Black and Scholes pricing and markets with transaction costs: An example (Q5957685)

The payoff of a stock dominates the payoff of a European call option and an upper bound for the price of a call is the price of the stock. In this paper it is shown that in the presence of proportional transaction costs there exists a viable price system (for definition and main properties see \textit{E. Jouini} and \textit{H. Kallal} [J. Econ. Theory 66, 178-197 (1995; Zbl 0830.90020)] and \textit{M. Harrison} and \textit{D. Kreps} [J. Econ. Theory 20, 381-408 (1979; Zbl 0431.90019)]) such that the prices of call options are arbitrarily close to this upper no-arbitrage bound, so the Black-Scholes model that determines the price of a call in frictionless markets may be a poor approximation in markets with transaction costs. The result is obtained by constructing an approximation process generated by a jump-Markov process and a diffusion.