In this paper we study the implications of the absence of statistical arbitrage opportunities (SAO) in a two-period incomplete market economy where default is allowed but there are collateral requirements. We study the existence of state price deflators and the existence of a solution for the individual optimality problem, obtaining modified versions of the fundamental theorems of asset pricing. Then, we address the existence of equilibrium.
We derive statistical arbitrage bounds for the buying and selling price of European derivatives under incomplete markets. In this paper, incompleteness is generated due to the fact that the market is dry, i.e., the underlying asset cannot be transacted at certain points in time. In particular, we refine the notion of statistical arbitrage in order to extend the procedure for the case where dryness is random, i.e., at each point in time the asset can be transacted with a given probability. We analytically characterize several properties of the statistical arbitrage-free interval, show that it is narrower than the super-replication interval and dominates somehow alternative intervals provided in the literarture. Moreover, we show that, for sufficiently incomplete markets, the statistical arbitrage interval contains the reservation price of the derivative.
In the framework of incomplete markets, due to the non-existence of trade at some points in time, and using a partial equilibrium analysis, we show how the bid-ask spread of an European derivative is generated. We also¯nd conditons for the existence of the spread. These conditions concern the market structure of the maret-makers, which can be a oligolopoly with price competition or a monopoly, as well as the riskaversion of the demand and supply of the market.
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