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

In the paper by Melnikov and Petrachenko ‘On option pricing in binomial market with transaction costs,’ Finance Stoch. 9 (2005), 141–149, a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counter-example to show that the option pricing formula stated in that paper can in fact lead to arbitrage. This is related to the fact that under transaction costs a superreplicating strategy may be less expensive to set up than a strictly replicating one.