An equilibrium model for commodity spot and forward prices
Antonis Papapantoleon (TU Berlin, Germany)
Joint work with Michail Anthropelos and Michael Kupper

Wednesday June 4, 16:30-17:00 | session 6.5 | Commodities | room G

The aim of this project is to determine the forward price of a consumption commodity via the interaction of agents in the spot and forward commodity market. We consider a market model that consists of three representative agents: producers of the commodity, consumers and financial investors (sometimes also called speculators). Producers produce a fixed amount of the commodity at each time point, but can choose how much they offer in the spot market and store the rest for selling at the next time period. They also have a position in forwards in order to hedge the commodity price uncertainty. Consumers are setting the spot price of the commodity at each time point by their demand. Finally, investors are investing in the financial markets and, in order to diversify their portfolios, also in the forward commodity market. The equilibrium prices for the commodity are the ones that clear out the spot and forward markets. We assume that producers and investors are utility maximizers and have exponential preferences, while the consumers' demand function is linear. Moreover, the exogenously priced financial market and the demand function are driven by Lévy processes. We solve the maximization problem for each agent and prove the existence of an equilibrium. This setting allows to derive explicit solutions for the equilibrium prices and to analyze the dependence of prices on the model parameters and the agent's risk aversion.

The return-volatility relation in commodity futures markets
Christina Nikitopoulos Sklibosios (University of Technology Sydney, Australia)
Joint work with Carl Chiarella, Boda Kang and Thuy-Duong To

Wednesday June 4, 17:00-17:30 | session 6.5 | Commodities | room G

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.