IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i4p1500-1540.html
   My bibliography  Save this article

Time homogeneous diffusion with drift and killing to meet a given marginal

Author

Listed:
  • Noble, John M.

Abstract

In this article, it is proved that for any probability law μ over R and a drift field b:R→R and killing field k:R→R+ which satisfy hypotheses stated in the article and a given terminal time t>0, there exists a string m, an α∈(0,1], an initial condition x0∈R and a process X with infinitesimal generator (12∂2∂m∂x+b∂∂m−∂K∂m) where k=∂K∂x such that for any Borel set B∈B(R), P(Xt∈B|X0=x0)=αμ(B). Firstly, it is shown the problem with drift and without killing can be accommodated, after a simple co-ordinate change, entirely by the proof in Noble (2013). The killing field presents additional problems and the proofs follow the lines of Noble (2013) with additional arguments.

Suggested Citation

  • Noble, John M., 2015. "Time homogeneous diffusion with drift and killing to meet a given marginal," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1500-1540.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1500-1540
    DOI: 10.1016/j.spa.2014.11.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914002725
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.11.006?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. Noble, John M., 2013. "Time homogeneous diffusions with a given marginal at a deterministic time," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 675-718.
    2. Forde, Martin, 2011. "A diffusion-type process with a given joint law for the terminal level and supremum at an independent exponential time," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2802-2817.
    3. Peter Carr & Sergey Nadtochiy, 2017. "Local Variance Gamma And Explicit Calibration To Option Prices," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 151-193, January.
    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. Fabien Le Floc'h, 2020. "An arbitrage-free interpolation of class $C^2$ for option prices," Papers 2004.08650, arXiv.org, revised May 2020.
    2. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    3. Julien Guyon, 2020. "Inversion of convex ordering in the VIX market," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1597-1623, October.
    4. Peter Carr & Sergey Nadtochiy, 2017. "Local Variance Gamma And Explicit Calibration To Option Prices," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 151-193, January.
    5. Pavel V. Gapeev & Neofytos Rodosthenous & V. L. Raju Chinthalapati, 2019. "On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes," Risks, MDPI, vol. 7(3), pages 1-15, August.
    6. Gapeev, Pavel V. & Rodosthenous, Neofytos & Chinthalapati, V.L Raju, 2019. "On the Laplace transforms of the first hitting times for drawdowns and drawups of diffusion-type processes," LSE Research Online Documents on Economics 101272, London School of Economics and Political Science, LSE Library.
    7. Gapeev, Pavel V. & Rodosthenous, Neofytos, 2016. "Perpetual American options in diffusion-type models with running maxima and drawdowns," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2038-2061.
    8. Peter Spoida, 2014. "Characterization of Market Models in the Presence of Traded Vanilla and Barrier Options," Papers 1411.4193, arXiv.org.
    9. Sergey Nadtochiy & Jan Obłój, 2017. "Robust Trading Of Implied Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-41, March.
    10. P. Carr & A. Itkin, 2021. "An Expanded Local Variance Gamma Model," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 949-987, April.
    11. Rene Carmona & Yi Ma & Sergey Nadtochiy, 2015. "Simulation of Implied Volatility Surfaces via Tangent Levy Models," Papers 1504.00334, arXiv.org.
    12. Noble, John M., 2013. "Time homogeneous diffusions with a given marginal at a deterministic time," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 675-718.
    13. Sergey Nadtochiy & Jan Obloj, 2016. "Robust Trading of Implied Skew," Papers 1611.05518, arXiv.org.
    14. Dilip B. Madan & Wim Schoutens, 2019. "Arbitrage Free Approximations to Candidate Volatility Surface Quotations," JRFM, MDPI, vol. 12(2), pages 1-21, April.
    15. Andrey Itkin, 2020. "Geometric Local Variance Gamma Model," World Scientific Book Chapters, in: Fitting Local Volatility Analytic and Numerical Approaches in Black-Scholes and Local Variance Gamma Models, chapter 6, pages 137-173, World Scientific Publishing Co. Pte. Ltd..

    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:spapps:v:125:y:2015:i:4:p:1500-1540. 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/505572/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.