Skip to main content
Article thumbnail
Location of Repository

Models for the price of a storable commodity

By Diana Ribeiro


The current literature does not provide efficient models for commodity prices and\ud futures valuation. This inadequacy is partly due to the fact that the two main streams\ud of the literature - structural models and reduced form models - are largely disjoint. In\ud particular, existing structural models are developed under rigid discrete time framework\ud that does not take into account the mean-reverting properties of commodity prices.\ud Furthermore, most of the literature within this class does not analyze the properties of the\ud futures prices. Current reduced-form models allow cash-and-carry arbitrage possibilities\ud and do not take into account the dependence between the spot price volatility and the\ud inventory levels.\ud This thesis investigates three new models for the price of a storable commodity\ud and futures valuation. Specifically, we develop a structural model and two reduced-form\ud models. In doing so, we expand the leading models within each of the two streams of\ud the literature, by establishing a link between them. Each of these models provide an\ud advance of their type.\ud This study makes several contributions to the literature. We provide a new\ud structural model in continuous time that takes into account the mean reversion of commodity\ud prices. This model is formulated as a stochastic dynamic control problem. The\ud formulation provided is flexible and can easily be extended to encompass alternative\ud microeconomic specifications of the market. The results provide an optimal storage\ud policy, the equilibrium prices and the spot price variability. We also develop a numerical\ud method that allows the construction and analysis of the forward curves implied by this\ud model. We provide a separate analysis considering a competitive storage and considering\ud a monopolistic storage. The results are consistent with the theory of storage. Furthermore,\ud the comparison between monopoly and competition confirm the economic theory.\ud We developed a simple reduced-form model that focuses both on the mean reverting\ud properties of commodity prices and excludes cash-and-carry arbitrage possibilities. This\ud model is compared with a standard single-factor model in the literature. This new model\ud adds two important features to the standard model and motivates the development of a\ud more sophisticated reduced-form model. Accordingly, the last model developed in this\ud thesis is a reduced-form model. It is a two-factor model that represents the spot price\ud and the convenience yield as two correlated stochastic factors. This model excludes\ud cash-and-carry arbitrage possibilities and takes into account the relationship between the spot price volatility and the inventory level. We find an analytical solution for the\ud futures prices. This model is tested empirically using crude oil futures data and it Is\ud compared with one of the leading models in the literature. Both models are calibrated\ud using Kalman filter techniques. The empirical results suggest that both models need to\ud be improved in order to better fit the long-term volatility structure of futures contracts

Topics: HB
OAI identifier:

Suggested articles


  1. (1999). A multi-factor model for energy derivatives. Working Paper, School of Finance and Economics,
  2. A simple competitive model with production and storage. doi
  3. (1998). A state-space approach to estimate and test multifactor cox-ingersoll-ross models of the term structute. Working Paper, doi
  4. (1930). A TreatiSe on Money: Volume //: The Applied Theory of Money. doi
  5. (1968). A two-dimensional interpolation function for irregulary sapced data.
  6. An equilibrium characterization if the term structure. doi
  7. (1995). Backwarclation in oil futures markets: Theory and empircal evidence. doi
  8. (1991). Bond and option pricing when short rates are lognormal. doi
  9. (1988). Business cycles and the behaviour of metals prices. doi
  10. Carryover levels for grains: A method for determining amounts that are optimal under specified conditions.
  11. (1996). Competitive storage and commodity price dynamics. doi
  12. (1992). Consumption betas and backwardation in commodity markets. doi
  13. (1996). Convergence of numerical method for multistate stochastic dynamic programming.
  14. (1993). Do futures prices for commodities embody risk premiums? doi
  15. (1957). Dynamic Programming. doi
  16. (1997). Energy Risk: Valuing and Managing Energy Den"vatives.
  17. (2000). Equilibrium forward curves for commodities. doi
  18. (1995). Estimatinh and testing exponential-affine term structure models by kalman filter. Woking Paper,
  19. Evaluating natural resource investments. doi
  20. Fundamentals and volatility: Storage, spreads and the dynamics of metal prices. doi
  21. (1996). Future trading and investor returns: An investigation of commodity market risk premiums. doi
  22. (1958). Futures trading and the storage of cotton and wheat. doi
  23. Implementing a stochastic model for oil futures prices. doi
  24. (1998). Implementing Derivatives Models. doi
  25. Implications of recent research on optimal storage rules. doi
  26. (1996). Interest rate volatility and the shape of the term structure. doi
  27. Investment under alternative return assumptions comparing random walks and mean reversion. doi
  28. Investment under uncertainty. doi
  29. Kalman filtering of generalized vasicek term structure models. Joumal of Financial and Quant1tative Analysis, doi
  30. (1995). Managin Energy Price Risk, chapter Valuing Energy Derivatives.
  31. Mean-reversion in equilibrium asset prices: Evidence from the futures term structure. doi
  32. (1991). Movements of the term structure of commodity futures and pricing of commodity contingent claims. Working Paper,
  33. Multi-factor term structure models.
  34. (1997). Non linear kalman filter techniques for term structure models of the term structure of interest rates. Working Paper, University of Aarhus,
  35. (1994). Numerical SolutiOn for Partial Differential Equations: an introduction. Cambridge: doi
  36. (1994). One-factor interest rate models and the valuation of interest-rate derivative securities. doi
  37. (1989). Optimal harvesting with both population and price dynamics. doi
  38. Optimal storage rule. doi
  39. Option pricing when underlying stock returns are discontinuous. doi
  40. Option pricing: A simplified approach. doi
  41. (1998). Pirrong. Price dynamics and derivatives prices for continuously produced, storable commodities. Working Paper, doi
  42. (1993). Pricing interest-rate-derivative securities. The Review of Financial Studies, doi
  43. (1998). Pricing of options on commodity futures with stochastic term structures of convenience yields and interest rates. doi
  44. (1965). Proof that properly anticipated prices fluctuate randomly.
  45. Rational expectations and the theory of price movements. doi
  46. Reversion, timing options, and long-term decision-making. doi
  47. Scatterend data interpolation: Tests of some methods. doi
  48. (2000). Short-term variations and longterm dynamics in commodity prices. doi
  49. (1939). Speculation and economic stability. doi
  50. Stochastic speculative price. doi
  51. (1991). Storage and Commodity Markets. doi
  52. (1992). The relation between forward prices and futures prices. doi
  53. (1997). The stochastic behaviour of commodity prices: Implications for valuation and hedging. doi
  54. The supply of storage in energy futures markets. doi
  55. (1981). The Theory of Commodity Price Stabilization: A Study in the Economics of Risk. doi
  56. (1949). The theory of price of storage.
  57. The valuation of a firm advertising optimally. The Quarterly Review of Economics and Finance, doi
  58. (1992). The valuation of commodity contingent claims. Anderson Graduate School of Management, doi
  59. The value of waiting to invest. doi
  60. Unit roots and the estimation of interest rate dynamics.
  61. Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusions on the spot. doi
  62. (1990). Valuing derivative secutiries using the explicit finite difference method. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.