The Return-Volatility Relation in Commodity Futures Markets

By employing a continuous time stochastic volatility model, the dynamic relation between price returns and volatility changes in the commodity futures markets is analysed. An extensive daily database of gold and crude oil futures and futures options is used to estimate the model that is well suited to assess the return-volatility relation for the entire term structure of futures prices. The empirical results indicate a positive relation in the gold futures market and a negative relation in the crude oil futures market, especially over periods of high volatility principally driven by market-wide shocks. However, the opposite reaction occurs over quiet volatility periods when typically commodity-specific effects dominate. As leverage effect, volatility feedback effect and inventory effect do not adequately explain this reaction especially for the crude oil futures, the convenience yield effect is proposed. Accordingly, commodity futures markets in backwardation entail a positive relation, while futures markets in contango entail a negative relation