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.
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