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