Viability and Equilibrium in Securities Markets with Frictions

25 Pages Posted: 11 Nov 2008

See all articles by Elyes Jouini

Elyes Jouini

Univ. Paris Dauphine - CEREMADE

Hédi Kallal

affiliation not provided to SSRN

Date Written: March 1999

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.

Keywords: Viability, equilibrium, absence of arbitrage, free lunch, market frictions, convex and sublinear pricing ruler, consistent bid-ask prices, arbitrage bounds, equilibrium bounds

Suggested Citation

Jouini, Elyes and Kallal, Hédi, Viability and Equilibrium in Securities Markets with Frictions (March 1999). NYU Working Paper No. FIN-99-036, Available at SSRN: https://ssrn.com/abstract=1297760

Elyes Jouini (Contact Author)

Univ. Paris Dauphine - CEREMADE ( email )

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Paris Cedex 16, 75775
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+ 33 1 44 05 45 99 (Fax)

Hédi Kallal

affiliation not provided to SSRN

No Address Available

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