IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v25y2022i02ns021902492250011x.html
   My bibliography  Save this article

Calibrating Local Volatility Models With Stochastic Drift And Diffusion

Author

Listed:
  • ORCAN ÖGETBIL

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

  • NARAYAN GANESAN

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

  • BERNHARD HIENTZSCH

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

Abstract

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign; each modeled by a Gaussian one-factor model with deterministic shift (G1 + +) process. For stochastic volatility, we model the variance for the exchange rate by a Cox–Ingersoll–Ross (CIR) process. We include tests to show the convergence and the accuracy of the proposed algorithms.

Suggested Citation

  • Orcan ÖGetbil & Narayan Ganesan & Bernhard Hientzsch, 2022. "Calibrating Local Volatility Models With Stochastic Drift And Diffusion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(02), pages 1-43, March.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:02:n:s021902492250011x
    DOI: 10.1142/S021902492250011X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021902492250011X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021902492250011X?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. Arun Kumar Polala & Bernhard Hientzsch, 2023. "Parametric Differential Machine Learning for Pricing and Calibration," Papers 2302.06682, arXiv.org, revised Feb 2023.
    2. Orcan Ogetbil & Bernhard Hientzsch, 2022. "A Flexible Commodity Skew Model with Maturity Effects," Papers 2212.07972, arXiv.org.

    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:wsi:ijtafx:v:25:y:2022:i:02:n:s021902492250011x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.