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Valuation of commodity derivatives in a new multi-factor model

Author

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  • Xuemin Yan
Abstract
This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • 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.
    • Handle: RePEc:kap:revdev:v:5:y:2002:i:3:p:251-271
    DOI: 10.1023/A:1020871616158
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    References listed on IDEAS

    as
    1. 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.
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    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    7. Eraker, Bjorn & Johannes, Michael & Polson, Nicholas, 2002. "The Impact of Jumps in Volatility and Returns," Working Papers 02-18, Duke University, Department of Economics.
    8. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    9. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    10. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    11. Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(1), pages 61-86, March.
    12. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. Zonggang Ma & Chaoqun Ma & Zhijian Wu, 2022. "Pricing commodity-linked bonds with stochastic convenience yield, interest rate and counterparty credit risk: application of Mellin transform methods," Review of Derivatives Research, Springer, vol. 25(1), pages 47-91, April.
    2. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    3. Gong, Xiaoye & Li, Ying & Wu, Yang-Che & Yang, Wan-Shiou, 2020. "Pricing various types of mortgage insurances with disposal and discount costs under a mean-reverting Lévy housing price process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    4. 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.
    5. Gareth William Peters & Mark Briers & Pavel Shevchenko & Arnaud Doucet, 2013. "Calibration and Filtering for Multi Factor Commodity Models with Seasonality: Incorporating Panel Data from Futures Contracts," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 841-874, December.
    6. Chou-Wen Wang & Ting-Yi Wu, 2007. "An Alternative Formulation for the Pricing of Stock Index Futures: Theoretical and Empirical Perspectives," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 6(2), pages 121-134, August.
    7. Roncoroni, Andrea & Prokopczuk, Marcel & Ronn, Ehud I., 2018. "Introduction—special issue on commodity and energy markets in the Journal of Banking and Finance," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 1-4.
    8. Crosby, John & Frau, Carme, 2022. "Jumps in commodity prices: New approaches for pricing plain vanilla options," Energy Economics, Elsevier, vol. 114(C).
    9. Rodriguez, J.C., 2007. "A Preference-Free Formula to Value Commodity Derivatives," Discussion Paper 2007-92, Tilburg University, Center for Economic Research.
    10. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    11. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    12. Delphine Lautier & Alain Galli, 2010. "Dynamic hedging strategies: an application to the crude oil market," Post-Print halshs-00640802, HAL.
    13. Cortazar, Gonzalo & Lopez, Matias & Naranjo, Lorenzo, 2017. "A multifactor stochastic volatility model of commodity prices," Energy Economics, Elsevier, vol. 67(C), pages 182-201.
    14. Gonzato, Luca & Sgarra, Carlo, 2021. "Self-exciting jumps in the oil market: Bayesian estimation and dynamic hedging," Energy Economics, Elsevier, vol. 99(C).
    15. Lourdes Gómez-Valle & Julia Martínez-Rodríguez, 2021. "Including Jumps in the Stochastic Valuation of Freight Derivatives," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    16. Chih-Chen Hsu & An-Sing Chen & Shih-Kuei Lin & Ting-Fu Chen, 2017. "The affine styled-facts price dynamics for the natural gas: evidence from daily returns and option prices," Review of Quantitative Finance and Accounting, Springer, vol. 48(3), pages 819-848, April.
    17. Max F. Schöne & Stefan Spinler, 2017. "A four-factor stochastic volatility model of commodity prices," Review of Derivatives Research, Springer, vol. 20(2), pages 135-165, July.
    18. repec:dau:papers:123456789/5470 is not listed on IDEAS
    19. Rodriguez, J.C., 2007. "A Preference-Free Formula to Value Commodity Derivatives," Other publications TiSEM 7354a9fa-3202-40c1-aeb2-a, Tilburg University, School of Economics and Management.
    20. Gareth W. Peters & Mark Briers & Pavel V. Shevchenko & Arnaud Doucet, 2011. "Calibration and filtering for multi factor commodity models with seasonality: incorporating panel data from futures contracts," Papers 1105.5850, arXiv.org.
    21. repec:dau:papers:123456789/95 is not listed on IDEAS
    22. Fileccia, Gaetano & Sgarra, Carlo, 2018. "A particle filtering approach to oil futures price calibration and forecasting," Journal of Commodity Markets, Elsevier, vol. 9(C), pages 21-34.

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