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Financial boundary conditions in a continuous model with discrete-delay for pricing commodity futures and its application to the gold market

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  • Gómez-Valle, Lourdes
  • López-Marcos, Miguel Ángel
  • Martínez-Rodríguez, Julia

Abstract

In this work, we approach the solution of a differential problem for pricing commodity futures when the spot price follows a stochastic diffusion process with memory, that is, it depends on two discrete times: the present instant and a delayed one. In this kind of models, a closed-form solution is not feasible to obtain and, in most of the cases, numerical methods should be applied. To this end, it is normal to introduce a bounded domain for the state variable, so suitable boundary conditions have to be established. The conditions based on mathematical reasons often introduce difficulties in the boundary and poor accuracy. Here, we propose new nonstandard boundary conditions based on some financial reasons and then, we face the numerical solution of the problem that arises. Some experiments are presented which show that the drawbacks in the behavior of the solutions are overcome, providing more accurate futures prices. This new procedure is implemented in order to obtain a more precise valuation of gold futures contracts traded on the Commodity Exchange Inc. (US).

Suggested Citation

  • Gómez-Valle, Lourdes & López-Marcos, Miguel Ángel & Martínez-Rodríguez, Julia, 2024. "Financial boundary conditions in a continuous model with discrete-delay for pricing commodity futures and its application to the gold market," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924010282
    DOI: 10.1016/j.chaos.2024.115476
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    References listed on IDEAS

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    1. Bessembinder, Hendrik, et al, 1995. "Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-375, March.
    2. Lingfei Li & Rafael Mendoza-Arriaga & Zhiyu Mo & Daniel Mitchell, 2016. "Modelling electricity prices: a time change approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1089-1109, July.
    3. Haque, Md. Aminul & Topal, Erkan & Lilford, Eric, 2014. "A numerical study for a mining project using real options valuation under commodity price uncertainty," Resources Policy, Elsevier, vol. 39(C), pages 115-123.
    4. Aminrostamkolaee, Behnam & Scroggs, Jeffrey S. & Borghei, Matin Sadat & Safdari-Vaighani, Ali & Mohammadi, Teymour & Hossein Pourkazemi, Mohammad, 2017. "Valuation of a hypothetical mining project under commodity price and exchange rate uncertainties by using numerical methods," Resources Policy, Elsevier, vol. 52(C), pages 296-307.
    5. Bessler, Wolfgang & Wolff, Dominik, 2015. "Do commodities add value in multi-asset portfolios? An out-of-sample analysis for different investment strategies," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 1-20.
    6. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    7. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    8. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    9. Eugene F. Fama & Kenneth R. French, 2015. "Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 4, pages 79-102, World Scientific Publishing Co. Pte. Ltd..
    10. Brian J. Henderson & Neil D. Pearson & Li Wang, 2015. "Editor's Choice New Evidence on the Financialization of Commodity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1285-1311.
    11. Nomikos, Nikos K. & Kyriakou, Ioannis & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Freight options: Price modelling and empirical analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 82-94.
    12. O'Connor, Fergal A. & Lucey, Brian M. & Batten, Jonathan A. & Baur, Dirk G., 2015. "The financial economics of gold — A survey," International Review of Financial Analysis, Elsevier, vol. 41(C), pages 186-205.
    13. Geman, Hélyette & Smith, William O., 2013. "Theory of storage, inventory and volatility in the LME base metals," Resources Policy, Elsevier, vol. 38(1), pages 18-28.
    14. Xuemin Yan, 2002. "Valuation of commodity derivatives in a new multi-factor model," Review of Derivatives Research, Springer, vol. 5(3), pages 251-271, October.
    15. Martin J. Nielsen & Eduardo S. Schwartz, 2004. "Theory of Storage and the Pricing of Commodity Claims," Review of Derivatives Research, Springer, vol. 7(1), pages 5-24.
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