TY - JOUR
AU - Lehmann,Bruce N.
TI - Notes for a Contingent Claims Theory of Limit Order Markets
JF - National Bureau of Economic Research Working Paper Series
VL - No. 11533
PY - 2005
Y2 - August 2005
DO - 10.3386/w11533
UR - http://www.nber.org/papers/w11533
L1 - http://www.nber.org/papers/w11533.pdf
N1 - Author contact info:
Bruce Lehmann
University of California, San Diego
IR/PS
1415 Robinson Building Complex
La Jolla, CA 92093-0519
Tel:
Fax:
E-Mail: blehmann@ucsd.edu
AB - 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.
ER -