Effective Vs. Efficient Securities in Arbitrage-Free Markets with Bid-Ask Spreads: A Linear Programming Characterization

29 Pages Posted: 29 May 2009

See all articles by Mariagiovanna Baccara

Mariagiovanna Baccara

Washington University in St. Louis

Fulvio Ortu

Bocconi University - Department of Finance

Anna Battauz

Bocconi University - Department of Finance

Date Written: 2003

Abstract

We consider a securities market with bid-ask spreads at any period, including liquidation. Although the minimum-cost super-replication problem is non-linear, we introduce an auxiliary problem that allows us to characterize no-arbitrage via linear programming techniques. Since no-arbitrage per se does not bound the bid-ask spread of a newly traded security, we introduce the notion of effective new security. We show that effectiveness restricts the no-arbitrage bid and ask prices of a new security to the interval defined by the minimum-cost problem. We discuss in details the cases in which the boundaries of this interval can be reached without violating no-arbitrage. We also compare effectiveness to efficiency as discussed in Jouini and Kallal (2001). We show that effectiveness is not sufficient for efficency, but is equivalent to the weaker notion of zero inefficiency cost.

Keywords: Transacation Costs, Linear Programming, arbitrage, bid-ask prices, linear programming, effective securities, efficient trading strategies

JEL Classification: G12

Suggested Citation

Baccara, Mariagiovanna and Ortu, Fulvio and Battauz, Anna, Effective Vs. Efficient Securities in Arbitrage-Free Markets with Bid-Ask Spreads: A Linear Programming Characterization (2003). Available at SSRN: https://ssrn.com/abstract=531127 or http://dx.doi.org/10.2139/ssrn.531127

Mariagiovanna Baccara (Contact Author)

Washington University in St. Louis ( email )

One Brookings Drive
Campus Box 1208
Saint Louis, MO MO 63130-4899
United States

Fulvio Ortu

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Anna Battauz

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

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