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Notes for a Contingent Claims Theory of Limit Order Markets

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  • Bruce N. Lehmann

Abstract

This paper provides a road map for building a contingent claims theory of limit order markets grounded in a simple observation: limit orders are equivalent to a portfolio of cash-or-nothing and asset-or-nothing digital options on market order flow. However, limit orders are not conventional derivative securities: order flow is an endogenous, non-price state variable; the underlying asset value is a construct, the value of the security in different order flow states; and arbitrage trading or hedging of limit orders is not feasible. Fortunately, none of these problems is fatal since options on order flow can be conceptualized as bets implicit in limit orders, arbitrage trading can be replaced by limit order substitution, and plausible assumptions can be made about the endogeneity of order flow states and their associated asset values. The analysis yields two main results: Arrow-Debreu prices for order flow %u2018%u2018states%u2019%u2019 are proportional to the slope of the limit order book and the limit order book at one time proves to be identical to that at an earlier time adjusted for the net order flow since that time when all information arrives via trades.

Suggested Citation

  • Bruce N. Lehmann, 2005. "Notes for a Contingent Claims Theory of Limit Order Markets," NBER Working Papers 11533, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:11533
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    References listed on IDEAS

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    1. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    2. Copeland, Thomas E & Galai, Dan, 1983. " Information Effects on the Bid-Ask Spread," Journal of Finance, American Finance Association, vol. 38(5), pages 1457-1469, December.
    3. Sandas, Patrik, 2001. "Adverse Selection and Competitive Market Making: Empirical Evidence from a Limit Order Market," Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 705-734.
    4. 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.
    5. Seppi, Duane J, 1997. "Liquidity Provision with Limit Orders and a Strategic Specialist," Review of Financial Studies, Society for Financial Studies, vol. 10(1), pages 103-150.
    6. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
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    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G19 - Financial Economics - - General Financial Markets - - - Other

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