Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot

This paper investigates the effects of stochastic convenience yields, stochastic interest rates, and jumps in the spot price on the pricing of commodity futures, forwards, and futures options. Numerical examples show that one-factor prices differ materially from the stochastic convenience yield two-factor prices when convenience yield is considerably above its long-term average. The extension to a three-factor model with stochastic interest rates leads to a different futures price but the forward price is unchanged. The extension of the three-factor model to include jumps in the spot price process does not affect forward or futures prices but it can have an impact on options prices. The model is applied to price the present value of future cash flows from a real asset.

[1]  N. Kaldor.  Speculation and Economic Stability , 1939 .

[2]  L. Telser.  Futures Trading and the Storage of Cotton and Wheat , 1958, Journal of Political Economy.

[3]  M. Brennan.  The Supply of Storage , 1976 .

[4]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[5]  F. Black.  The pricing of commodity contracts , 1976 .

[6]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[7]  S. Richard,et al.  A continuous time equilibrium model of forward prices and futures prices in a multigood economy , 1981 .

[8]  S. Ross,et al.  The relation between forward prices and futures prices , 1981 .

[9]  M. Sundaresan.  A study of commodity futures prices , 1981 .

[10]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[11]  S. Sundaresan,et al.  The Valuation of Options on Futures Contracts , 1985 .

[12]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[13]  E. Fama,et al.  Commodity futures prices: some evidence on forecast power , 1987 .

[14]  Louis O. Scott.  Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application , 1987, Journal of Financial and Quantitative Analysis.

[15]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[16]  E. Fama,et al.  Business Cycles and the Behavior of Metals Prices , 1988 .

[17]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[18]  J. Hull.  Options, futures, and other derivative securities , 1989 .

[19]  Eduardo S. Schwartz,et al.  Stochastic Convenience Yield and the Pricing of Oil Contingent Claims , 1990 .

[20]  David S. Bates.  The Crash of ʼ87: Was It Expected? The Evidence from Options Markets , 1991 .

[21]  D. Duffie.  Dynamic Asset Pricing Theory , 1992 .

[22]  Peter H. Ritchken,et al.  VOLATILITY STRUCTURES OF FORWARD RATES AND THE DYNAMICS OF THE TERM STRUCTURE1 , 1995 .

[23]  Eduardo S. Schwartz.  The stochastic behavior of commodity prices: Implications for valuation and hedging , 1997 .

[24]  Eduardo S. Schwartz,et al.  Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates , 1998, Journal of Financial and Quantitative Analysis.