Effective securities in arbitrage-free markets with bid–ask spreads at liquidation: a linear programming characterization

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. We introduce the notion of ef...

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Bibliographic Details
Published in:Journal of economic dynamics & control 2006, Vol.30 (1), p.55-79
Main Authors: Baccara, Mariagiovanna, Battauz, Anna, Ortu, Fulvio
Format: Article
Language:English
Subjects:
Arbitrage
Asked price
Asset valuation
Bid–ask prices
Effective securities
Financial economics
Financial models
Linear programming
Liquidity
Mathematical methods
Securities markets
Studies
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Summary: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. We introduce the notion of effective new security and 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 detail the cases in which the boundaries of this interval can be reached without violating no-arbitrage.
ISSN:0165-1889
1879-1743
DOI:10.1016/j.jedc.2004.11.003