A discrete stochastic model for investment with an application to the transaction costs case
The authors study a model where investments are completely defined through their generated cash flows, the latter having a dynamics given by a binomial tree. The model is assumed to be stationary, i.e. each project is available at every date and in every state of the world at the same conditions. (In the deterministic case this kind of models has been studied e.g. by \textit{I. Adler} and \textit{D. Gale} [Math. Finance 7, 73-81 (1997; Zbl 0884.90011)].) Under some technical condition, the assumption of no-arbitrage implies the existence of an interest rate and a particular probability measure under which the expected value of the total investments is non-positive if there are short-selling constraints and equal to zero otherwise. In the second part of the paper an economie model is presented in which the price of the underlying asset follows a binomial process. It is assumed that there are transaction costs on the underlying asset and the options under consideration. Applying the results in the first part the authors show e.g. that at the equilibrium the Cox-Rosse-Rubinstein (CRR) price is always between the buying and selling price. In the particular case where there are only transaction costs on the underlying asset and not on the options, the options' price equals the CRR-price which is a new result about transaction costs.
scientific article; zbMATH DE number 1428354