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

Published electronically:
February 4, 2016

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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