IDEAS home Printed from https://ideas.repec.org/p/cfi/fseres/cf177.html
   My bibliography  Save this paper

Pricing Average Options on Commodities

Author

Listed:
  • Kenichiro Shiraya

    (Mizuho-DL Financial Technology Co.,Ltd.)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper proposes a new approximation formula for pricing average options on commodities under a stochastic volatility environment. In particular, it derives an option pricing formula under Heston and an extended λ-SABR stochastic volatility models (which includes an extended SABR model as a special case). Moreover, numerical examples support the accuracy of the proposed average option pricing formula.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2009. "Pricing Average Options on Commodities," CARF F-Series CARF-F-177, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2012.
    • Handle: RePEc:cfi:fseres:cf177
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    References listed on IDEAS

    as
    1. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Average Options under Stochastic Volatility Models," CARF J-Series CARF-J-059, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. 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.
    3. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    4. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
    6. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    7. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    8. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    9. Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    10. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    11. 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.
    12. Jean-Pierre Fouque & Chuan-Hsiang Han, 2004. "Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 597-606.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2017. "Most-likely-path in Asian option pricing under local volatility models," Papers 1706.02408, arXiv.org, revised Aug 2018.
    2. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kenichiro Shiraya & Akihiko Takahashi, 2010. "Pricing Average Options on Commodities," CIRJE F-Series CIRJE-F-747, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kenichiro Shiraya & Akihiko Takahashi & Akira Yamazaki, 2010. "Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models," CARF F-Series CARF-F-214, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    4. Akihiko Takahashi & Toshihiro Yamada, 2014. "On Error Estimates for Asymptotic Expansions with Malliavin Weights -Application to Stochastic Volatility Model- (Revised version of CARF-F-324; Forthcoming in "Mathematics of Operations Research," CARF F-Series CARF-F-347, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2014.
    5. Akihiko Takahashi & Toshihiro Yamada, 2015. "On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 513-541, March.
    6. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2010. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-745, CIRJE, Faculty of Economics, University of Tokyo.
    7. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CARF F-Series CARF-F-165, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CARF F-Series CARF-F-176, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised May 2010.
    9. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2010. "Pricing Discrete Barrier Options under Stochastic Volatility," CARF F-Series CARF-F-210, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2011.
    10. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2010. "On Pricing Barrier Options with Discrete Monitoring," CIRJE F-Series CIRJE-F-725, CIRJE, Faculty of Economics, University of Tokyo.
    11. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    12. Kenichiro Shiraya & Akihiko Takahashi & Toshihiro Yamada, 2012. "Pricing Discrete Barrier Options Under Stochastic Volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(3), pages 205-232, September.
    13. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CIRJE F-Series CIRJE-F-654, CIRJE, Faculty of Economics, University of Tokyo.
    14. Akihiko Takahashi & Toshihiro Yamada, 2013. "On Error Estimates for Asymptotic Expansions with Malliavin Weights -- Application to Stochastic Volatility Model --," CIRJE F-Series CIRJE-F-897, CIRJE, Faculty of Economics, University of Tokyo.
    15. Kohta Takehara & Masashi Toda & Akihiko Takahashi, 2010. "Application Of A High-Order Asymptotic Expansion Scheme To Long-Term Currency Options," CARF F-Series CARF-F-225, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Akihiko Takahashi & Toshihiro Yamada, 2013. "On Error Estimates for Asymptotic Expansions with Malliavin Weights -Application to Stochastic Volatility Model-," CARF F-Series CARF-F-324, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Mar 2014.
    17. Kohta Takehara & Masashi Toda & Akihiko Takahashi, 2010. "Application of a High-Order Asymptotic Expansion Scheme to Long-Term Currency Options," CIRJE F-Series CIRJE-F-753, CIRJE, Faculty of Economics, University of Tokyo.
    18. Kohta Takehara & Akihiko Takahashi & Masashi Toda, 2010. "New Unified Computational Algorithm in a High-Order Asymptotic Expansion Scheme ( Forthcoming in "The Proceedings of KIER-TMU International Workshop on Financial Engineering 2009".)," CARF F-Series CARF-F-212, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    19. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
    20. Akihiko Takahashi & Masashi Toda, 2013. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-312, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cfi:fseres:cf177. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/catokjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.