IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v116y2016icp55-61.html
   My bibliography  Save this article

Characteristic function of time-inhomogeneous Lévy-driven Ornstein–Uhlenbeck processes

Author

Listed:
  • Vrins, Frédéric

Abstract

We derive the characteristic function (CF) of integrals of Lévy-driven Ornstein–Uhlenbeck processes with time-inhomogeneous coefficients. The resulting expression takes the form of the exponential integral of the time-changed characteristic exponent. This result is applied to some examples leading to closed form expressions. In particular, it drastically simplifies the calculations of the CF of integrated Compound Poisson processes compared to the standard approach relying on joint conditioning on inter-arrival jump times.

Suggested Citation

  • Vrins, Frédéric, 2016. "Characteristic function of time-inhomogeneous Lévy-driven Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 55-61.
    • Handle: RePEc:eee:stapro:v:116:y:2016:i:c:p:55-61
    DOI: 10.1016/j.spl.2016.04.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215303849
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.04.013?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. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    Full references (including those not matched with items on IDEAS)

    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. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    2. 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.
    3. Riccardo Brignone & Carlo Sgarra, 2020. "Asian options pricing in Hawkes-type jump-diffusion models," Annals of Finance, Springer, vol. 16(1), pages 101-119, March.
    4. Li, Chenxu & Wu, Linjia, 2019. "Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 275(2), pages 768-779.
    5. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    6. Dimitrios D. Thomakos & Michail S. Koubouros, 2011. "The Role of Realised Volatility in the Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 15(1-2), pages 87-124, March - J.
    7. Goovaerts, M. J. & Dhaene, J., 1999. "Supermodular ordering and stochastic annuities," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 281-290, May.
    8. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    9. Dan Pirjol, 2024. "Subleading correction to the Asian options volatility in the Black-Scholes model," Papers 2407.05142, arXiv.org, revised Aug 2024.
    10. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    11. Aleksey S. Polunchenko & Andrey Pepelyshev, 2018. "Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval," Statistical Papers, Springer, vol. 59(4), pages 1351-1377, December.
    12. Rafal M. Wojakowski & M. Shahid Ebrahim & Aziz Jaafar & Murizah Osman Salleh, 2019. "Can Loan Valuation Adjustment (LVA) approach immunize collateralized debt from defaults?," Financial Markets, Institutions & Instruments, John Wiley & Sons, vol. 28(2), pages 141-158, May.
    13. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    14. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    15. Ole Barndorff-Nielsen & Neil Shephard, 2004. "Multipower Variation and Stochastic Volatility," Economics Papers 2004-W30, Economics Group, Nuffield College, University of Oxford.
    16. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    17. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    18. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    19. A. Aghamohammadi & S. Mohammadi, 2017. "Bayesian analysis of penalized quantile regression for longitudinal data," Statistical Papers, Springer, vol. 58(4), pages 1035-1053, December.
    20. Robert Brooks & Robert Faff & Sirimon Treepongkaruna & Eliza Wu, 2015. "Do Sovereign Re-Ratings Destabilize Equity Markets during Financial Crises? New Evidence from Higher Return Moments," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 42(5-6), pages 777-799, June.

    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:eee:stapro:v:116:y:2016:i:c:p:55-61. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.