Options under proportional transaction costs: An algorithmic approach to pricing and hedging
The question of pricing and hedging of European options in the presence of proportional transaction costs has been examined by many authors. The work presented in this paper studies the ask and bid option prices that determine the no-arbitrage interval. Its main contribution is an algorithm for computing the ask and bid prices of options with arbitrary payoffs in an arbitrary discrete market model with arbitrary proportional transaction costs of any magnitude. Another important contribution is an optimal hedging algorithm, which also applies to arbitrary option payoffs and arbitrary discrete models under proportional transaction costs of any magnitude. These extend previous work, which has been focused on the binomial tree model and options with specific payoffs such as calls or puts, often under certain bounds on the magnitude of transaction costs. All such restrictions are hereby removed. The results apply to European options with general payoffs, exercised by the delivery of a portfolio of cash and stock, in any discrete market model, and with no restrictions on the model or the transaction costs other than the lack of arbitrage. Numerical examples are presented to illustrate the results. These extend existing numerical work in various directions including much wider parameter ranges, arbitrary option payoffs, including option baskets, a wider range of models with transaction costs, including the standard binomial and trinomial approximations to the Black-Scholes model, and no restrictions on the magnitude of transaction costs.
scientific article; zbMATH DE number 5324298
scientific article