Option replication with large transactions costs

In a binomial model, exact replication of options is possible in the presence of proportional transactions costs, but is this an efficient strategy? We show that the transactions cost factor is bounded above if all investors face the same factor. This constraint ensures that exact replication is optimal. However, when there are differential transactions costs super-replicating strategies may be dominant. The optimal replicating strategies for European call options are derived for large costs. The value of a long option can be found computationally easily, and a closed-form solution is given for a short option. While this least initial endowment is preference free, the replicating strategy of a short option is preference dependent.