An Integer Programming Model for Pricing American Contingent Claims under Transaction Costs
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We study the problem of computing the lower hedging price of an American contingent claim in a finite-state discrete-time market setting under proportional transaction costs. We derive a new mixed-integer linear programming formulation for calculating the lower hedging price. The linear programming relaxation of the formulation is exact in frictionless markets. Our results imply that it might be optimal for the holder of several identical American claims to exercise portions of the portfolio at different time points in the presence of proportional transaction costs while this incentive disappears in their absence.
KeywordsAmerican Contingent Claims Transaction Costs Mixed-integer Programming Linear Programming Martingales Incomplete Markets Pricing Hedging Dividends
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- Bensoussan A. (1984) On the theory of option pricing. Acta Applicanda Mathematica 2: 139–158Google Scholar
- Bouchard B., Temam E. (2005) On the hedging of American options in discrete time markets with proportional transaction costs. Electronic Journal of Probability 10(22): 746–760Google Scholar
- Davis M., Zariphopoulou T. (1995) American options and transaction fees. In: Davis M. (eds) The IMA Volumes in mathematics and its applications (Vol. 65). Springer-Verlag, Berlin, pp 47–62Google Scholar
- Detemple, J.(2005). American style derivatives: Valuation and computation. Boca Raton: Chapman & Hall/CRC Financial Mathematics Series.Google Scholar
- Föllmer H., Schied A. (2004) Stochastic finance: An introduction in discrete time. De Gruyter studies in mathematics (2nd ed., Vol. 27). W. De Gruyter and Co, BerlinGoogle Scholar
- Jaschke, S. (1996). Super-hedging and arbitrage pricing in markets with transaction and trading constraints. Discussion paper 1998-11, SFB 373, Humboldt-Universität Berlin.Google Scholar
- Myeni R. (1992) The pricing of the American option. Annals of Applied Probability 2: 1992Google Scholar
- Pennanen, T., & King, A. (2006). Arbitrage pricing of American contingent claims in incomplete markets—a convex optimization approach. Working paper, June 2006. http://math.tkk.fi/~teemu/american.pdf.
- Roux, A., & Zastawniak, T. (2006). American options under proportional transaction costs: Seller’s price algorithm, hedging strategy and optimal stopping. Preprint, University of York.Google Scholar