THE LEAST COST SUPER REPLICATING PORTFOLIO IN THE BOYLE–VORST MODEL WITH TRANSACTION COSTS

Guan-Yu Chen (), Ken Palmer () and Yuan-Chung Sheu ()
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Guan-Yu Chen: Department of Mathematics, Cornell University, Ithaca, New York, USA
Ken Palmer: Department of Mathematics, and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan
Yuan-Chung Sheu: Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 01, 55-85

Abstract: Boyle and Vorst work in the framework of the binomial model and derive self-financing strategies perfectly replicating the final payoffs to long and short positions in call and put options, assuming proportional transactions costs on trades in the stock and no transactions costs on trades in the bond. Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Bensaid et al. gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalized by Stettner, Rutkowski and Palmer to the case of asymmetric transaction costs.In this paper, we first determine the number of replicating portfolios and then compute the least cost super replicating portfolio for any contingent claim in a one-period binomial model. By using the fundamental theorem of linear programming, we show that there are only finitely many possibilities for a least cost super replicating portfolio for any contingent claim in a two-period binomial model. As an application of our results, we give an example in which we compute the least cost super replicating portfolio for a butterfly spread in a two-period model.

Keywords: Option pricing; transactions costs; binomial model; super replicating (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024908004725

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