Pricing Swing Options with Typical Constraints

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 Jaillet, Ronn and Tompaidis (2004), and Barrera-Esteve et al. (2006) 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.