Computation of reservation prices of options with proportional transaction costs

In this paper, we consider the problem of computing reservation prices of options in the model proposed in a companion paper by Damgaard [2003. Journal of Economic Dynamics and Control 27, 667-700]. For the problem concerning European options, we show that the value functions of the associated portfolio maximization problems are unique viscosity solutions of their respective Hamilton-Jacobi-Bellman equations. Moreover, we suggest a numerical procedure for computing reservation prices, and provide convergence proofs of the involved discretization schemes. We implement the procedures and present numerical examples that illustrate the convergence pattern along which the discrete time prices convergence to their continuous time limits. Furthermore, we describe how to extend the numerical procedure to handle computation of reservation buy prices of American options. Also the latter algorithm is implemented, and we present an example showing that in an economy with transaction costs, premature exercise of an American call option written on a non-dividend paying stock maybe optimal.