Gido A. Haarbrücker

Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation of decision stages, discretization of the probability space, and reparameterization of the decision space. We report on numerical results and discuss analytically tractable limiting cases.

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are ? up to a certain size ? easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ? based on the solutions at the previous ?-1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).

This paper provides a set of stochastic multistage programs where the evolvement of uncertain factors is given by stochastic processes. We treat a practical problem statement within the field of managing fixed-income securities. Detailed information on the used parameter values in various interest rate models is given. Barycentric approximation is applied to obtain computational results; different measures of the achieved goodness of approximation are indicated.