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
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
MathSciNet review:
3364125
Full-text PDF Free Access
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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.
References
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- Rüdiger U. Seydel, Lattice approach and implied trees, Handbook of computational finance, Springer Handb. Comput. Stat., Springer, Heidelberg, 2012, pp. 551–577. MR 2908485, DOI https://doi.org/10.1007/978-3-642-17254-0_20
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- C. Chiarella, L. Clewlow, and B. Kang, The Evaluation of Gas Swing Contracts with Regime Switching, Topics in Numerical Methods for Finance (M. Cummins et al., eds), Springer, New York, 2012, pp. 155–176.
- M. I. M. Wahab and Chi-Guhn Lee, Pricing swing options with regime switching, Ann. Oper. Res. 185 (2011), 139–160. MR 2788791, DOI https://doi.org/10.1007/s10479-009-0599-z
- M. I. M. Wahab, Z. Yin, and N. C. P. Edirisinghe, Pricing swing options in the electricity markets under regime-switching uncertainty, Quant. Finance 10 (2010), no. 9, 975–994. MR 2738822, DOI https://doi.org/10.1080/14697680903547899
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- Gianluca Fusai and Andrea Roncoroni, Implementing models in quantitative finance: methods and cases, Springer Finance, Springer, Berlin, 2008. MR 2386793
References
- J. C. Cox, S. Ross, and M. Rubinstein, Option pricing: A simplified approach, J. Financial Economics 7 (1979), no. 3, 229–264.
- M. R. Seydel, Lattice Approach and Implied Trees, Handbook of Computational Finance, Second Edition (J.-C. Duan et al., eds.), Springer, New York, 2012, pp. 551–577. MR 2908485
- J. Breslin, L. Clewlow, C. Strickland, and D. van der Zee, Swing contracts: take it or leave it?, Energy Risk (2008), no. 2, 64–68.
- C. Chiarella, L. Clewlow, and B. Kang, The Evaluation of Gas Swing Contracts with Regime Switching, Topics in Numerical Methods for Finance (M. Cummins et al., eds), Springer, New York, 2012, pp. 155–176.
- M. I. M. Wahab and C.-G. Lee, Pricing swing options with regime switching, Ann. Oper. Res. 185 (2011), no. 1, 139–160. MR 2788791
- M. I. M. Wahab, Z. Yin, and N. C. Edirsinghe, Pricing swing options in the electricity markets under regime-switching uncertainty, Quantitative Finance 10 (2010), no. 9, 975–994. MR 2738822 (2012a:91211)
- N. Bollen, Valuing options in regime-switching models, J. Derivatives 6 (1998), no. 1, 38–49.
- O. Bardou, S. Bouthemy, and G. Pages, When are swing options bang-bang?, Internat. J. Theoret. Appl. Finance 13 (2010), no. 7, 867–899. MR 2718983 (2012d:91194)
- G. Fusai and A. Roncoroni, Implementing Models in Quantitative Finance: Methods and Cases, Springer-Verlag, Berlin, 2008. MR 2386793 (2009g:65003)
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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
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
