Viability and Equilibrium in Securities Markets with Frictions
March 1999
Elyès Jouini, Hédi Kallal
ABSTRACT
In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model
market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the
pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities
price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium
if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity
set, and hence for whom supply equals demand. This is equivalent to the existence of a positive linear pricing
rule on the entire space of contingent claims - an underlying frictionless linear pricing rule - that lies below
the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free
lunches - a generalization of opportunities of arbitrage. When a market for a non marketed contingent claim opens,
a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable
economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing
rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is
equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also
show that there exists a unique extended consistent sublinear pricing rule - the supremum of the underlying frictionless
linear pricing rules - for which the original equilibrium does not collapse, when a new market opens, regardless
of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model,
we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing
rules.
Subject: Investment/Derivatives, Valuation, Economics/Theory
Classification: Theoretical
Jouini : (212) 998-0279 ejouini@stern.nyu.edu
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