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
Effective securities in arbitrage-free markets with bid-ask spreads at liquidation: a linear programming characterization
BATTAUZ, ANNA;ORTU, FULVIO
2006
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. 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-arbitrageFile in questo prodotto:
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