Hedging Of Option In Discrete Time Under Proportional Transaction Costs

In the paper, using auxiliary martingales, we obtain the lower bound for super-replication cost of American and European option in a discrete time financial market with proportional transaction costs. Under sufficiently small transaction costs, super-replication cost is equal to replication cost and replicating strategy is optimal hedging strategy. Similar to no-cost,we denote replication cost with expectation. In the CRR model, some special results are obtained.The main results are as follows:The super-replication cost of the European option c given the initial holding θ-1 satisfiesUnder Assumption 3.1, for any attainable European option , replication cost is equal to super-replication cost, the replication cost of C with initial holding θ-1 is given byreplicating strategy is unique and optimal hedging strategy.The super-replication cost of the American option / given the initial holding θ-1 satisfiesUnder Assumption 3.1, for any attainable American option , replication cost is equal to super-replication cost, the replication cost of / with initial holding θ-1 is given bythe replication strategy is optimal.In the CRR model,any contingent claim is attainable.