IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2014cf917.html
   My bibliography  Save this paper

A New Improvement Scheme for Approximation Methods of Probability Density Functions

Author

Listed:
  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

  • Yukihiro Tsuzuki

    (Graduate School of Economics, The University of Tokyo)

Abstract

　　 This paper develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in the Hilbert space projection theorem . Moreover, we apply "Dykstra's cyclic projections algorithm" for its implementation. Numerical examples for application to an symptotic expansion method in option pricing demonstrate the effectiveness of our scheme under SABR model.

Suggested Citation

  • Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-917, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2014cf917
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2014/2014cf917.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme For A High-Order Asymptotic Expansion Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-25.
    3. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-276, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Rama Cont, 2008. "Frontiers in Quantitative Finance: credit risk and volatility modeling," Post-Print hal-00437588, HAL.
    5. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme for a High-Order Asymptotic Expansion Method," CARF F-Series CARF-F-272, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-290, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    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. Sergio Albeverio & Francesco Cordoni & Luca Persio & Gregorio Pellegrini, 2019. "Asymptotic expansion for some local volatility models arising in finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 527-573, December.

    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. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-350, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-341, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CIRJE F-Series CIRJE-F-874, CIRJE, Faculty of Economics, University of Tokyo.
    4. Akihiko Takahashi & Yukihiro Tsuzuki, 2013. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-305, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. 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.
    6. 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.
    7. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CIRJE F-Series CIRJE-F-860, CIRJE, Faculty of Economics, University of Tokyo.
    8. 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.
    9. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CARF F-Series CARF-F-286, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2012.
    10. 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.
    11. 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.
    12. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    13. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
    14. Masaaki Fujii & Akihiko Takahshi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," CIRJE F-Series CIRJE-F-954, CIRJE, Faculty of Economics, University of Tokyo.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Akihiko Takahashi & Toshihiro Yamada, 2015. "An Asymptotic Expansion of Forward-Backward SDEs with a Perturbed Driver," CARF F-Series CARF-F-363, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    20. Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Options," CARF F-Series CARF-F-290, Center for Advanced Research in Finance, Faculty of Economics, The 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:2014cf917. 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.