Price Functionals with Bid-Ask Spreads :An Axiomatic Approach
May 1999
Elyès Jouini
ABSTRACT
In Jouini and Kallal (1995a), the authors characterized the absence of arbitrage opportunities for contingent claims
with cash delivery in the presence of bid-ask spreads. Other authors obtained similar results for a more general
definition of the contingent claims but assuming some specific price processes and transaction costs rather than
bid-ask spreads in general see for instance, Cvitanic and Karatzas, 1996). The main difference consists in the
fact that the bid-ask ratio is constant in this last reference. This assumption does not permit to encompass situations
where the prices are determined by the buying and selling limit orders or by a (resp. competitive) specialist (resp.
market-makers). We derive in this paper some implications from the no-arbitrage assumption on the price functionals
that generalizes all the previous results in a very general setting. Indeed, under some minimal assumptions on
the price functional, we prove that the prices of the contingent claims are necessarily in some minimal interval.
This result opens the way to many empirical analyses.
Subject: Investment/Derivatives, Valuation, Economics/Theory
Classification: Theoretical
Jouini : (212) 998-0279 ejouini@stern.nyu.edu
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