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Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models


  • Samuel Hikspoors
  • Sebastian Jaimungal


It is well known that stochastic volatility is an essential feature of commodity spot prices. By using methods of singular perturbation theory, we obtain approximate but explicit closed-form pricing equations for forward contracts and options on single- and two-name forward prices. The expansion methodology is based on a fast mean-reverting stochastic volatility driving factor and leads to pricing results in terms of constant volatility prices, their Deltas and their Delta-Gammas. Both the standard single-factor mean-reverting spot model and a two-factor generalization, in which the long-run mean is itself mean-reverting, are extended to include stochastic volatility and each is analysed in detail. The stochastic volatility corrections can be used to efficiently calibrate option prices and compute sensitivities.

Suggested Citation

  • Samuel Hikspoors & Sebastian Jaimungal, 2008. "Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 449-477.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:449-477 DOI: 10.1080/13504860802170432

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    References listed on IDEAS

    1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    2. Peter Buchen & Otto Konstandatos, 2005. "A New Method Of Pricing Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 245-259.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    4. Conze, Antoine & Viswanathan, 1991. " Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    5. Goldman, M Barry & Sosin, Howard B & Shepp, Lawrence A, 1979. "On Contingent Claims That Insure Ex-post Optimal Stock Market Timing," Journal of Finance, American Finance Association, vol. 34(2), pages 401-413, May.
    6. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
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    Cited by:

    1. Cartea, Álvaro & González-Pedraz, Carlos, 2012. "How much should we pay for interconnecting electricity markets? A real options approach," Energy Economics, Elsevier, vol. 34(1), pages 14-30.
    2. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.
    3. repec:kap:rqfnac:v:48:y:2017:i:3:d:10.1007_s11156-016-0569-x is not listed on IDEAS
    4. repec:kap:revdev:v:20:y:2017:i:2:d:10.1007_s11147-016-9126-y is not listed on IDEAS
    5. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332,
    6. Tsekrekos, Andrianos E. & Yannacopoulos, Athanasios N., 2016. "Optimal switching decisions under stochastic volatility with fast mean reversion," European Journal of Operational Research, Elsevier, vol. 251(1), pages 148-157.
    7. 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.
    8. repec:eee:spapps:v:128:y:2018:i:2:p:461-486 is not listed on IDEAS


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