Extracting and applying smooth forward curves from average-based commodity contracts with seasonal variation

In this article, we propose a method of computing a smooth curve from observed forward prices with settlement over a period. We consider the electricity market, where such contracts are based on an average of the spot price for electricity over a specified period ranging from one day up to a year. From observed market data, we construct a smooth curve which is supposed to model the prices of forward contracts with settlement at a fixed time, if such would have been traded in the market. Since electricity prices are seasonally dependent, we propose to decompose the curve into a seasonal component and a residual or correction term. The correction term is defined as a polynomial spline function with a maximum smoothness property, so that the constructed curve replicates the observed market prices perfectly. We apply our smoothing algorithm to market data from Nord Pool. The user supplied seasonality affects the shape of the forward curve in the long end. We investigate the term structure of volatility using historical data. From a modeling perspective, we suggest modeling the average-based contracts directly (swap-price modeling) in favour of fixed-delivery forwards (forward-curve modeling), since the former method seems less affected by the seasonality specification.