The least cost superreplicating portfolio for short puts and calls in the boyle-vorst model with transaction costs

Since Black and Scholes (1973) introduced their option-pricing model in frictionless markets, many authors have attempted to develop models incorporating transaction costs. The groundwork of modeling the effects of transaction costs was done by Leland (1985). The Leland model was put into a binomial setting by Boyle and Vorst (1992). Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist superreplicating portfolios of lower cost. However, it is known that there is no superreplicating portfolio for long calls and puts of lower cost than the replicating portfolio. Nevertheless, this is not true for short calls and puts. As the negative of the cost of the least cost superreplicating portfolios for such a position is a lower bound for the call or put price, it is important to determine this least cost. In this paper, we consider two-period binomial models and show that, for a special class of claims including short call and put options, there are just four possibilities so that the least cost superreplicating portfolios can be easily calculated for such positions. Also we show that, in general, the least cost superreplicating portfolio is path-dependent.