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Arrow-Debreu Meets Kyle: Price Discovery Across Derivatives

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  • Christian Keller
  • Michael C. Tseng

Abstract

We analyze price discovery in a model where an agent has arbitrary private information about state probabilities and trades state-contingent claims. Our model integrates the seminal frameworks of Arrow and Debreu (1954) and Kyle (1985). In an equivalent options formulation, the informed agent has arbitrary information about an underlying asset's payoff distribution and trades option portfolios. We characterize the informed demand and information dynamics across markets. Our results offer the first equilibrium-based explanations for longstanding empirical practices and phenomena in option markets, including common trading patterns and the volatility smile across option strikes.

Suggested Citation

  • Christian Keller & Michael C. Tseng, 2023. "Arrow-Debreu Meets Kyle: Price Discovery Across Derivatives," Papers 2302.13426, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2302.13426
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    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Jean-Charles Rochet & Jean-Luc Vila, 1994. "Insider Trading without Normality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 131-152.
    3. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    4. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    5. Pierre Collin‐Dufresne & Vyacheslav Fos, 2016. "Insider Trading, Stochastic Liquidity, and Equilibrium Prices," Econometrica, Econometric Society, vol. 84(4), pages 1441-1475, July.
    6. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    7. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    8. Charles Cao & Zhiwu Chen & John M. Griffin, 2005. "Informational Content of Option Volume Prior to Takeovers," The Journal of Business, University of Chicago Press, vol. 78(3), pages 1073-1109, May.
    9. Georgy Chabakauri & Kathy Yuan & Konstantinos E Zachariadis, 2022. "Multi-asset Noisy Rational Expectations Equilibrium with Contingent Claims," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2445-2490.
    10. Jun Pan & Allen M. Poteshman, 2006. "The Information in Option Volume for Future Stock Prices," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 871-908.
    11. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    12. Huang, Roger D & Stoll, Hans R, 1997. "The Components of the Bid-Ask Spread: A General Approach," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 995-1034.
    13. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    14. Sophie X. Ni & Jun Pan & Allen M. Poteshman, 2008. "Volatility Information Trading in the Option Market," Journal of Finance, American Finance Association, vol. 63(3), pages 1059-1091, June.
    15. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    16. Makarov, Igor & Schoar, Antoinette, 2020. "Trading and arbitrage in cryptocurrency markets," LSE Research Online Documents on Economics 100409, London School of Economics and Political Science, LSE Library.
    17. Goyal, Amit & Saretto, Alessio, 2009. "Cross-section of option returns and volatility," Journal of Financial Economics, Elsevier, vol. 94(2), pages 310-326, November.
    18. Pierre Collin‐Dufresne & Vyacheslav Fos, 2016. "Insider Trading, Stochastic Liquidity, and Equilibrium Prices," Econometrica, Econometric Society, vol. 84, pages 1441-1475, July.
    19. Roll, Richard & Schwartz, Eduardo & Subrahmanyam, Avanidhar, 2009. "Options trading activity and firm valuation," Journal of Financial Economics, Elsevier, vol. 94(3), pages 345-360, December.
    20. 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.
    21. Cao, Jie & Han, Bing, 2013. "Cross section of option returns and idiosyncratic stock volatility," Journal of Financial Economics, Elsevier, vol. 108(1), pages 231-249.
    22. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    23. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    24. Bali, Turan G. & Murray, Scott, 2013. "Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(4), pages 1145-1171, August.
    25. Xintong (Eunice) Zhan & Bing Han & Jie Cao & Qing Tong, 2022. "Option Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 35(3), pages 1394-1442.
    26. Collin-Dufresne, Pierre & Fos, Vyacheslav & Muravyev, Dmitry, 2021. "Informed Trading in the Stock Market and Option-Price Discovery," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 56(6), pages 1945-1984, September.
    27. Glosten, Lawrence R. & Harris, Lawrence E., 1988. "Estimating the components of the bid/ask spread," Journal of Financial Economics, Elsevier, vol. 21(1), pages 123-142, May.
    28. Makarov, Igor & Schoar, Antoinette, 2020. "Trading and arbitrage in cryptocurrency markets," Journal of Financial Economics, Elsevier, vol. 135(2), pages 293-319.
    29. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li, 2021. "Implied Stochastic Volatility Models [Testing continuous-time models of the spot interest rate]," The Review of Financial Studies, Society for Financial Studies, vol. 34(1), pages 394-450.
    30. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    31. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    32. Caballe, Jordi & Krishnan, Murugappa, 1994. "Imperfect Competition in a Multi-security Market with Risk Neutrality," Econometrica, Econometric Society, vol. 62(3), pages 695-704, May.
    33. Lin, Ji-Chai & Sanger, Gary C & Booth, G Geoffrey, 1995. "Trade Size and Components of the Bid-Ask Spread," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1153-1183.
    34. Joost Driessen & Pascal J. Maenhout & Grigory Vilkov, 2009. "The Price of Correlation Risk: Evidence from Equity Options," Journal of Finance, American Finance Association, vol. 64(3), pages 1377-1406, June.
    35. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li & Ralph Koijen, 2021. "Implied Stochastic Volatility Models," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 394-450.
    36. Patrick Augustin & Menachem Brenner & Marti G. Subrahmanyam, 2019. "Informed Options Trading Prior to Takeover Announcements: Insider Trading?," Management Science, INFORMS, vol. 65(12), pages 5697-5720, December.
    37. Biais, Bruno & Hillion, Pierre, 1994. "Insider and Liquidity Trading in Stock and Options Markets," The Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 743-780.
    38. Foster, F Douglas & Viswanathan, S, 1996. "Strategic Trading When Agents Forecast the Forecasts of Others," Journal of Finance, American Finance Association, vol. 51(4), pages 1437-1478, September.
    39. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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