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

*(English. Russian original)*Zbl 1335.91084
Theory Probab. Math. Stat. 91, 81-92 (2015); translation from Teor. Jmovirn. Mat. Stat. 91, 74-85 (2014).

The authors use the lattice method to price a swing option in the Cox-Ross-Rubinstein binomial model. They consider the normalized swing option which means that one can purchase not more than one unit of the underlying asset at each moment. More precisely, the amount of purchase of the underlying asset varies from zero to one at every instance of time. It is proved in the binomial framework that the optimal strategy corresponds to the so called “bang-bang” regime, under the additional assumption that the loan at some moment is expressed as an integer number. The optimal purchased quantity at any of such moments is equal to either 0 or 1. Moreover, it is established that the pay-off function at every node of the tree is concave and stepwise linear. Discussing the property of concavity of the pay-off function of a swing option, the authors provide a clear financial explanation of this property.

Reviewer: Yuliya S. Mishura (Kyïv)

##### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

PDF
BibTeX
Cite

\textit{A. V. Kulikov} and \textit{N. O. Malykh}, Theory Probab. Math. Stat. 91, 81--92 (2015; Zbl 1335.91084); translation from Teor. Jmovirn. Mat. Stat. 91, 74--85 (2014)

Full Text:
DOI

##### References:

[1] | [k5] J. C. Cox, S. Ross, and M. Rubinstein, Option pricing: A simplified approach, J. Financial Economics 7 (1979), no. 3, 229-264. · Zbl 1131.91333 |

[2] | [k7] 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. · Zbl 1229.91348 |

[3] | [k3] 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. |

[4] | [k4] 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. · Zbl 1296.91261 |

[5] | [k8] M. I. M. Wahab and C.-G. Lee, Pricing swing options with regime switching, Ann. Oper. Res. 185 (2011), no. 1, 139-160. |

[6] | [k9] 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. · Zbl 1210.91125 |

[7] | [k2] N. Bollen, Valuing options in regime-switching models, J. Derivatives 6 (1998), no. 1, 38-49. |

[8] | [k1] O. Bardou, S. Bouthemy, and G. Pages, When are swing options bang-bang?, Internat. J. Theoret. Appl. Finance 13 (2010), no. 7, 867-899. · Zbl 1233.91255 |

[9] | [k6] G. Fusai and A. Roncoroni, Implementing Models in Quantitative Finance: Methods and Cases, Springer-Verlag, Berlin, 2008. · Zbl 1213.91008 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.