Notes for a Contingent Claims Theory of Limit Order Markets

23 Pages Posted: 19 Sep 2005 Last revised: 26 Dec 2022

See all articles by Bruce N. Lehmann

Bruce N. Lehmann

University of California, San Diego; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT)

Date Written: August 2005


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 ''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 net order flow since that time when all information arrives via trades.

Suggested Citation

Lehmann, Bruce, Notes for a Contingent Claims Theory of Limit Order Markets (August 2005). NBER Working Paper No. w11533, Available at SSRN:

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