Risk Management of Co-Integrated Commodities

Abstract

Coal, natural gas, CO2 and electrical power are examples of commodities with strong interrelations. Using co-integrated price processes for these commodities implies much more realistic price distributions for spark and dark spreads. Simple correlation based price models heavily overestimate the spread variation over longer time horizons. In this paper we propose a straightforward framework for modeling co-integration between a set of futures prices of different commodities. Using data relevant for spark and dark spreads in the German market we provide empirical evidence of co-integration relationships between different sets of commodities. We apply the estimated models, with and without co-integration, to the calculation of Value-at-Risk for different spread positions. Our results show that ignoring co-integration can lead to drastically overestimated Value-at-Risk and excessive capital requirements.