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Notes for a Contingent Claims Theory of Limit Order Markets

In: Advances In Quantitative Analysis Of Finance And Accounting Essays in Microstructure in Honor of David K Whitcomb

Author

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  • Bruce N. Lehmann

    (Graduate School of International Relations and Pacific Studies, University of California at San Diego and National Bureau of Economic Research, Cambridge, USA)

Abstract

This paper provides a roadmap 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, nonprice 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 "states" 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 intervening net order flow when all information arrives via trades.

Suggested Citation

  • Bruce N. Lehmann, 2006. "Notes for a Contingent Claims Theory of Limit Order Markets," World Scientific Book Chapters, in: Ivan E Brick & Tavy Ronen & Cheng-Few Lee (ed.), Advances In Quantitative Analysis Of Finance And Accounting Essays in Microstructure in Honor of David K Whitcomb, chapter 3, pages 39-56, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812707291_0003
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