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On the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman Filter

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  • Christian-Oliver Ewald

    (University of Glasgow)

  • Aihua Zhang

    (University of Leicester)

  • Zhe Zong

    (University of Glasgow)

Abstract

The Schwartz (J Finance 52(3):923–973, 1997) two factor model serves as a benchmark for pricing commodity contracts, futures and options. It is normally calibrated to fit the term-structure of a range of future contracts with varying maturities. In this paper, we investigate the effects on parameter estimates, if the model is fitted to prices of options, with varying maturities and strikes instead of futures, as is commonly done. The use of option prices rather than futures in the calibration leads to non-linearities, which the standard Kalman filter approach is unable to cope with. To overcome these issues, we use the extended Kalman Filter. We find that some parameters sensitively depend on the choice of strikes of the corresponding options, and are different from those estimates obtained from using futures prices. This effect is analogue to varying implied volatilities in the Black–Scholes model. This realization is important, as the use of ill-fitted models for pricing options in the Schwartz (1997) framework may cause traders to bear serious financial losses.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-2770-x
    DOI: 10.1007/s10479-018-2770-x
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    References listed on IDEAS

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    1. 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.
    2. Ramaswamy, Krishna & Sundaresan, Suresh M, 1985. "The Valuation of Options on Futures Contracts," Journal of Finance, American Finance Association, vol. 40(5), pages 1319-1340, December.
    3. Eduardo S. Schwartz, 1998. "Valuing Long-Term Commodity Assets," Financial Management, Financial Management Association, vol. 27(1), Spring.
    4. Shastri, Kuldeep & Tandon, Kishore, 1986. "An Empirical Test of a Valuation Model for American Options on Futures Contracts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(4), pages 377-392, December.
    5. Schwartz, Eduardo, 1998. "Valuing long-term commodity assets," Journal of Energy Finance & Development, Elsevier, vol. 3(2), pages 85-99.
    6. 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.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    8. 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.
    9. Pasricha, Gurnain Kaur, 2006. "Kalman Filter and its Economic Applications," MPRA Paper 22734, University Library of Munich, Germany.
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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. Peilun He & Karol Binkowski & Nino Kordzakhia & Pavel Shevchenko, 2021. "On Modelling of Crude Oil Futures in a Bivariate State-Space Framework," Papers 2108.01886, arXiv.org.
    3. Peilun He & Karol Binkowski & Nino Kordzakhia & Pavel Shevchenko, 2021. "On Modelling of Crude Oil Futures in a Bivariate State-Space Framework," Springer Books, in: Marco Corazza & Manfred Gilli & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 273-278, Springer.
    4. Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
    5. Karol Binkowski & Peilun He & Nino Kordzakhia & Pavel Shevchenko, 2021. "On the Parameter Estimation in the Schwartz-Smiths Two-Factor Model," Papers 2108.01881, arXiv.org.
    6. Giuseppe Orlando & Michele Bufalo, 2022. "A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(8), pages 1608-1622, December.
    7. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.
    8. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 357-385, October.
    9. Ewald, Christian & Zou, Yihan, 2021. "Analytic formulas for futures and options for a linear quadratic jump diffusion model with seasonal stochastic volatility and convenience yield: Do fish jump?," European Journal of Operational Research, Elsevier, vol. 294(2), pages 801-815.

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