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Optimal Market-Making with Risk Aversion

Author

Listed:
  • Kan Huang

    () (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • David Simchi-Levi

    () (Department of Civil and Environmental Engineering, the Engineering Systems Division and the Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Miao Song

    () (Department of Industrial and Manufacturing Systems Engineering, University of Hong Kong, Hong Kong)

Abstract

Market-makers have the obligation to trade any given amount of assets at quoted bid or ask prices, and their inventories are exposed to the potential loss when the market price moves in an undesirable direction. One approach to reduce the risk brought by price uncertainty is to adjust the inventory at the price of losing potential spread gain. Using stochastic dynamic programming, we show that a threshold inventory control policy is optimal with respect to an exponential utility criterion and a mean-variance trade-off model. Symmetric and monotone properties of the threshold levels are also established.

Suggested Citation

  • Kan Huang & David Simchi-Levi & Miao Song, 2012. "Optimal Market-Making with Risk Aversion," Operations Research, INFORMS, vol. 60(3), pages 541-565, June.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:3:p:541-565
    DOI: 10.1287/opre.1120.1039
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    File URL: http://dx.doi.org/10.1287/opre.1120.1039
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    References listed on IDEAS

    as
    1. Foster, F Douglas & Viswanathan, S, 1993. "Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models," Journal of Finance, American Finance Association, vol. 48(1), pages 187-211, March.
    2. Madhavan, Ananth & Smidt, Seymour, 1993. "An Analysis of Changes in Specialist Inventories and Quotations," Journal of Finance, American Finance Association, vol. 48(5), pages 1595-1628, December.
    3. Mokrane Bouakiz & Matthew J. Sobel, 1992. "Inventory Control with an Exponential Utility Criterion," Operations Research, INFORMS, vol. 40(3), pages 603-608, June.
    4. Madhavan, Ananth & Smidt, Seymour, 1991. "A Bayesian model of intraday specialist pricing," Journal of Financial Economics, Elsevier, vol. 30(1), pages 99-134, November.
    5. Stoll, Hans R, 1989. " Inferring the Components of the Bid-Ask Spread: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 44(1), pages 115-134, March.
    6. Xin Chen & Melvyn Sim & David Simchi-Levi & Peng Sun, 2007. "Risk Aversion in Inventory Management," Operations Research, INFORMS, vol. 55(5), pages 828-842, October.
    7. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    8. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    9. Sasha Stoikov & Mehmet Sağlam, 2009. "Option market making under inventory risk," Review of Derivatives Research, Springer, vol. 12(1), pages 55-79, April.
    10. Ho, Thomas S Y & Stoll, Hans R, 1983. "The Dynamics of Dealer Markets under Competition," Journal of Finance, American Finance Association, vol. 38(4), pages 1053-1074, September.
    11. Cheung, Yin-Wong & Chinn, Menzie David, 2001. "Currency traders and exchange rate dynamics: a survey of the US market," Journal of International Money and Finance, Elsevier, vol. 20(4), pages 439-471, August.
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    Cited by:

    1. Christopher D. Clack & Elias Court & Dmitrijs Zaparanuks, 2020. "Dynamic Coupling and Market Instability," Papers 2005.13621, arXiv.org.

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