Efficient Option Replication in the Presence of Transactions Costs

In the presence of transaction costs, a risk-return trade-off exists between the quality and the cost of a replicating strategy. In that context, I show how to expand the set of all possible time-based strategies through the introduction of a multi-scale class of strategies, which consist in rebalancing different fractions of an option portfolio at different time frequencies. The method, based on time-scale diversification, is to dynamic replication what investment in diversified portfoliosis to static portfolio selection: in a dynamic context, one may enjoy the benefits of diversification by using different time scales in trading the same asset. Copyright Kluwer Academic Publishers 2000