IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v20y2013i5p461-488.html
   My bibliography  Save this article

A Simple Stochastic Rate Model for Rate Equity Hybrid Products

Author

Listed:
  • Eberlein
  • Madan
  • Pistorius
  • Yor

Abstract

A positive spot rate model driven by a gamma process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r , its integral y and the logarithm of the stock price s under the T -forward measure. The law of the triple is expressed as a nonlinear transform of three independent processes, a gamma process, a variance gamma process and a Wiener integral with respect to the Dirichlet process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics , 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk , 14(1), pp. 95--122).

Suggested Citation

  • Eberlein & Madan & Pistorius & Yor, 2013. "A Simple Stochastic Rate Model for Rate Equity Hybrid Products," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(5), pages 461-488, November.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:461-488
    DOI: 10.1080/1350486X.2013.770240
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1350486X.2013.770240
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486X.2013.770240?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yoshihiro Shirai, 2023. "Acceptable Bilateral Gamma Parameters," Papers 2301.05333, arXiv.org.
    2. Yoshihiro Shirai, 2022. "Extreme Measures in Continuous Time Conic Finace," Papers 2210.13671, arXiv.org, revised Oct 2023.
    3. Yoshihiro Shirai, 2023. "A Levy-driven Ornstein-Uhlenbeck process for the valuation of credit index swaptions," Papers 2301.05332, arXiv.org, revised Oct 2023.
    4. Imdade Chitou & Gilles Dufrénot & Julien Esposito, 2021. "Linking Covid-19 epidemic and emerging market OAS: Evidence using dynamic copulas and Pareto distributions," Working Papers halshs-03297198, HAL.
    5. Fan Jiang & Xin Zang & Jingping Yang, 2020. "Asymptotic expansion for the transition densities of stochastic differential equations driven by the gamma processes," Papers 2003.06218, arXiv.org.

    More about this item

    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:taf:apmtfi:v:20:y:2013:i:5:p:461-488. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.