Rebalancing static super-replications

Abstract

This paper proposes a trading strategy that dynamically rebalances static super-replicating portfolios, which is very useful for both investment and hedging strategies. In order to investigate general properties of the strategy, we derive the Doob–Meyer decomposition for the value process without any specifications of models under the continuous processes of the underlying variables. In particular, we find that the increasing part of the decomposition characterizes the performance of the strategy. Also, we obtain more concrete features for cross-currency and one-touch options based on our general framework. Moreover, numerical examples for cross-currency options demonstrate the effectiveness of our strategy for investment and hedging.