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Pricing swing options with typical constraints. (English) Zbl 1235.91174
Summary: We propose a pricing method by mathematical programming for swing options with typical constraints on a lattice model. We show that the problem of pricing typical swing options has a particular optimal solution such that there are only seven kinds of changed amounts in the solution. Using the solution, we formulate the pricing problem as a linear program. The solution can be applied to the methods of P. Jaillet, E. I. Ronn and S. Tompaidis [Manage. Sci. 50, No. 7, 909–921 (2004; Zbl 1232.90340)] and C. Barrera-Esteve et al. [Methodol. Comput. Appl. Probab. 8, No. 4, 517–540 (2006; Zbl 1142.91502)] for improving time complexity.
Another feature of our method is the capability to price swing options in an incomplete market. In an incomplete market, the price of a swing option is defined as an upper and a lower bound of arbitrage-free prices. We formulate the problem of finding an upper bound as a linear program. For a lower bound, we give a bilinear programming formulation.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
90C05 Linear programming
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