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Multi-Period Risk Measures and Optimal Investment Policies Read chapter Read first chapter

2017 | OriginalPaper | Chapter

6. Pricing Multiple Exercise American Options by Linear Programming

Authors : Monia Giandomenico, Mustafa Ç. Pınar

Published in: Optimal Financial Decision Making under Uncertainty

Publisher: Springer International Publishing

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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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Footnotes
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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Metadata
Title
Pricing Multiple Exercise American Options by Linear Programming
Authors
Monia Giandomenico
Mustafa Ç. Pınar
Copyright Year
2017
Book
Optimal Financial Decision Making under Uncertainty

Print ISBN: 978-3-319-41611-3

Electronic ISBN: 978-3-319-41613-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-41613-7_6