Browse > Article
http://dx.doi.org/10.4134/BKMS.2014.51.6.1791

COMMODITY FUTURES TERM STRUCTURE MODEL  

Choi, Hyeong In (Department of Mathematics & Research Institute of Mathematics Seoul National University)
Kwon, Song-Hwa (Department of Mathematics The Catholic University of Korea)
Kim, Jun Yeol (OTC Products Dealing Team KYOBO Securities Co., Ltd.)
Jung, Du-Seop (Department of Mathematics Seoul National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.6, 2014 , pp. 1791-1804 More about this Journal
Abstract
A new approach to the commodity futures term structure model is introduced. The most salient feature of this model is that, once the interest rate model is given, the commodity futures price volatility is the only quantity that completely determines the model. As a consequence this model enables one to do away with the drudgeries of having to deal with the convenience yield altogether, which has been the most thorny point so far.
Keywords
commodity futures; term structure; convenience yield; volatility; European option; HJM;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Borovkova and H. Geman, Seasonal and stochastic effects in commodity forward curves, Review of Derivatives Research 9 (2006), no. 2, 167-186.
2 L. B. G. Andersen, Markov models for commodity futures: theory and practice, Quant. Finance 10 (2010), no. 8, 831-854.   DOI   ScienceOn
3 H. Bessembinder, J. F. Coughenour, P. J. Seguin, and M. M. Smoller, Mean reversion in equilibrium asset prices: evidence from the futures term structure, J. Finance 50 (1995), no. 1, 361-375.   DOI   ScienceOn
4 T. Bjork, Arbitrage Theory in Continuous Time, Oxford University Press, 2004.
5 M. J. Brennan, The price of convenience and the valuation of commodity contingent claims, in Lund, D. and Oksendal, B. (eds.), Stochastic Models and Option Values (North-Holland, Amsterdam).
6 J. Casassus and P. Collin-Dufresne, Stochastic convenience yield implied from commodity futures and interest rates, J. Finance 60 (2005), no. 5, 2283-2331.   DOI   ScienceOn
7 J. Casassus, P. Collin-Dufresne, and B. R. Routledge, Equilibrium commodity prices with irreversible investment and non-linear technologies, Available at SSRN: http://ssrn.com/abstract=686542 or http://dx.doi.org/10.2139/ssrn.686542, 2009.
8 S. Deng, Stochastic models of energy commodity prices and their applications: mean-reversion with jumps and spikes, POWER working papers, Program onWorkable Energy Regulation, University of California Energy Institute, 2000.
9 R. Gibson and E. S. Schwartz, Stochastic convenience yield and the pricing of oil contingent claims, J. Finance 15 (1990), no. 3, 959-967.
10 B. Dupire, Pricing and hedging with smiles, in Mathematics of Derivative Securities (Cambridge, 1995), 103-111, Publ. Newton Inst., 15, Cambridge Univ. Press, Cambridge, 1997.
11 H. Geman, Commodities and Commodity Derivatives, Wiley, 2005.
12 H. Geman and A. Roncoroni, Understanding the fine structure of electricity prices, The Journal of Business 79 (2006), no. 3, 1225-1261.   DOI   ScienceOn
13 D. Heath, R. Jarrow, and A. Morton, Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica 60 (1992), no. 1, 77-105.   DOI   ScienceOn
14 J. E. Hilliard and J. Reis,Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusions in the spot, Journal of Financial and Quantitative Analysis 33 (1998), no. 1, 61-86.   DOI   ScienceOn
15 R. H. Litzenberger and N. Rabinowitz, Backwardation in oil futures markets: theory and empirical evidence, J. Finance 50 (1995), no. 5, 1517-1545.   DOI   ScienceOn
16 R. S. Pindyck, The dynamics of commodity spot and futures markets: a primer, The Energy Journal 22 (2001), no. 3, 1-30.
17 N. T. Milonas, Measuring seasonalities in commodity markets and the half-month effect, Journal of Futures Markets 11 (1991), no. 3, 331-346.   DOI
18 K. R. Miltersen and E. S. Schwartz, Pricing of options on commodity futures with stochastic term structures of convenience yield and interest rates, Journal of Financial Quantitative Analysis 33 (1998), no. 1, 33-59.   DOI   ScienceOn
19 V. K. Ng and S. C. Pirrong, Fundamentals and volatility: storage, spreads, and the dynamics of metals prices, The Journal of Business 67 (1994), no. 2, 203-230.   DOI   ScienceOn
20 D. R. Ribeiro and S. D. Hodges, A two-factor model for commodity prices and futures valuation, EFMA 2004 Basel Meetings Paper.
21 M. C. Richter and C. Sorensen, Stochastic volatility and seasonality in commodity futures and options: the case of soybeans, EFA 2002 Berlin Meetings Presented Paper.
22 E. Schwartz and J. E. Smith, Short-term variations and long-term dynamics in commodity prices, Management Science 46 (2000), no. 7, 893-911.   DOI   ScienceOn
23 Y. Tian and P. Fackler, A seasonal stochastic volatility model for futures price term structure, Working Paper, North California State University, 2000.
24 A. B. Trolle and E. S. Schwartz, Unspanned stochastic volatility and the pricing of commodity derivatives, EFA 2008 Athens Meetings Paper, 2008.
25 E. S. Schwartz, The stochastic behavior of commodity prices: implications for valuation and hedging, J. Finance 52 (1997), no. 3, 923-973.   DOI   ScienceOn
26 N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, 2nd Edition, North-Holland Publishing Co., 1989.