Power Forward Curve Model with Mitigated Swell Based on Constrained Least Square Error Approach

Abstract

To construct a power forward curve (PFC), which is indispensable for decision-making such as pricing of electricity transactions, we propose a modeling method with relatively small error while satisfying the reasonable PFC requirements summarized in the previous study. In particular, we focus on the problem that the PFC obtained by the existing method, which simultaneously satisfies the smoothness and arbitrage-free conditions, tends to "swell" significantly when the price of electricity futures rises, and the fit deteriorates significantly, and propose a method to mitigate this problem. Specifically, using B-spline basis functions, we solve a constrained least-square-error-based optimization problem instead of minimizing the integral of squared curvature, which has been used in previous studies. The empirical study examines the errors between the realized spot prices and the PFCs using multiple futures products for different observation points, and finds that our method effectively mitigates the "swell" problem and is more accurate overall than the previous method. Furthermore, it is shown that the fit of the forward curve can be improved by, for example, incorporating the seasonal trend of the holiday effect to calculate the structural pattern of the PFC, providing useful suggestions for modeling practitioners.