Abstracts

The dynamic relation between price returns and volatility changes in the commodity futures markets is analysed via a continuous time stochastic volatility model within the Heath, Jarrow, and Morton (1992) framework. As the model possesses finite-dimensional affine realizations for the commodity futures price and quasi-analytical prices for options on commodity futures, the model is estimated by fitting to both futures prices and options prices. Two of the most active commodities markets, namely gold and crude oil are considered which are, though, principally different as gold is classified as an investment commodity whereas crude oil as a consumption commodity. The model is estimated by using a database of daily futures and option prices extending to 31 years for gold and 21 years for crude oil.
Our 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. However, the opposite reaction occurs over quiet volatility periods. As leverage effect, volatility feedback effect and inventory effect do not adequately explain this reaction especially for the crude oil futures, we propose the convenience yield effect. We argue that commodity futures markets in backwardation entail a positive relation, while futures markets in contango entail a negative relation.
Thus during high volatile periods which are predominantly driven by market-wide shocks, the gold futures volatility is inverted asymmetric (implying a positive relation) as explained by the safe haven property of gold, while the crude oil futures volatility is asymmetric (implying a negative relation) as explained by the convenience yield effect. However, during less volatile market conditions, typically commodity-specific effects dominate that yield to a negative relation in the gold futures market and a positive relation in the crude oil futures market. Thus when markets are quiet, gold futures respond similarly to other financial assets like equities, while crude oil futures preserves a typically high convenience yield that stimulates a positive relation. It has further been illustrated that for these two commodity futures markets, when the market uncertainty is high, then market wide shock effects dominate, while when the market is quiet then commodity-specific shock effects dominate. Finally, it is shown that the relation is consistent with the option-derived implied volatility skew.