IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v24y2017i6p485-519.html

Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps

Author

Listed:
  • Andrey Itkin

Abstract

It is known that the implied volatility skew of Forex (FX) options demonstrates a stochastic behaviour which is called stochastic skew. In this paper, we create stochastic skew by assuming the spot/instantaneous variance (InV) correlation to be stochastic. Accordingly, we consider a class of Stochastic Local Volatility (SLV) models with stochastic correlation where all drivers – the spot, InV and their correlation – are modelled by processes. We assume all diffusion components to be fully correlated, as well as all jump components. A new fully implicit splitting finite-difference scheme is proposed for solving forward PIDE which is used when calibrating the model to market prices of the FX options with different strikes and maturities. The scheme is unconditionally stable, of second order of approximation in time and space, and achieves a linear complexity in each spatial direction. The results of simulation obtained by using this model demonstrate the capacity of the presented approach in modelling stochastic skew.

Suggested Citation

  • Andrey Itkin, 2017. "Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(6), pages 485-519, November.
    • Handle: RePEc:taf:apmtfi:v:24:y:2017:i:6:p:485-519
    DOI: 10.1080/1350486X.2017.1409641
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1350486X.2017.1409641
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486X.2017.1409641?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 look for a different version below or

    for a different version of it.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Igor Halperin & Andrey Itkin, 2025. "Marketron Through the Looking Glass: From Equity Dynamics to Option Pricing in Incomplete Markets," Papers 2508.09863, arXiv.org, revised Aug 2025.
    2. Julien Hok & Shih-Hau Tan, 2019. "Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 609-637, December.
    3. Peter Carr & Andrey Itkin & Sasha Stoikov, 2019. "A model-free backward and forward nonlinear PDEs for implied volatility," Papers 1907.07305, 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:24:y:2017:i:6:p:485-519. 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.