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A Stochastic Volatility Model for Crude Oil Futures Curves and the Pricing of Calendar Spread Options

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  • Lorenz Schneider
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    Abstract

    We introduce a multi-factor stochastic volatility model based on the CIR/Heston stochastic volatility process. In order to capture the Samuelson effect displayed by commodity futures contracts, we add expiry-dependent exponential damping factors to their volatility coefficients. The pricing of single underlying European options on futures contracts is straightforward and can incorporate the volatility smile or skew observed in the market. We calculate the joint characteristic function of two futures contracts in the model and use the two-dimensional FFT method of Hurd and Zhou (SIFIN 2010) to price calendar spread options. The model leads to stochastic correlation between the returns of two futures contracts. We illustrate the distribution of this correlation in an example.

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    File URL: http://arxiv.org/pdf/1401.7913
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    Paper provided by arXiv.org in its series Papers with number 1401.7913.

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    Date of creation: Jan 2014
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    Handle: RePEc:arx:papers:1401.7913

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    1. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    2. Aanand Venkatramanan & Carol Alexander, 2011. "Closed Form Approximations for Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(5), pages 447-472, January.
    3. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
    4. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, Elsevier, vol. 55(2), pages 205-238, February.
    5. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    6. 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, INFORMS, vol. 55(12), pages 1914-1932, December.
    7. Bjerksund, Petter & Stensland, Gunnar, 2006. "Closed form spread option valuation," Discussion Papers, Department of Business and Management Science, Norwegian School of Economics 2006/20, Department of Business and Management Science, Norwegian School of Economics.
    8. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    10. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, American Finance Association, vol. 33(1), pages 177-86, March.
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