Replication strategies of derivatives under proportional transaction costs - An extension to the Boyle and Vorst model

When we introduce transaction costs the perfect Black and Scholes hedge, consisting of the underlying stock and a risk free asset, becomes infinitely expensive. By loosening the pure arbitrage argument and only considering the expected transaction costs, one can find an upper bound on the price of an option. In this essay this is done by using a framework presented by Leland (1985) and Boyle and Vorst(1992), which is based on rebalancing the hedge at predefined time-steps. However, their model is somewhat incomplete as they do not include the initial transaction cost of buying the hedge and the transaction cost of selling the hedge at maturity date. In this essay, an extension to their model is presented. This extension provides a framework that is consistent with their underlying model assumptions but incorporates the transaction costs mentioned above. In addition, we prove that these transaction costs have a significant effect on the price of an option