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Pricing commodity futures options in the Schwartz multi factor model with stochastic volatility: An asymptotic method

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  • Chen, Jilong
  • Ewald, Christian-Oliver

Abstract

In this paper we investigate the applicability of the asymptotic approach developed in Fouque et al. (2000) for pricing commodity futures options in a Schwartz (1997) multi factor model, featuring both stochastic convenience yield and stochastic volatility. We show that the zero order term in the expansion coincides with the Schwartz (1997) two factor term, with expected long-term volatility replacing the constant volatility term, and provide an explicit expression for the first order correction term. Using empirical data from the natural gas futures market, we demonstrate that a significantly better calibration can be achieved by involving the correction term as compared to the standard Schwartz (1997) two factor expression. This improvement comes at virtually no extra effort.

Suggested Citation

  • Chen, Jilong & Ewald, Christian-Oliver, 2017. "Pricing commodity futures options in the Schwartz multi factor model with stochastic volatility: An asymptotic method," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 144-151.
    • Handle: RePEc:eee:finana:v:52:y:2017:i:c:p:144-151
    DOI: 10.1016/j.irfa.2017.05.002
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    1. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    2. Zaevski, Tsvetelin S. & Kim, Young Shin & Fabozzi, Frank J., 2014. "Option pricing under stochastic volatility and tempered stable Lévy jumps," International Review of Financial Analysis, Elsevier, vol. 31(C), pages 101-108.
    3. Ting, Sai Hung Marten & Ewald, Christian-Oliver & Wang, Wen-Kai, 2013. "On the investment–uncertainty relationship in a real option model with stochastic volatility," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 22-32.
    4. 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.
    5. Cassese, Gianluca & Guidolin, Massimo, 2006. "Modelling the implied volatility surface: Does market efficiency matter?: An application to MIB30 index options," International Review of Financial Analysis, Elsevier, vol. 15(2), pages 145-178.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Ankush Agarwal & Sandeep Juneja & Ronnie Sircar, 2016. "American options under stochastic volatility: control variates, maturity randomization & multiscale asymptotics," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 17-30, January.
    8. Rauch, Johannes & Krayzler, Mikhail & Brunner, Bernhard & Zagst, Rudi, 2013. "Pricing of derivatives on commodity indices," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 143-151.
    9. 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.
    10. Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(1), pages 33-59, March.
    11. Carl Chiarella & Boda Kang & Christina Sklibosios Nikitopoulos & Thuy‐Duong Tô, 2016. "The Return–Volatility Relation in Commodity Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(2), pages 127-152, February.
    12. Sai Hung Marten Ting & Christian-Oliver Ewald, 2013. "On the performance of asymptotic locally risk minimising hedges in the Heston stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 939-954, May.
    13. 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.
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    Cited by:

    1. Chen, Jilong & Xu, Liao & Xu, Hao, 2022. "The impact of COVID-19 on commodity options market: Evidence from China," Economic Modelling, Elsevier, vol. 116(C).
    2. Christian-Oliver Ewald & Aihua Zhang & Zhe Zong, 2019. "On the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman Filter," Annals of Operations Research, Springer, vol. 282(1), pages 119-130, November.

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