Abstract
In this paper we build a discrete time model for the structure of the limit order book, so that the price per share depends on the size of the transaction. We deduce the value of a portfolio when the investor trades using market orders and a bank account with different interest rates for lending and borrowing. In this setting, we deduce conditions to rule out arbitrage and solve the problem of pricing and hedging an European call and put option with maturity one and physical delivery. By using primal-dual optimization we show that the price of European options can be written as an optimization problem over some set of probability measures.
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