Theory of Probability and Mathematical Statistics
The concavity of the payoff function of a swing option in a binomial model
A. V. Kulikov, N. O. Malykh
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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.
Keywords: Swing option, tree method, bang-bang control, energy derivatives
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