Abstract
We consider the problem of computing the lower hedging price of American options of the call and put type written on a non-dividend paying stock in a non-recombinant tree model with multiple exercise rights. We prove using a simple argument that an optimal exercise policy for an option with h exercise rights is to delay exercise until the last h periods. The result implies that the mixed-integer programming model for computing the lower hedging price and the optimal exercise and hedging policy has a linear programming relaxation that is exact, i.e., the relaxation admits an optimal solution where all variables required to be integral have integer values.
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Notes
- 1.
An earlier version of the paper had quite a long proof for the case h = 2 and restricted to binomial and trinomial trees. It was based on an elaborate primal-dual construction. The present proof was offered by an anonymous reviewer of the earlier version, to whom we are thankful.
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Acknowledgements
Supported in part by a grant from the University of L’Aquila, as part of Research Grant Reti per la conoscenza e l’orientamento tecnico-scientifico per lo sviluppo della competitività (RE.C.O.TE.S.S.C.) POR 2007–2013-Action 4, funded by Regione Abruzzo and the European Social Fund 2007–2013. Revised twice, November and December 2013. The paper benefited from the comments of two anonymous reviewers.
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Giandomenico, M., Pınar, M.Ç. (2017). Pricing Multiple Exercise American Options by Linear Programming. In: Consigli, G., Kuhn, D., Brandimarte, P. (eds) Optimal Financial Decision Making under Uncertainty. International Series in Operations Research & Management Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-41613-7_6
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