Extracting and Applying Smooth Forward Curves From Average-Based Commodity Contracts with Seasonal Variation

Abstract

Several important new classes of derivative instruments, notably those related to weather and to electricity, have payoffs based on the average value of the underlying over some period of time. For electricity in the Nord Pool market, for example, actively traded contracts exist for a variety of partly overlapping averaging periods out several years into the future. Current market prices for such contracts inherently depend on the market's projection of the future spot price of electricity over the averaging periods, i.e., instantaneous forward prices for the relevant time periods. But since these forward prices are not observable directly, and they can be expected to exhibit the seasonality embedded in the spot market, extracting a smooth implied instantaneous forward curve from market data is a challenging task. This article offers a procedure for doing just that, by modeling the forwards to include both a seasonal component and a noise component, and requiring the noise to have maximum smoothness over the term structure of forward prices.