A counter-example to an option pricing formula under transaction costs (Q881422)

The authors analyse the paper by \textit{A. V. Melnikov} and \textit{Yu. G. Petrachenko} [Finance Stoch. 9, No. 1, 141--149 (2005; Zbl 1060.62121)], where a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. They present a counter-example to show that the mentioned above option pricing formula can in fact lead to arbitrage, in particular, for calls with cash settlement. However, it is mentioned that, if restricted to call options with physical delivery or to small (in some sense) transaction costs, this pricing formula is free of arbitrage.