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Theory of Probability and Mathematical Statistics

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The concavity of the payoff function of a swing option in a binomial model


Authors: A. V. Kulikov and N. O. Malykh
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 81-92
MSC (2010): Primary 91G20; Secondary 91-02
DOI: https://doi.org/10.1090/tpms/968
Published electronically: February 4, 2016
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Abstract: We use the lattice method to price a swing option. We show that the payoff function at each node of the lattice is concave and piecewise linear. A corollary of this result is that there exists a bang-bang control such that if the loan at a certain moment is integer, then the optimal purchased quantity at this moment is equal to either 0 or 1. If the loan at a certain moment is not integer, then the fair price is a convex combination of the nearest pay-off values with integer loans.


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Additional Information

A. V. Kulikov
Affiliation: Department of Higher Mathematics, Faculty for Innovations and High Technologies, Moscow Institute of Physics and Technology State University, Institutskaya lane, 9, Dolgoprudny, Moscow Region, 141700, Russian Federation
Email: kulikov_av@pochta.ru

N. O. Malykh
Affiliation: Department of Innovation Economics, Faculty for Innovations and High Technologies, Moscow Institute of Physics and Technology State University, Institutskaya lane, 9, Dolgoprudny, Moscow Region, 141700, Russian Federation
Email: malykh@phystech.edu

DOI: https://doi.org/10.1090/tpms/968
Keywords: Swing option, tree method, bang-bang control, energy derivatives
Received by editor(s): May 19, 2013
Published electronically: February 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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