Abstract
In the paper by Melnikov and Petrachenko (Finance Stoch. 9: 141–149, 2005), 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.
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References
Bensaid B., Lesne J., Pagès H., Scheinkman J. (1992): Derivative asset pricing with transaction costs. Math. Financ. 2, 63–86
Boyle P., Vorst T. (1992): Option replication in discrete time with transaction costs. J. Financ. 47, 271–293
Dermody J.C., Rockafellar R.T. (1991): Cash stream valuation in the face of transaction costs and taxes. Math. Financ. 1, 31–54
Kociński M. (2004): Hedging of the European option in discrete time under proportional transaction costs. Math. Methods Oper. Res. 59, 315–328
Koehl P.-F., Pham H., Touzi N. (1999): Hedging in discrete time under transaction costs and continuous-time limit. J. Appl. Probab. 36, 163–178
Melnikov A.V., Petrachenko Y.G. (2005): On option pricing in binomial market with transaction costs. Financ. Stoch. 9, 141–149
Palmer K. (2001): A note on the Boyle-Vorst discrete-time option pricing model with transaction costs. Math. Financ. 11, 357–363
Palmer, K.: Replicating and super-replicating portfolios in the Boyle-Vorst discrete-time option pricing model with transaction costs. Working paper, University of Melbourne (2001)
Rutkowski M. (1998): Optimality of replication in the CRR model with transaction costs. Appl. Math. (Warsaw) 25, 29–53
Stettner Ł (1997): Option pricing in the CRR model with proportional transaction costs: a cone transformation approach. Appl. Math. (Warsaw) 24, 475–514
Stettner Ł. (2000): Option pricing in discrete-time incomplete market models. Math. Financ. 10, 305–321
Tokarz, K.: European and American option pricing under proportional transaction costs. Ph.D. Thesis, University of Hull (2004)
Tokarz, K., Zastawniak, T.: American contingent claims under small proportional transaction costs. Preprint, 2005, http://www-users.york.ac.uk/~tz506/ZastawniakTokarz2005.pdf
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Roux, A., Zastawniak, T. A counter-example to an option pricing formula under transaction costs. Finance Stoch 10, 575–578 (2006). https://doi.org/10.1007/s00780-006-0016-2
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DOI: https://doi.org/10.1007/s00780-006-0016-2