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From the Samuelson volatility effect to a Samuelson correlation effect : An analysis of crude oil calendar spread options

Author

Listed:
  • Bertrand Tavin

    (EM - EMLyon Business School)

  • Lorenz Schneider

Abstract

Our first aim in this paper is to introduce a futures-based model able of capturing the main features displayed by Crude Oil futures and options contracts, such as the Samuelson volatility effect and the volatility smile. We calculate the joint characteristic function of two futures contracts in the model in analytic form and use it to price calendar spread options. In an empirical application we show that the model, in contrast to simpler nested models, can be successfully calibrated to market prices of vanilla and calendar spread options. Our second aim is to use this model to analyze the dependence structure of Crude Oil futures contracts. To this end, we propose analytical expressions giving the copula and copula density directly in terms of the joint characteristic function. These tools allow us to perform an in-depth analysis for pairs of futures, and we observe a phenomenon we call the Samuelson correlation effect.

Suggested Citation

  • Bertrand Tavin & Lorenz Schneider, 2018. "From the Samuelson volatility effect to a Samuelson correlation effect : An analysis of crude oil calendar spread options," Post-Print hal-02311970, HAL.
    • Handle: RePEc:hal:journl:hal-02311970
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    References listed on IDEAS

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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. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Olivier Le Courtois & Christian Walter, 2014. "The Computation of Risk Budgets under the Lévy Process Assumption," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 87-108.
    5. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    6. Mu, Xiaoyi, 2007. "Weather, storage, and natural gas price dynamics: Fundamentals and volatility," Energy Economics, Elsevier, vol. 29(1), pages 46-63, January.
    7. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    10. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    11. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    12. Les Clewlow & Chris Strickland, 1999. "Valuing Energy Options in a One Factor Model Fitted to Forward Prices," Research Paper Series 10, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    14. 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.
    15. Louis O. Scott, 1997. "Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 413-426, October.
    16. 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.
    17. Bjerksund, Petter & Stensland, Gunnar, 2006. "Closed form spread option valuation," Discussion Papers 2006/20, Norwegian School of Economics, Department of Business and Management Science.
    18. Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
    19. Aanand Venkatramanan & Carol Alexander, 2011. "Closed Form Approximations for Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(5), pages 447-472, January.
    20. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    21. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    22. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. Piccirilli, Marco & Schmeck, Maren Diane & Vargiolu, Tiziano, 2021. "Capturing the power options smile by an additive two-factor model for overlapping futures prices," Energy Economics, Elsevier, vol. 95(C).
    2. Kang, Boda & Nikitopoulos, Christina Sklibosios & Prokopczuk, Marcel, 2020. "Economic determinants of oil futures volatility: A term structure perspective," Energy Economics, Elsevier, vol. 88(C).
    3. Brooks, Robert & Brooks, Joshua A., 2022. "Samuelson hypothesis and carry arbitrage: U.S. and China," Journal of International Money and Finance, Elsevier, vol. 128(C).
    4. Yuyang Cheng & Marcos Escobar-Anel & Zhenxian Gong, 2019. "Generalized Mean-Reverting 4/2 Factor Model," JRFM, MDPI, vol. 12(4), pages 1-21, October.
    5. Annika Kemper & Maren D. Schmeck & Anna Kh. Balci, 2020. "The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets," Papers 2002.07561, arXiv.org, revised Jun 2022.
    6. Kemper, Annika & Schmeck, Maren Diane & Kh.Balci, Anna, 2022. "The market price of risk for delivery periods: Pricing swaps and options in electricity markets," Energy Economics, Elsevier, vol. 113(C).
    7. Thomas Deschatre & Xavier Warin, 2023. "A Common Shock Model for multidimensional electricity intraday price modelling with application to battery valuation," Papers 2307.16619, arXiv.org.
    8. Kemper, Annika & Schmeck, Maren Diane & Khripunova Balci, Anna, 2020. "The Market Price of Risk for Delivery Periods: Pricing Swaps and Options in Electricity Markets," Center for Mathematical Economics Working Papers 635, Center for Mathematical Economics, Bielefeld University.
    9. Sania Wadud & Robert D. Durand & Marc Gronwald, 2021. "Connectedness between the Crude Oil Futures and Equity Markets during the Pre- and Post-Financialisation Eras," CESifo Working Paper Series 9202, CESifo.

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