Dry markets and statistical arbitrage bounds for European derivatives

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 re¯ne 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 arbitragefree interval, show that it is narrower than the super-replication interval and dominates somehow alternative intervals provided in the literature. Moreover, we show that, for su±ciently incomplete markets, the statistical arbitrage interval contains the reservation price of the derivative.