IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2015cf980.html
   My bibliography  Save this paper

Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models

Author

Listed:
  • Kenichiro Shiraya

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

This paper presents a new approximation formula for pricing multi-dimensional discretely monitored average options in a local-stochastic volatility (LSV) model with jumps by applying an asymptotic expansion technique. Moreover, it provides a justification of the approximation method with some asymptotic error estimates for general payoff functions. Particularly, our model includes local volatility functions and jump components in the underlying asset price as well as its volatility processes. To the best of our knowledge, the proposed approximation is the first one which achieves analytic approximations for the average option prices in this environment. In numerical experiments, by employing several models, we provide approximate prices for the listed average and calendar spread options on the WTI futures based on the parameters through calibration to the listed (plain-vanilla) futures options prices. Then, we compare those with the CME settlement prices, which confirms the validity of the method. Moreover, we show that the LSV with jumps model is able to replicate consistently and precisely listed futures option, calendar spread option and average option prices with common parameters.

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CIRJE F-Series CIRJE-F-980, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf980
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2015/2015cf980.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ning Cai & Chenxu Li & Chao Shi, 2014. "Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 789-822, August.
    2. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
    3. Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
    4. Stefano Pagliarani & Andrea Pascucci, 2013. "Local Stochastic Volatility With Jumps: Analytical Approximations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-35.
    5. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    6. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    7. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    8. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    9. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.
    10. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    11. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Pricing Multiasset Cross‐Currency Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(1), pages 1-19, January.
    12. Kenichiro Shiraya & Akihiko Takahashi, 2011. "Pricing average options on commodities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(5), pages 407-439, May.
    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. Yasaman Karami & Kenichiro Shiraya, 2018. "An approximation formula for normal implied volatility under general local stochastic volatility models," CARF F-Series CARF-F-427, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

    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, 2015. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models," CARF F-Series CARF-F-365, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Kenichiro Shiraya & Akihiko Takahashi, 2017. "Pricing Average and Spread Options under Local-Stochastic Volatility Jump-Diffusion Models (Revised version of CARF-F-365 : Subsequently published in Mathematics of Operations Research)," CARF F-Series CARF-F-426, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Kenichiro Shiraya & Akihiko Takahashi, 2019. "Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 303-333, February.
    4. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
    5. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    6. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    7. Zhenyu Cui & Chihoon Lee & Yanchu Liu, 2016. "On "A General Framework for Pricing Asian Options Under Markov Processes"," Papers 1601.05306, arXiv.org.
    8. Cui, Zhenyu & Lee, Chihoon & Liu, Yanchu, 2018. "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1134-1139.
    9. Yoshida, Nakahiro, 2023. "Asymptotic expansion and estimates of Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 176-248.
    10. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
    11. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    12. Weinan Zhang & Pingping Zeng, 2023. "A transform-based method for pricing Asian options under general two-dimensional models," Quantitative Finance, Taylor & Francis Journals, vol. 23(11), pages 1677-1697, November.
    13. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion," Papers 2306.09084, arXiv.org.
    14. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    15. Kenichiro Shiraya & Akihiko Takahashi, 2014. "Pricing Basket Options under Local Stochastic Volatility with Jumps," CIRJE F-Series CIRJE-F-913, CIRJE, Faculty of Economics, University of Tokyo.
    16. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An approximation formula for basket option prices under local stochastic volatility with jumps: an application to commodity markets," CARF F-Series CARF-F-361, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    17. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    18. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    19. 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.
    20. Kenichiro Shiraya & Akihiko Takahashi, 2015. "An Approximation Formula for Basket Option Prices under Local Stochastic Volatility with Jumps: an Application to Commodity Markets," CIRJE F-Series CIRJE-F-973, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tky:fseres:2015cf980. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.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.