交易成本下路徑獨立選擇權之複製

Abstract

Working in the binomial framework, Boyle and Vorst (1992) derive unique self-financing strategies which perfectly replicate European call and put options for long positions with settlement by delivery, assuming proportional transaction costs on trades in the stocks. Here we consider a more general situation including short positions. First, we give conditions such that a unique replicating portfolio exists in a two-period model for a path independent contingent claim. Then we extend them to the multi-period case, yielding a result which extends the results of Boyle-Vorst to short positions. Furthermore, we conclude that some path independent options which are mixtures of long and short portions, such as spreads, have a unique replicating strategy for multi-period model under some conditions. We also show that long call (put) with cash settlement or with settlement up to the seller has a unique replicating portfolio for multi-period model.