IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v7y2005i3d10.1007_s11009-005-4517-9.html
   My bibliography  Save this article

Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion

Author

Listed:
  • Kazuyuki Ishiyama

    (Nagoya University)

Abstract

The purpose of this paper is to present a survey on Yor's formula on the probability densities of the exponential functionals represented as integrals in time of geometric Brownian motions and to present results on numerical computations for the densities. We perform the computations via another formula for the densities obtained by Dufresne and we show numerically the desired coincidence in some cases. As an application, we compute the price of an Asian option.

Suggested Citation

  • Kazuyuki Ishiyama, 2005. "Methods for Evaluating Density Functions of Exponential Functionals Represented as Integrals of Geometric Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 271-283, September.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:3:d:10.1007_s11009-005-4517-9
    DOI: 10.1007/s11009-005-4517-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-005-4517-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-005-4517-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    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. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    2. Nicolas Privault & Wayne Isaac Uy, 2013. "Monte Carlo Computation of the Laplace Transform of Exponential Brownian Functionals," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 511-524, September.
    3. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    4. Angelos Dassios & Luting Li, 2018. "An Economic Bubble Model and Its First Passage Time," Papers 1803.08160, arXiv.org.
    5. N. N. Leonenko & M. D. Ruiz-Medina, 2008. "Gaussian Scenario for the Heat Equation with Quadratic Potential and Weakly Dependent Data with Applications," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 595-620, 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. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    2. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    3. Dan Pirjol, 2024. "Subleading correction to the Asian options volatility in the Black-Scholes model," Papers 2407.05142, arXiv.org, revised Dec 2024.
    4. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    5. Chueh-Yung Tsao & Chao-Ching Liu, 2012. "Asian Options with Credit Risks: Pricing and Sensitivity Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 48(S3), pages 96-115, September.
    6. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    7. Dan Pirjol, 2020. "Asymptotic expansion for the Hartman-Watson distribution," Papers 2001.09579, arXiv.org, revised Dec 2024.
    8. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    9. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    10. Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2006. "The square-root process and Asian options," LSE Research Online Documents on Economics 2851, London School of Economics and Political Science, LSE Library.
    11. 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.
    12. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Hideharu Funahashi & Masaaki Kijima, 2017. "A unified approach for the pricing of options relating to averages," Review of Derivatives Research, Springer, vol. 20(3), pages 203-229, October.
    14. Araceli Matías González & María Teresa Verónica Martínez-Palacios & Ambrosio Ortiz-Ramírez, 2019. "Consumo e inversión óptimos y valuación de opciones asiáticas en un entorno estocástico con fundamentos microeconómicos y simulación Monte Carlo," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 14(3), pages 397-414, Julio - S.
    15. Jinke Zhou & Xiaolu Wang, 2008. "Accurate closed‐form approximation for pricing Asian and basket options," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(4), pages 343-358, July.
    16. Michael Schröder, 2015. "Discrete-Time Approximation of Functionals in Models of Ornstein–Uhlenbeck Type, with Applications to Finance," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 285-313, June.
    17. Ghomrasni, Raouf & Graversen, Svend Erik, 2002. "An extension of Seshadri's identities for Brownian motion," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 379-384, October.
    18. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 26, pages 341-362, Abril.
    19. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    20. Jang, Jiwook & Qu, Yan & Zhao, Hongbiao & Dassios, Angelos, 2023. "A Cox model for gradually disappearing events," LSE Research Online Documents on Economics 112754, London School of Economics and Political Science, LSE Library.

    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:spr:metcap:v:7:y:2005:i:3:d:10.1007_s11009-005-4517-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.