On Computation of Arbitrage for Markets with Friction
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FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
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In this paper we consider a frictional market with finitely many securities and finite and discrete future times. The frictions under consideration include fixed and proportional transaction costs, bid-ask spreads, and taxes. In such a market, we find that whether there exists an arbitrage opportunity does not dependent on the fixed transaction costs. Under a reasonable assumption, the no-arbitrage is equivalent to the condition that the optimal value of some linear programming problem is zero, and to the existence of a so-called consistent term structure. These results permit us to identify and to find arbitrage and consistent term structures in polynomial time. Two linear programming problems are proposed, each of which can identify and find the arbitrage opportunity or the consistent term structure if either exists.