed trading typically treat noise trader demand as purely exogenous. In reality, many market participants react to price movements and news, generating feedback effects that can significantly alter market dynamics. This paper develops a continuous-time Kyle framework in which two types of price-responsive traders (momentum and contrarian traders) adjust their demand in response to price signals. This extension yields a finite-dimensional Kalman filter for price discovery and leads to a forward-backward Riccati system characterizing equilibrium. We show that when feedback is weak, equilibrium exists and is unique as a smooth perturbation of the classical Kyle solution, allowing us to derive explicit comparative statics for insider profits and price informativeness. For stronger feedback, the model generates rich dynamics, including potential multiplicity of equilibria and amplification effects. Our framework thus bridges the gap between purely exogenous noise and more realistic, behaviorally motivated trading.

Suggested Citation

  • Eunjung Noh, 2026. "A continuous-time Kyle model with price-responsive traders," Papers 2601.09872, arXiv.org.
    • Handle: RePEc:arx:papers:2601.09872
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    References listed on IDEAS

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    1. Umut Çetin, 2018. "Financial equilibrium with asymmetric information and random horizon," Finance and Stochastics, Springer, vol. 22(1), pages 97-126, January.
    2. Kerry Back & C. Henry Cao & Gregory A. Willard, 2000. "Imperfect Competition among Informed Traders," Journal of Finance, American Finance Association, vol. 55(5), pages 2117-2155, October.
    3. De Long, J Bradford, et al, 1990. "Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-395, June.
    4. Sentana, Enrique & Wadhwani, Sushil B, 1992. "Feedback Traders and Stock Return Autocorrelations: Evidence from a Century of Daily Data," Economic Journal, Royal Economic Society, vol. 102(411), pages 415-425, March.
    5. Giovanni Cespa & Xavier Vives, 2012. "Dynamic Trading and Asset Prices: Keynes vs. Hayek," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 539-580.
    6. Campi, Luciano & Cetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," LSE Research Online Documents on Economics 31538, London School of Economics and Political Science, LSE Library.
    7. Xiong, Wei, 2001. "Convergence trading with wealth effects: an amplification mechanism in financial markets," Journal of Financial Economics, Elsevier, vol. 62(2), pages 247-292, November.
    8. Brunnermeier, Markus K., 2001. "Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding," OUP Catalogue, Oxford University Press, number 9780198296980.
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    10. Shiller, Robert J, 1990. "Speculative Prices and Popular Models," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 55-65, Spring.
    11. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October.
    12. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September.
    13. Çetin, Umut, 2018. "Financial equilibrium with asymmetric information and random horizon," LSE Research Online Documents on Economics 84495, London School of Economics and Political Science, LSE Library.
    14. Back, Kerry, 1992. "Insider Trading in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409.
    15. Campi, Luciano & Çetin, Umut & Danilova, Albina, 2011. "Dynamic Markov bridges motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 534-567, March.
    16. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh, 2025. "Solvability of the Gaussian Kyle model with imperfect information and risk aversion," Papers 2501.16488, arXiv.org.
    17. Ibrahim Ekren & Brad Mostowski & Gordan Žitković, 2025. "Kyle’s model with stochastic liquidity," Finance and Stochastics, Springer, vol. 29(4), pages 1195-1231, October.
    18. Xiaoting Dai & Jie Zhang & Victor Chang, 2025. "Noise traders in an agent-based artificial stock market," Annals of Operations Research, Springer, vol. 352(3), pages 715-744, September.
    19. repec:dau:papers:123456789/4436 is not listed on IDEAS
    20. Baruch, Shmuel, 2002. "Insider trading and risk aversion," Journal of Financial Markets, Elsevier, vol. 5(4), pages 451-464, October.
    21. Zhiguo He & Arvind Krishnamurthy, 2013. "Intermediary Asset Pricing," American Economic Review, American Economic Association, vol. 103(2), pages 732-770, April.
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